Constraint Answer Set Programming (CASP) integrates the high-level modeling capabilities of Answer Set Programming (ASP) with the efficient numerical computation of Constraint Programming (CP). By partitioning the problem space, CASP leverages the complementary strengths of its underlying solvers: the ASP component facilitates rich relational modeling and non-monotonic reasoning, specifically the handling of defaults and exceptions, while the CP component manages variables over expansive numeric domains via specialized propagators However, this synthesis introduces significant semantic challenges regarding the interaction between stable model semantics and classical constraint theory. Central to ASP is the ability to differentiate between founded and unfounded atoms, a departure from the classical treatment of variables in SAT where truth is typically a matter of assignment rather than derivation. As CASP systems have evolved, diverse interpretations of foundedness have emerged regarding how these logical requirements should extend to constraints and numeric variables. This talk examines the semantic foundations of several CASP systems to illustrate these nuances. In particular, we present /flingo/, a CASP system designed to preserve the declarative richness of ASP within constraint satisfaction problems. By supporting default values, undefined variables, non-deterministic assignments, and aggregates directly within numeric constraints, /flingo/ restores the expressive power often lost in traditional CASP translations. We explore how this approach allows for a more natural integration of numeric attributes without sacrificing the foundational principles of ASP.

We introduce the Multi-Objective Combinatorial Reconfiguration Optimization Problem (MO-CROP), and propose an Answer Set Programming (ASP) based approach for its solution. MO-CROP involves finding the Pareto-optimal sequences (or Pareto front) of adjacent feasible solutions between two given feasible solutions of a combinatorial problem, considering both cost and length. Our algorithm is compactly implemented through multi-shot ASP solving, and its implementing solver optirecon provides an effective tool for solving MO-CROP. As a concrete example of MO-CROP, we present an ASP encoding for solving the multi-objective independent set reconfiguration optimization problem. Experimental results on the benchmark set from the recent CoRe Challenge demonstrate our approach’s ability to capture diverse optimal sequences that reveal trade-offs between cost and length, a capability often lacking in traditional combinatorial reconfiguration methods.

Abstract Reasoning about dynamic systems with a fine-grained temporal and numeric resolution presents significant challenges for logic-based approaches like Answer Set Programming (ASP). To address this, we introduce and elaborate upon a novel temporal and constraint-based extension of the logic of Here-and-There and its nonmonotonic equilibrium extension, representing, to the best of our knowledge, the first approach to nonmonotonic temporal reasoning with constraints specifically tailored for ASP. This expressive system is achieved by a synergistic combination of two foundational ASP extensions: the linear-time logic of Here-and-There, providing robust nonmonotonic temporal reasoning capabilities, and the logic of Here-and-There with constraints, enabling the direct integration and manipulation of numeric constraints, among others. This work establishes the foundational logical framework for tackling complex dynamic systems with high resolution within the ASP paradigm.

Abstract ANTHEM 2.0 is a tool to aid in the verification of logic programs written in an expressive fragment of CLINGO ’s input language named MINI-GRINGO, which includes arithmetic operations and simple choice rules but not aggregates. It can translate logic programs into formula representations in the logic of here-and-there and analyze properties of logic programs such as tightness. Most importantly, ANTHEM 2.0 can support program verification by invoking first-order theorem provers to confirm that a program adheres to a first-order specification or to establish strong and external equivalence of programs. This paper serves as an overview of the system’s capabilities. We demonstrate how to use ANTHEM 2.0 effectively and interpret its results.

Abstract We present plingo, an extension of the answer set programming (ASP) system clingo that incorporates various probabilistic reasoning modes. Plingo is based on $\textit{Lpmln}^{\pm }$ , a simple variant of the probabilistic language Lpmln, which follows a weighted scheme derived from Markov logic. This choice is motivated by the fact that the main probabilistic reasoning modes can be mapped onto enumeration and optimization problems and that $\textit{Lpmln}^{\pm }$ may serve as a middle-ground formalism connecting to other probabilistic approaches. Plingo offers three alternative frontends, for Lpmln, P-log, and ProbLog. These input languages and reasoning modes are implemented by means of clingo’s multi-shot and theory-solving capabilities. In this way, the core of plingo is an implementation of $\textit{Lpmln}^{\pm }$ in terms of modern ASP technology. On top of that, plingo implements a new approximation technique based on a recent method for answer set enumeration in the order of optimality. Additionally, in this work, we introduce a novel translation from $\textit{Lpmln}^{\pm }$ to ProbLog. This leads to a new solving method in plingo where the input program is translated and a ProbLog solver is executed. Our empirical evaluation shows that the different solving approaches of plingo are complementary and that plingo performs similarly to other probabilistic reasoning systems.

Abstract The representation of a temporal problem in answer set programming (ASP) usually boils down to using copies of variables and constraints, one for each time stamp, no matter whether it is directly encoded or expressed via an action or temporal language. The multiplication of variables and constraints is commonly done during grounding, and the solver is completely ignorant about the temporal relationship among the different instances. On the other hand, a key factor in the performance of today’s ASP solvers is conflict-driven constraint learning. Our question in this paper is whether a constraint learned for particular time steps can be generalized and reused at other time steps, and ultimately whether this enhances the overall solver performance on temporal problems. Knowing well the domain of time, we study conditions under which learned dynamic constraints can be generalized. Notably, we identify a property of temporal representations that enables the generalization of learned constraints across all time steps. It turns out that most ASP planning encodings either satisfy this property or can be easily adapted to do so. In addition, we propose a general translation that transforms programs to fulfill this property. Finally, we empirically evaluate the impact of adding the generalized constraints to an ASP solver.

We propose Large Neighborhood Prioritized Search (LNPS) for solving combinatorial optimization problems in Answer Set Programming (ASP). LNPS is a metaheuristic that starts with an initial solution and then iteratively tries to find better solutions by alternately destroying and prioritized searching for a current solution. Due to the variability of neighborhoods, LNPS allows for flexible search without strongly depending on the destroy operators. We present an implementation of LNPS based on ASP. The resulting heulingo solver demonstrates that LNPS can significantly enhance the solving performance of ASP for optimization. Furthermore, we establish the competitiveness of our LNPS approach by empirically contrasting it to (adaptive) large neighborhood search.

Abstract In temporal extensions of answer set programming (ASP) based on linear time, the behavior of dynamic systems is captured by sequences of states. While this representation reflects their relative order, it abstracts away the specific times associated with each state. However, timing constraints are important in many applications like, for instance, when planning and scheduling go hand in hand. We address this by developing a metric extension of linear-time temporal equilibrium logic, in which temporal operators are constrained by intervals over natural numbers. The resulting Metric Equilibrium Logic (MEL) provides the foundation of an ASP-based approach for specifying qualitative and quantitative dynamic constraints. To this end, we define a translation of metric formulas into monadic first-order formulas and give a correspondence between their models in MEL and Monadic Quantified Equilibrium Logic, respectively. Interestingly, our translation provides a blue print for implementation in terms of ASP modulo difference constraints.

Abstract We are interested in automating reasoning with and about study regulations, catering to various stakeholders, ranging from administrators, over faculty, to students at different stages. Our work builds on an extensive analysis of various study programs at the University of Potsdam. The conceptualization of the underlying principles provides us with a formal account of study regulations. In particular, the formalization reveals the properties of admissible study plans. With these at end, we propose an encoding of study regulations in Answer Set Programming that produces corresponding study plans. Finally, we show how this approach can be extended to a generic user interface for exploring study plans.

Abstract We present the Answer Set Programming (ASP)-based visualization tool clingraph, which aims at visualizing various concepts of ASP by means of ASP itself. This idea traces back to the aspviz tool and clingraph redevelops and extends it in the context of modern ASP systems. More precisely, clingraph takes graph specifications in terms of ASP facts and hands them over to the graph visualization system graphviz. The use of ASP provides a great interface between logic programs and/or answer sets and their visualization. Also, clingraph offers a Python application programming interface (API) that extends this ease of interfacing to clingo’s API and in turn to connect and monitor various aspects of the solving process.

Abstract The dominating set reconfiguration problem is defined as determining, for a given dominating set problem and two among its feasible solutions, whether one is reachable from the other via a sequence of feasible solutions subject to a certain adjacency relation. This problem is PSPACE-complete in general. The concept of the dominating set is known to be quite useful for analyzing wireless networks, social networks, and sensor networks. We develop an approach to solve the dominating set reconfiguration problem based on answer set programming (ASP). Our declarative approach relies on a high-level ASP encoding, and both the grounding and solving tasks are delegated to an ASP-based combinatorial reconfiguration solver. To evaluate the effectiveness of our approach, we conduct experiments on a newly created benchmark set.

Multi-agent pathfinding is the task of navigating a set of agents in a shared environment without collisions. Finding an optimal plan is a computationally hard problem, therefore, one may want to sacrifice optimality for faster computation time. In this paper, we present our preliminary work on finding a valid solution using only a predefined path for each agent with the possibility of adding wait actions. This restriction makes some instances unsolvable, however, we show instances where this approach is guaranteed to find a solution.

Abstract In this survey, we present an overview on (Modal) Temporal Logic Programming in view of its application to Knowledge Representation and Declarative Problem Solving. The syntax of this extension of logic programs is the result of combining usual rules with temporal modal operators, as in Linear-time Temporal Logic (LTL). In the paper, we focus on the main recent results of the non-monotonic formalism called Temporal Equilibrium Logic (TEL) that is defined for the full syntax of LTL but involves a model selection criterion based on Equilibrium Logic, a well known logical characterization of Answer Set Programming (ASP). As a result, we obtain a proper extension of the stable models semantics for the general case of temporal formulas in the syntax of LTL. We recall the basic definitions for TEL and its monotonic basis, the temporal logic of Here-and-There (THT), and study the differences between finite and infinite trace length. We also provide further useful results, such as the translation into other formalisms like Quantified Equilibrium Logic and Second-order LTL, and some techniques for computing temporal stable models based on automata constructions. In the remainder of the paper, we focus on practical aspects, defining a syntactic fragment called (modal) temporal logic programs closer to ASP, and explaining how this has been exploited in the construction of the solver telingo, a temporal extension of the well-known ASP solver clingo that uses its incremental solving capabilities.

Abstract Answer Set Programming, or ASP for short, has become a popular and sophisticated approach to declarative problem solving. Its popularity is due to its attractive modeling-grounding-solving workflow that provides an easy approach to problem solving, even for laypersons outside computer science. However, in contrast to ASP’s ease of use, the high degree of sophistication of the underlying technology makes it even hard for ASP experts to put ideas into practice whenever this involves modifying ASP’s machinery. For addressing this issue, this tutorial aims at enabling users to build their own ASP-based systems. More precisely, we show how the ASP system clingo can be used for extending ASP and for implementing customized special-purpose systems. To this end, we propose two alternatives. We begin with a traditional AI technique and show how metaprogramming can be used for extending ASP. This is a rather light approach that relies on clingo ’s reification feature to use ASP itself for expressing new functionalities. The second part of this tutorial uses traditional programming (in Python) for manipulating clingo via its application programming interface. This approach allows for changing and controlling the entire model-ground-solve workflow of ASP. Central to this is clingo ’s new Application class that allows us to draw on clingo ’s infrastructure by customizing processes similar to the one in clingo . For instance, we may apply manipulations to programs’ abstract syntax trees, control various forms of multi-shot solving, and set up theory propagators for foreign inferences. A cross-sectional structure, spanning meta as well as application programming, is clingo ’s intermediate format, aspif , that specifies the interface among the underlying grounder and solver. We illustrate the aforementioned concepts and techniques throughout this tutorial by means of examples and several nontrivial case studies. In particular, we show how clingo can be extended by difference constraints and how guess-and-check programming can be implemented with both meta and application programming.

Abstract We provide a comprehensive elaboration of the theoretical foundations of variable instantiation, or grounding, in Answer Set Programming (ASP). Building on the semantics of ASP’s modeling language, we introduce a formal characterization of grounding algorithms in terms of (fixed point) operators. A major role is played by dedicated well-founded operators whose associated models provide semantic guidance for delineating the result of grounding along with on-the-fly simplifications. We address an expressive class of logic programs that incorporates recursive aggregates and thus amounts to the scope of existing ASP modeling languages. This is accompanied with a plain algorithmic framework detailing the grounding of recursive aggregates. The given algorithms correspond essentially to the ones used in the ASP grounder gringo .

Abstract Answer Set Planningrefers to the use ofAnswer Set Programming (ASP)to computeplans, that is, solutions to planning problems, that transform a given state of the world to another state. The development of efficient and scalable answer set solvers has provided a significant boost to the development of ASP-based planning systems. This paper surveys the progress made during the last two and a half decades in the area of answer set planning, from its foundations to its use in challenging planning domains. The survey explores the advantages and disadvantages of answer set planning. It also discusses typical applications of answer set planning and presents a set of challenges for future research.

This paper extends a study on improving the performance of reduction-based solvers for the problem of multi-agent pathfinding. The task is to navigate a set of agents in a graph without collisions. Solvers that reduce this problem to other formalisms often have issues scaling to larger instances in terms of the graph size. A previous study suggests that pruning the graph of most vertices based on a randomly chosen shortest path for each agent. In this paper, we study the effect of different choices of these paths.

Abstract We present a solution to real-world train scheduling problems, involving routing, scheduling, and optimization, based on Answer Set Programming (ASP). To this end, we pursue a hybrid approach that extends ASP with difference constraints to account for a fine-grained timing. More precisely, we exemplarily show how the hybrid ASP system clingo[DL] can be used to tackle demanding planning and scheduling problems. In particular, we investigate how to boost performance by combining distinct ASP solving techniques, such as approximations and heuristics, with preprocessing and encoding techniques for tackling large-scale, real-world train-scheduling instances.

Abstract We present a general approach to planning with incomplete information in Answer Set Programming (ASP). More precisely, we consider the problems of conformant and conditional planning with sensing actions and assumptions. We represent planning problems using a simple formalism where logic programs describe the transition function between states, the initial states and the goal states. For solving planning problems, we use Quantified Answer Set Programming (QASP), an extension of ASP with existential and universal quantifiers over atoms that is analogous to Quantified Boolean Formulas (QBFs). We define the language of quantified logic programs and use it to represent the solutions different variants of conformant and conditional planning. On the practical side, we present a translation-based QASP solver that converts quantified logic programs into QBFs and then executes a QBF solver, and we evaluate experimentally the approach on conformant and conditional planning benchmarks.

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We elaborate upon the formal foundations of hybrid Answer Set Programming (ASP) and extend its underlying logical framework with aggregate functions over constraint values and variables. This is achieved by introducing the construct of conditional expressions, which allow for considering two alternatives while evaluating constraints. Which alternative is considered is interpretation-dependent and chosen according to an associated condition. We put some emphasis on logic programs with linear constraints and show how common ASP aggregates can be regarded as particular cases of so-called conditional linear constraints. Finally, we introduce a polynomial-size, modular and faithful translation from our framework into regular (condition-free) Constraint ASP, outlining an implementation of conditional aggregates on top of existing hybrid ASP solvers.

Characterizing hybrid ASP solving in a generic way is difficult since one needs to abstract from specific theories. Inspired by lazy SMT solving, this is usually addressed by treating theory atoms as opaque. Unlike this, we propose a slightly more transparent approach that includes an abstract notion of a term. Rather than imposing a syntax on terms, we keep them abstract by stipulating only some basic properties. With this, we further develop a semantic framework for hybrid ASP solving and provide aggregate functions for theory variables that adhere to different semantic principles, show that they generalize existing aggregate semantics in ASP and how we can rely on off-the-shelf hybrid solvers for implementation.

Abstract We elaborate upon the theoretical foundations of a metric temporal extension of Answer Set Programming. In analogy to previous extensions of ASP with constructs from Linear Temporal and Dynamic Logic, we accomplish this in the setting of the logic of Here-and-There and its non-monotonic extension, called Equilibrium Logic. More precisely, we develop our logic on the same semantic underpinnings as its predecessors and thus use a simple time domain of bounded time steps. This allows us to compare all variants in a uniform framework and ultimately combine them in a common implementation.

Abstract We describe eclingo, a solver for epistemic logic programs under Gelfond 1991 semantics built upon the Answer Set Programming system clingo. The input language of eclingo uses the syntax extension capabilities of clingo to define subjective literals that, as usual in epistemic logic programs, allow for checking the truth of a regular literal in all or in some of the answer sets of a program. The eclingo solving process follows a guess and check strategy. It first generates potential truth values for subjective literals and, in a second step, it checks the obtained result with respect to the cautious and brave consequences of the program. This process is implemented using the multi-shot functionalities of clingo. We have also implemented some optimisations, aiming at reducing the search space and, therefore, increasing eclingo ’s efficiency in some scenarios. Finally, we compare the efficiency of eclingo with two state-of-the-art solvers for epistemic logic programs on a pair of benchmark scenarios and show that eclingo generally outperforms their obtained results.

Abstract Standardization of solver input languages has been a main driver for the growth of several areas within knowledge representation and reasoning, fostering the exploitation in actual applications. In this document, we present the ASP-CORE-2 standard input language for Answer Set Programming, which has been adopted in ASP Competition events since 2013.

Abstract This paper continues the line of research aimed at investigating the relationship between logic programs and first-order theories. We extend the definition of program completion to programs with input and output in a subset of the input language of the ASP grounder gringo, study the relationship between stable models and completion in this context, and describe preliminary experiments with the use of two software tools, anthem and vampire, for verifying the correctness of programs with input and output. Proofs of theorems are based on a lemma that relates the semantics of programs studied in this paper to stable models of first-order formulas.

Conditional preference networks (CP-nets) express qualitative preferences over features of interest.A Boolean CP-net can express that a feature is preferable under some conditions, as long as all other features have the same value.This is often a convenient representation, but sometimes one would also like to express a preference for maximizing a set of features, or some other objective function on the features of interest.ASPRIN is a flexible framework for preferences in ASP, where one can mix heterogeneous preference relations, and this paper reports on the integration of Boolean CP-nets.In general, we extend ASPRIN with a preference program for CP-nets in order to compute most preferred answer sets via an iterative algorithm.For the specific case of acyclic CP-nets, we provide an approximation by partially ordered set preferences, which are in turn normalized by ASPRIN to take advantage of several highly optimized algorithms implemented by ASP solvers for computing optimal solutions.Finally, we take advantage of a linear-time computable function to address dominance testing for tree-shaped CP-nets.

In Multi-Agent Path Finding (MAPF), a team of agents needs to find collision-free paths from their starting locations to their respective targets. Combined Target Assignment and Path Finding (TAPF) extends MAPF by including the problem of assigning targets to agents as a precursor to the MAPF problem. A limitation of both models is their assumption that the number of agents and targets are equal, which is invalid in some applications. We address this limitation by generalizing TAPF to allow for (1) unequal number of agents and tasks; (2) tasks to have deadlines by which they must be completed; (3) ordering of groups of tasks to be completed; and (4) tasks that are composed of a sequence of checkpoints that must be visited in a specific order. Further, we model the problem using answer set programming (ASP) to show that customizing the desired variant of the problem is simple -- one only needs to choose the appropriate combination of ASP rules to enforce it. We also demonstrate experimentally that if problem specific information can be incorporated into the ASP encoding then ASP based methods can be efficient and can scale up to solve practical applications.

Abstract We describe the new version of the Planning Domain Definition Language (PDDL)-to-Answer Set Programming (ASP) translator plasp . First, it widens the range of accepted PDDL features. Second, it contains novel planning encodings, some inspired by Satisfiability Testing (SAT) planning and others exploiting ASP features such as well-foundedness. All of them are designed for handling multivalued fluents in order to capture both PDDL as well as SAS planning formats. Third, enabled by multishot ASP solving, it offers advanced planning algorithms also borrowed from SAT planning. As a result, plasp provides us with an ASP-based framework for studying a variety of planning techniques in a uniform setting. Finally, we demonstrate in an empirical analysis that these techniques have a significant impact on the performance of ASP planning.

Abstract Metabolic networks play a crucial role in biology since they capture all chemical reactions in an organism. While there are networks of high quality for many model organisms, networks for less studied organisms are often of poor quality and suffer from incompleteness. To this end, we introduced in previous work an answer set programming (ASP)-based approach to metabolic network completion. Although this qualitative approach allows for restoring moderately degraded networks, it fails to restore highly degraded ones. This is because it ignores quantitative constraints capturing reaction rates. To address this problem, we propose a hybrid approach to metabolic network completion that integrates our qualitative ASP approach with quantitative means for capturing reaction rates. We begin by formally reconciling existing stoichiometric and topological approaches to network completion in a unified formalism. With it, we develop a hybrid ASP encoding and rely upon the theory reasoning capacities of the ASP system clingo for solving the resulting logic program with linear constraints over reals. We empirically evaluate our approach by means of the metabolic network of Escherichia coli . Our analysis shows that our novel approach yields greatly superior results than obtainable from purely qualitative or quantitative approaches.

Abstract We introduce a new flexible paradigm of grounding and solving in Answer Set Programming (ASP), which we refer to as multi-shot ASP solving, and present its implementation in the ASP system clingo . Multi-shot ASP solving features grounding and solving processes that deal with continuously changing logic programs. In doing so, they remain operative and accommodate changes in a seamless way. For instance, such processes allow for advanced forms of search, as in optimization or theory solving, or interaction with an environment, as in robotics or query answering. Common to them is that the problem specification evolves during the reasoning process, either because data or constraints are added, deleted, or replaced. This evolutionary aspect adds another dimension to ASP since it brings about state changing operations. We address this issue by providing an operational semantics that characterizes grounding and solving processes in multi-shot ASP solving. This characterization provides a semantic account of grounder and solver states along with the operations manipulating them. The operative nature of multi-shot solving avoids redundancies in relaunching grounder and solver programs and benefits from the solver's learning capacities. clingo accomplishes this by complementing ASP's declarative input language with control capacities. On the declarative side, a new directive allows for structuring logic programs into named and parameterizable subprograms. The grounding and integration of these subprograms into the solving process is completely modular and fully controllable from the procedural side. To this end, clingo offers a new application programming interface that is conveniently accessible via scripting languages. By strictly separating logic and control, clingo also abolishes the need for dedicated systems for incremental and reactive reasoning, like iclingo and oclingo , respectively, and its flexibility goes well beyond the advanced yet still rigid solving processes of the latter.

Recently, it has been shown that constraint-based symbolic solving techniques offer an efficient way for deciding binding and routing options in order to obtain a feasible system level implementation. In combination with various background theories, a feasibility analysis of the resulting system may already be performed on partial solutions. That is, infeasible subsets of mapping and routing options can be pruned early in the decision process, which fastens the solving accordingly. However, allowing a proper design space exploration including multi-objective optimization also requires an efficient structure for storing and managing non-dominated solutions. In this work, we propose and study the usage of the Quad-Tree data structure in the context of partial assignment evaluation during system synthesis. Out experiments show that unnecessary dominance checks can be avoided, which indicates a preference of Quad-Trees over a commonly used list-based implementation for large combinatorial optimization problems.

An efficient Design Space Exploration (DSE) is imperative for the design of modern, highly complex embedded systems in order to steer the development towards optimal design points. The early evaluation of design decisions at system-level abstraction layer helps to find promising regions for subsequent development steps in lower abstraction levels by diminishing the complexity of the search problem. In recent works, symbolic techniques, especially Answer Set Programming (ASP) modulo Theories (ASPmT), have been shown to find feasible solutions of highly complex system-level synthesis problems with non-linear constraints very efficiently. In this paper, we present a novel approach to a holistic system-level DSE based on ASPmT. To this end, we include additional background theories that concurrently guarantee compliance with hard constraints and perform the simultaneous optimization of several design objectives. We implement and compare our approach with a state-of-the-art preference handling framework for ASP. Experimental results indicate that our proposed method produces better solutions with respect to both diversity and convergence to the true Pareto front.

Answer set programming (ASP) is a prominent knowledge representation and reasoning paradigm that found both industrial and scientific applications. The success of ASP is due to the combination of two factors: a rich modeling language and the availability of efficient ASP implementations. In this paper we trace the history of ASP systems, describing the key evaluation techniques and their implementation in actual tools.

Abstract In this paper, we introduce an alternative approach to Temporal Answer Set Programming that relies on a variation of Temporal Equilibrium Logic (TEL) for finite traces. This approach allows us to even out the expressiveness of TEL over infinite traces with the computational capacity of (incremental) Answer Set Programming (ASP). Also, we argue that finite traces are more natural when reasoning about action and change. As a result, our approach is readily implementable via multi-shot ASP systems and benefits from an extension of ASP's full-fledged input language with temporal operators. This includes future as well as past operators whose combination offers a rich temporal modeling language. For computation, we identify the class of temporal logic programs and prove that it constitutes a normal form for our approach. Finally, we outline two implementations, a generic one and an extension of the ASP systemclingo. Under consideration for publication in Theory and Practice of Logic Programming (TPLP)

Abstract We introduce theasprilo1framework to facilitate experimental studies of approaches addressing complex dynamic applications. For this purpose, we have chosen the domain of robotic intra-logistics. This domain is not only highly relevant in the context of today's fourth industrial revolution but it moreover combines a multitude of challenging issues within a single uniform framework. This includes multi-agent planning, reasoning about action, change, resources, strategies, etc. In return,aspriloallows users to study alternative solutions as regards effectiveness and scalability. Althoughasprilorelies on Answer Set Programming and Python, it is readily usable by any system complying with its fact-oriented interface format. This makes it attractive for benchmarking and teaching well beyond logic programming. More precisely,aspriloconsists of a versatile benchmark generator, solution checker and visualizer as well as a bunch of reference encodings featuring various ASP techniques. Importantly, the visualizer's animation capabilities are indispensable for complex scenarios like intra-logistics in order to inspect valid as well as invalid solution candidates. Also, it allows for graphically editing benchmark layouts that can be used as a basis for generating benchmark suites.

Abstract Automated storage and retrieval systems are principal components of modern production and warehouse facilities. In particular, automated guided vehicles nowadays substitute human-operated pallet trucks in transporting production materials between storage locations and assembly stations. While low-level control systems take care of navigating such driverless vehicles along programmed routes and avoid collisions even under unforeseen circumstances, in the common case of multiple vehicles sharing the same operation area, the problem remains how to set up routes such that a collection of transport tasks is accomplished most effectively. We address this prevalent problem in the context of car assembly at Mercedes-Benz Ludwigsfelde GmbH, a large-scale producer of commercial vehicles, where routes for automated guided vehicles used in the production process have traditionally been hand-coded by human engineers. Such ad-hoc methods may suffice as long as a running production process remains in place, while any change in the factory layout or production targets necessitates tedious manual reconfiguration, not to mention the missing portability between different production plants. Unlike this, we propose a declarative approach based on Answer Set Programming to optimize the routes taken by automated guided vehicles for accomplishing transport tasks. The advantages include a transparent and executable problem formalization, provable optimality of routes relative to objective criteria, as well as elaboration tolerance towards particular factory layouts and production targets. Moreover, we demonstrate that our approach is efficient enough to deal with the transport tasks evolving in realistic production processes at the car factory of Mercedes-Benz Ludwigsfelde GmbH.

The design of embedded systems is becoming continuously more complex such that efficient system-level design methods are becoming crucial. Recently, combined Answer Set Programming (ASP) and Quantifier Free Integer Difference Logic (QF-IDL) solving has been shown to be a promising approach in system synthesis. However, this approach still has several restrictions limiting its applicability. In the paper at hand, we propose a novel ASP modulo Theories (ASPmT) system synthesis approach, which (i) supports more sophisticated system models, (ii) tightly integrates the QF-IDL solving into the ASP solving, and (iii) makes use of partial assignment checking. As a result, more realistic systems are considered and an early exclusion of infeasible solutions improves the entire system synthesis.

Algorithm selection (AS) techniques -- which involve choosing from a set of algorithms the one expected to solve a given problem instance most efficiently -- have substantially improved the state of the art in solving many prominent AI problems, such as SAT, CSP, ASP, MAXSAT and QBF. Although several AS procedures have been introduced, not too surprisingly, none of them dominates all others across all AS scenarios. Furthermore, these procedures have parameters whose optimal values vary across AS scenarios. In this extended abstract of our 2015 JAIR article of the same title, we summarize AutoFolio, which uses an algorithm configuration procedure to automatically select an AS approach and optimize its parameters for a given AS scenario. AutoFolio allows researchers and practitioners across a broad range of applications to exploit the combined power of many different AS methods and to automatically construct high-performance algorithm selectors. We demonstrate that AutoFolio was able to produce new state-of-the-art algorithm selectors for 7 well-studied AS scenarios and matches state-of-the-art performance statistically on all other scenarios. Compared to the best single algorithm for each AS scenario, AutoFolio achieved average speedup factors between 1.3 and 15.4.

In Multi-Agent Path Finding (MAPF), a team of agents needs to find collision-free paths from their starting locations to their respective targets. Combined Target Assignment and Path Finding (TAPF) extends MAPF by including the problem of assigning targets to agents as a precursor to the MAPF problem. A limitation of both models is their assumption that the number of agents and targets are equal, which is invalid in some applications such as autonomous warehouse systems. We address this limitation by generalizing TAPF to allow for (1)~unequal number of agents and tasks; (2)~tasks to have deadlines by which they must be completed; (3)~ordering of groups of tasks to be completed; and (4)~tasks that are composed of a sequence of checkpoints that must be visited in a specific order. Further, we model the problem using answer set programming (ASP) to show that customizing the desired variant of the problem is simple one only needs to choose the appropriate combination of ASP rules to enforce it. We also demonstrate experimentally that if problem specific information can be incorporated into the ASP encoding then ASP based method can be efficient and can scale up to solve practical applications.

Abstract We present the third generation of the constraint answer set system clingcon , combining Answer Set Programming (ASP) with finite domain constraint processing (CP). While its predecessors rely on a black-box approach to hybrid solving by integrating the CP solver gecode , the new clingcon system pursues a lazy approach using dedicated constraint propagators to extend propagation in the underlying ASP solver clasp . No extension is needed for parsing and grounding clingcon 's hybrid modeling language since both can be accommodated by the new generic theory handling capabilities of the ASP grounder gringo . As a whole, clingcon 3 is thus an extension of the ASP system clingo 5, which itself relies on the grounder gringo and the solver clasp . The new approach of clingcon offers a seamless integration of CP propagation into ASP solving that benefits from the whole spectrum of clasp 's reasoning modes, including, for instance, multi-shot solving and advanced optimization techniques. This is accomplished by a lazy approach that unfolds the representation of constraints and adds it to that of the logic program only when needed. Although the unfolding is usually dictated by the constraint propagators during solving, it can already be partially (or even totally) done during preprocessing. Moreover, clingcon 's constraint preprocessing and propagation incorporate several well-established CP techniques that greatly improve its performance. We demonstrate this via an extensive empirical evaluation contrasting, first, the various techniques in the context of CSP solving and, second, the new clingcon system with other hybrid ASP systems.

Abstract The recent series 5 of the Answer Set Programming (ASP) system clingo provides generic means to enhance basic ASP with theory reasoning capabilities. We instantiate this framework with different forms of linear constraints and elaborate upon its formal properties. Given this, we discuss the respective implementations, and present techniques for using these constraints in a reactive context. More precisely, we introduce extensions to clingo with difference and linear constraints over integers and reals, respectively, and realize them in complementary ways. Finally, we empirically evaluate the resulting clingo derivatives clingo [ dl ] and clingo [ lp ] on common language fragments and contrast them to related ASP systems.

Goal Recognition Design involves identifying the best ways to modify an underlying environment that agents operate in, typically by making asubset of feasible actions infeasible, so that agents are forced to reveal their goals as early as possible. Thus far, existing work has focused exclusively on imperative classical planning. In this paper, we address the same problem with a different paradigm, namely, declarative approaches based on Answer Set Programming (ASP). Our experimental results show that one of our ASP encodings is more scalable and is significantly faster by up to three orders of magnitude than thecurrent state of the art.

We investigate minimization-based approaches to iterated belief change in multi-agent systems. A network of agents is represented by an undirected graph, where propositional formulas are associated with vertices. Information is shared between vertices via a procedure where each vertex minimizes disagreement with other vertices in the graph. Each iterative approach takes into account the proximity between vertices, with the underlying assumption that information from nearby sources is given higher priority than information from more distant sources. We have identified two main approaches to iteration: in the first approach, a vertex takes into account the information at its immediate neighbours only, and information from more distant vertices is propagated via iteration; in the second approach, a vertex first takes into account information from distance-1 neighbours, then from distance-2 neighbours, and so on, in a prioritized fashion. There prove to be three distinct ways to define the second approach, so in total we have four types of iteration. We define these types formally, find relationships between them, and investigate their basic logical properties. We also implemented the approaches in a software system called Equibel.

Answer Set Programming (ASP) is a powerful declarative programming paradigm that has been successfully applied to many different domains. Recently, ASP has also proved successful for hard optimization problems like course timetabling and travel allotment. In this paper, we approach another important task, namely, the shift design problem, aiming at an alignment of a minimum number of shifts in order to meet required numbers of employees (which typically vary for different time periods) in such a way that over- and understaffing is minimized. We provide an ASP encoding of the shift design problem, which, to the best of our knowledge, has not been addressed by ASP yet. Our experimental results demonstrate that ASP is capable of improving the best known solutions to some benchmark problems. Other instances remain challenging and make the shift design problem an interesting benchmark for ASP-based optimization methods.

Acyclicity constraints are prevalent in knowledge representation and applications where acyclic data structures such as DAGs and trees play a role. Recently, such constraints have been considered in the satisfiability modulo theories (SMT) framework, and in this paper we carry out an analogous exte nsion to the answer set programming (ASP) paradigm. The resulting formalism, ASP modulo acyclicity, offers a rich set of primitives to express constraints related to recursive structures. In the technical results of the paper, we relate the new generalization with standard ASP by showing (i) how acyclicity extensions translate into normal rules, (ii) how weight constraint programs can be instrumented by acyclicity extensions to capture stability in analogy to unfounded set checking, and (iii) how the gap between supported and stable models is effectively closed in the presence of such an extension. Moreover, we present an efficient implementation of acyclicity constraints by incorporating a respective propagator into the state-of-the-art ASP solver CLASP. The implementation provides a unique combination of traditional unfounded set checking with acyclicity propagation. In the experimental part, we evaluate the interplay of these orthogonal checks by equipping logic programs with supplementary acyclicity constraints. The performance results show that native support for acyclicity constraints is a worthwhile addition, furnishing a complementary modeling construct in ASP itself as well as effective means for translation-based ASP solving.

In this paper we describe asprin, a general, flexible, and extensible framework for handling preferences among the stable models of a logic program. We show how complex preference relations can be specified through user-defined preference types and their arguments. We describe how preference specifications are handled internally by so-called preference programs, which are used for dominance testing. We also give algorithms for computing one, or all, optimal stable models of a logic program. Notably, our algorithms depend on the complexity of the dominance tests and make use of multi-shot answer set solving technology.

During the Vienna Summer of Logic, the first FLoC Olympic Games were organized, bringing together a dozen competitions related to logic. Here we present the highlights of the Satisfiability (SAT) and Answer Set Programming (ASP) competitions.

Algorithm selection (AS) techniques -- which involve choosing from a set of algorithms the one expected to solve a given problem instance most efficiently -- have substantially improved the state of the art in solving many prominent AI problems, such as SAT, CSP, ASP, MAXSAT and QBF. Although several AS procedures have been introduced, not too surprisingly, none of them dominates all others across all AS scenarios. Furthermore, these procedures have parameters whose optimal values vary across AS scenarios. This holds specifically for the machine learning techniques that form the core of current AS procedures, and for their hyperparameters. Therefore, to successfully apply AS to new problems, algorithms and benchmark sets, two questions need to be answered: (i) how to select an AS approach and (ii) how to set its parameters effectively. We address both of these problems simultaneously by using automated algorithm configuration. Specifically, we demonstrate that we can automatically configure claspfolio 2, which implements a large variety of different AS approaches and their respective parameters in a single, highly-parameterized algorithm framework. Our approach, dubbed AutoFolio, allows researchers and practitioners across a broad range of applications to exploit the combined power of many different AS methods. We demonstrate AutoFolio can significantly improve the performance of claspfolio 2 on 8 out of the 13 scenarios from the Algorithm Selection Library, leads to new state-of-the-art algorithm selectors for 7 of these scenarios, and matches state-of-the-art performance (statistically) on all other scenarios. Compared to the best single algorithm for each AS scenario, AutoFolio achieves average speedup factors between 1.3 and 15.4.

Abstract This paper defines the syntax and semantics of the input language of the ASP grounder gringo . The definition covers several constructs that were not discussed in earlier work on the semantics of that language, including intervals, pools, division of integers, aggregates with non-numeric values, and lparse-style aggregate expressions. The definition is abstract in the sense that it disregards some details related to representing programs by strings of ASCII characters. It serves as a specification for gringo from Version 4.5 on.

Abstract Although Boolean Constraint Technology has made tremendous progress over the last decade, the efficacy of state-of-the-art solvers is known to vary considerably across different types of problem instances, and is known to depend strongly on algorithm parameters. This problem was addressed by means of a simple, yet effective approach using handmade, uniform, and unordered schedules of multiple solvers inppfolio, which showed very impressive performance in the 2011 Satisfiability Testing (SAT) Competition. Inspired by this, we take advantage of the modeling and solving capacities of Answer Set Programming (ASP) to automatically determine more refined, that is, nonuniform and ordered solver schedules from the existing benchmarking data. We begin by formulating the determination of such schedules as multi-criteria optimization problems and provide corresponding ASP encodings. The resulting encodings are easily customizable for different settings, and the computation of optimum schedules can mostly be done in the blink of an eye, even when dealing with large runtime data sets stemming from many solvers on hundreds to thousands of instances. Also, the fact that our approach can be customized easily enabled us to swiftly adapt it to generate parallel schedules for multi-processor machines.

Abstract Building on the award-winning, portfolio-based ASP solverclaspfolio, we presentclaspfolio2, a modular and open solver architecture that integrates several different portfolio-based algorithm selection approaches and techniques. Theclaspfolio2 solver framework supports various feature generators, solver selection approaches, solver portfolios, as well as solver-schedule-based pre-solving techniques. The default configuration ofclaspfolio2 relies on a light-weight version of the ASP solverclaspto generate static and dynamic instance features. The flexible open design ofclaspfolio2 is a distinguishing factor even beyond ASP. As such, it provides a unique framework for comparing and combining existing portfolio-based algorithm selection approaches and techniques in a single, unified framework. Taking advantage of this, we conducted an extensive experimental study to assess the impact of different feature sets, selection approaches and base solver portfolios. In addition to gaining substantial insights into the utility of the various approaches and techniques, we identified a default configuration ofclaspfolio2 that achieves substantial performance gains not only overclasp's default configuration and the earlier version ofclaspfolio, but also over manually tuned configurations ofclasp.

We introduce a general declarative framework for incorporating domain-specific heuristics into ASP solving. We accomplish this by extending the first-order modeling language of ASP by a distinguished heuristic predicate. The resulting heuristic information is processed as an equitable part of the logic program and subsequently exploited by the solver when it comes to non-deterministically assigning a truth value to an atom. We implemented our approach as a dedicated heuristic in the ASP solver clasp and show its great prospect by an empirical evaluation.

We address the problem of belief change in (nonmonotonic) logic programming under answer set semantics. Our formal techniques are analogous to those of distance-based belief revision in propositional logic. In particular, we build upon the model theory of logic programs furnished by SE interpretations, where an SE interpretation is a model of a logic program in the same way that a classical interpretation is a model of a propositional formula. Hence we extend techniques from the area of belief revision based on distance between models to belief change in logic programs. We first consider belief revision: for logic programs P and Q , the goal is to determine a program R that corresponds to the revision of P by Q , denoted P * Q . We investigate several operators, including (logic program) expansion and two revision operators based on the distance between the SE models of logic programs. It proves to be the case that expansion is an interesting operator in its own right, unlike in classical belief revision where it is relatively uninteresting. Expansion and revision are shown to satisfy a suite of interesting properties; in particular, our revision operators satisfy all or nearly all of the AGM postulates for revision. We next consider approaches for merging a set of logic programs, P 1 , ..., P n . Again, our formal techniques are based on notions of relative distance between the SE models of the logic programs. Two approaches are examined. The first informally selects for each program P i those models of P i that vary the least from models of the other programs. The second approach informally selects those models of a program P 0 that are closest to the models of programs P 1 , ..., P n . In this case, P 0 can be thought of as a set of database integrity constraints. We examine these operators with regards to how they satisfy relevant postulate sets. Last, we present encodings for computing the revision as well as the merging of logic programs within the same logic programming framework. This gives rise to a direct implementation of our approach in terms of off-the-shelf answer set solvers. These encodings also reflect the fact that our change operators do not increase the complexity of the base formalism.

We introduce formal proof systems based on tableau methods for analyzing computations in Answer Set Programming (ASP). Our approach furnishes fine-grained instruments for characterizing operations as well as strategies of ASP solvers. The granularity is detailed enough to capture a variety of propagation and choice methods of algorithms used for ASP solving, also incorporating SAT-based and conflict-driven learning approaches to some extent. This provides us with a uniform setting for identifying and comparing fundamental properties of ASP solving approaches. In particular, we investigate their proof complexities and show that the run-times of best-case computations can vary exponentially between different existing ASP solvers. Apart from providing a framework for comparing ASP solving approaches, our characterizations also contribute to their understanding by pinning down the constitutive atomic operations. Furthermore, our framework is flexible enough to integrate new inference patterns, and so to study their relation to existing ones. To this end, we generalize our approach and provide an extensible basis aiming at a modular incorporation of additional language constructs. This is exemplified by augmenting our basic tableau methods with cardinality constraints and disjunctions.

Abstract The course timetabling problem can be generally defined as the task of assigning a number of lectures to a limited set of timeslots and rooms, subject to a given set of hard and soft constraints. The modeling language for course timetabling is required to be expressive enough to specify a wide variety of soft constraints and objective functions. Furthermore, the resulting encoding is required to be extensible for capturing new constraints and for switching them between hard and soft, and to be flexible enough to deal with different formulations. In this paper, we propose to make effective use of ASP as a modeling language for course timetabling. We show that our ASP-based approach can naturally satisfy the above requirements, through an ASP encoding of the curriculum-based course timetabling problem proposed in the third track of the second international timetabling competition (ITC-2007). Our encoding is compact and human-readable, since each constraint is individually expressed by either one or two rules. Each hard constraint is expressed by using integrity constraints and aggregates of ASP. Each soft constraint S is expressed by rules in which the head is the form of penalty(S,V,C), and a violation V and its penalty cost C are detected and calculated respectively in the body. We carried out experiments on four different benchmark sets with five different formulations. We succeeded either in improving the bounds or producing the same bounds for many combinations of problem instances and formulations, compared with the previous best known bounds.

Abstract Proposing relevant perturbations to biological signaling networks is central to many problems in biology and medicine because it allows for enabling or disabling certain biological outcomes. In contrast to quantitative methods that permit fine-grained (kinetic) analysis, qualitative approaches allow for addressing large-scale networks. This is accomplished by more abstract representations such as logical networks. We elaborate upon such a qualitative approach aiming at the computation of minimal interventions in logical signaling networks relying on Kleene's three-valued logic and fixpoint semantics. We address this problem within answer set programming and show that it greatly outperforms previous work using dedicated algorithms.

Abstract We present the new multi-threaded version of the state-of-the-art answer set solverclasp. We detail its component and communication architecture and illustrate how they support the principal functionalities ofclasp. Also, we provide some insights into the data representation used for different constraint types handled byclasp. All this is accompanied by an extensive experimental analysis of the major features related to multi-threading inclasp.

Abstract We present the hybrid ASP solver clingcon , combining the simple modeling language and the high performance Boolean solving capacities of Answer Set Programming (ASP) with techniques for using non-Boolean constraints from the area of Constraint Programming (CP). The new clingcon system features an extended syntax supporting global constraints and optimize statements for constraint variables. The major technical innovation improves the interaction between ASP and CP solver through elaborated learning techniques based on irreducible inconsistent sets . A broad empirical evaluation shows that these techniques yield a performance improvement of an order of magnitude.

We show how Finite Model Computation (FMC) of first-order theories can efficiently and transparentlybe solved by taking advantage of an extension of Answer Set Programming, called incremental Answer Set Programming (iASP). The idea is to use the incremental parameter in iASP programs to account for the domain size of a model. The FMC problem is then successively addressed for increasing domain sizes until an answer set, representing a finite model of the original first-order theory, is found. We developed a system based on the iASP solver iClingo and demonstrate its competitiveness.

Abstract Building biological models by inferring functional dependencies from experimental data is an important issue in Molecular Biology. To relieve the biologist from this traditionally manual process, various approaches have been proposed to increase the degree of automation. However, available approaches often yield a single model only, rely on specific assumptions, and/or use dedicated, heuristic algorithms that are intolerant to changing circumstances or requirements in the view of the rapid progress made in Biotechnology. Our aim is to provide a declarative solution to the problem by appeal to Answer Set Programming (ASP) overcoming these difficulties. We build upon an existing approach to Automatic Network Reconstruction proposed by part of the authors. This approach has firm mathematical foundations and is well suited for ASP due to its combinatorial flavor providing a characterization of all models explaining a set of experiments. The usage of ASP has several benefits over the existing heuristic algorithms. First, it is declarative and thus transparent for biological experts. Second, it is elaboration tolerant and thus allows for an easy exploration and incorporation of biological constraints. Third, it allows for exploring the entire space of possible models. Finally, our approach offers an excellent performance, matching existing, special-purpose systems.

Abstract Preference handling and optimization are indispensable means for addressing nontrivial applications in Answer Set Programming (ASP). However, their implementation becomes difficult whenever they bring about a significant increase in computational complexity. As a consequence, existing ASP systems do not offer complex optimization capacities, supporting, for instance, inclusion-based minimization or Pareto efficiency. Rather, such complex criteria are typically addressed by resorting to dedicated modeling techniques, like saturation . Unlike the ease of common ASP modeling, however, these techniques are rather involved and hardly usable by ASP laymen. We address this problem by developing a general implementation technique by means of meta-prpogramming, thus reusing existing ASP systems to capture various forms of qualitative preferences among answer sets. In this way, complex preferences and optimization capacities become readily available for ASP applications.

Abstract We introduce an approach to detecting inconsistencies in large biological networks by using answer set programming. To this end, we build upon a recently proposed notion of consistency between biochemical/genetic reactions and high-throughput profiles of cell activity. We then present an approach based on answer set programming to check the consistency of large-scale data sets. Moreover, we extend this methodology to provide explanations for inconsistencies by determining minimal representations of conflicts. In practice, this can be used to identify unreliable data or to indicate missing reactions.

Today's molecular biology is confronted with enormous amounts of data, generated by new high-throughput technologies, along with an increasing number of biological models available over web repositories. This poses new challenges for bioinformatics to invent methods coping with incompleteness, heterogeneity, and mutual inconsistency of data and models. To this end, we built the library BioASP, providing a framework for analyzing biological data and models with Answer Set Programming (ASP). Due to the expressive modeling language, the inherent tolerance of incomplete knowledge, and efficient solving engines, ASP has proven to be an excellent tool for solving a variety of biological questions. The BioASP library implements methods for analyzing metabolic and gene regulatory networks, consistency checking, diagnosing, and repairing biological data and models. In particular, it allows for computing predictions and generating hypotheses about required expansions of biological models. To accomplish this, expert knowledge of both the biological application and the ASP paradigm needs to be combined. In fact, the functionalities provided by the BioASP library exploit technical know-how of modeling (biological) problems in ASP and gearing ASP solvers' parameters to them. Often, such best-practice technology is the result of an exhaustive series of tests. The BioASP library %, we gather % this knowledge integrates our practical experience and offers them via easy-to-use Python functions, thus enabling ASP non-experts to solve biological questions with ASP.

The Logic Programming (LP) community, through the Association for Logic Programming (ALP) and its Executive Committee, decided to introduce for 2010 important changes in the way the main yearly results in LP and related areas are published. Whereas such results have appeared to date in standalone volumes of proceedings of the yearly International Conferences on Logic Programming (ICLP), and this method—fully in the tradition of Computer Science (CS)—has served the community well, it was felt that an effort needed to be made to achieve a higher level of compatibility with the publishing mechanisms of other fields outside CS.

Answer set programming (ASP) does not allow for incrementally constructing answer sets or locally validating constructions like proofs by only looking at a part of the given program. In this article, we elaborate upon an alternative approach to ASP that allows for incremental constructions. Our approach draws its basic intuitions from the area of default logics. We investigate the feasibility of the concept of semi-monotonicity known from default logics as a basis of incrementality. On the one hand, every logic program has at least one answer set in our alternative setting, which moreover can be constructed incrementally based on generating rules. On the other hand, the approach may produce answer sets lacking characteristic properties of standard answer sets, such as being a model of the given program. We show how integrity constraints can be used to re-establish such properties, even up to correspondence with standard answer sets. Furthermore, we develop an SLD-like proof procedure for our incremental approach to ASP, which allows for query-oriented computations. Also, we provide a characterization of our definition of answer sets via a modification of Clarks completion. Based on this notion of program completion, we present an algorithm for computing the answer sets of a logic program in our approach.

Puerto de Cajas serves as a vital high-altitude passage in Ecuador, connecting the coastal region to the city of Cuenca. The stability of this rocky massif is carefully managed through the assessment of blocks and discontinuities, ensuring safe travel. This study presents a novel approach, employing rapid and cost-effective methods to evaluate an unexplored area within the protected expanse of Cajas. Using terrestrial photogrammetry and strategically positioned geomechanical stations along the slopes, we generated a detailed point cloud capturing elusive terrain features. We have used terrestrial photogrammetry for digitalization of the slope. Validation of the collected data was achieved by comparing directional data from Cloud Compare software with manual readings using a digital compass integrated in a phone at control points. The analysis encompasses three slopes, employing the SMR, Q-slope, and kinematic methodologies. Results from the SMR system closely align with kinematic analysis, indicating satisfactory slope quality. Nonetheless, continued vigilance in stability control remains imperative for ensuring road safety and preserving the site's integrity. Moreover, this research lays the groundwork for the creation of a publicly accessible 3D repository, enhancing visualization capabilities through Google Virtual Reality. This initiative not only aids in replicating the findings but also facilitates access to an augmented reality environment, thereby fostering collaborative research endeavors.

We elaborate upon the usage of action language C for representing and reasoning about biological models. First, we provide a simple extension of C allowing for variables and show its usefulness in modeling biochemical reactions according to the well-known model of BIOCHAM. Second, we show how the biological action description language CTAID can be mapped onto C. Finally, we describe a toolbox for using action languages, including among them, a compiler mapping C and CTAID to logic programs under answer sets semantics along with a web-service integrating different front- and back-ends for addressing dynamical systems by means of action description languages via answer set programming. This is accompanied by an empirical evaluation with existing systems for processing action description languages.

We consider the problem of representing arbitrary preferences in causal reasoning and planning systems. In planning, a preference may be seen as a goal or constraint that is desirable, but not necessary, to satisfy. To begin, we define a very general query language for histories, or interleaved sequences of world states and actions. Based on this, we specify a second language in which preferences are defined. A single preference defines a binary relation on histories, indicating that one history is preferred to the other. From this, one can define global preference orderings on the set of histories, the maximal elements of which are the preferred histories. The approach is very general and flexible; thus it constitutes a ‘base’ language in terms of which higher-level preferences may be defined. To this end, we investigate two fundamental types of preferences that we call choice and temporal preferences. We consider concrete strategies for these types of preferences and encode them in terms of our framework. We suggest how to express aggregates in the approach, allowing, e.g. the expression of a preference for histories with lowest total action costs. Last, our approach can be used to express other approaches and so serves as a common framework in which such approaches can be expressed and compared. We illustrate this by indicating how an approach due to Son and Pontelli can be encoded in our approach, as well as the language PDDL3.

We investigate the usage of rule dependency graphs and their colorings for characterizing and computing answer sets of logic programs. This approach provides us with insights into the interplay between rules when inducing answer sets. We start with different characterizations of answer sets in terms of totally colored dependency graphs that differ in graph-theoretical aspects. We then develop a series of operational characterizations of answer sets in terms of operators on partial colorings. In analogy to the notion of a derivation in proof theory, our operational characterizations are expressed as (non-deterministically formed) sequences of colorings, turning an uncolored graph into a totally colored one. In this way, we obtain an operational framework in which different combinations of operators result in different formal properties. Among others, we identify the basic strategy employed by the noMoRe system and justify its algorithmic approach. Furthermore, we distinguish operations corresponding to Fitting's operator as well as to well-founded semantics.

Reiter's default logic is one of the best known and most studied of the approaches to nonmonotonic reasoning. Several variants of default logic have subsequently been proposed to give systems with properties differing from the original. In this paper, we examine the relationship between default logic and its major variants. We accomplish this by translating a default theory under a variant interpretation into a second default theory, under the original Reiter semantics, wherein the variant interpretation is respected. That is, in each case we show that, given an extension of a translated theory, one may extract an extension of the original variant default logic theory. We show how constrained, rational, justified, and cumulative default logic can be expressed in Reiter's default logic. As well, we show how Reiter's default logic can be expressed in rational default logic. From this, we suggest that any such variant can be similarly treated. Consequently, we provide a unification of default logics, showing how the original formulation of default logic may express its variants. Moreover, the translations clearly express the relationships between alternative approaches to default logic. The translations themselves are shown to generally have good properties. Thus, in at least a theoretical sense, we show that these variants are in a sense superfluous, in that for any of these variants of default logic, we can exactly mimic the behaviour of a variant in standard default logic. As well, the translations lend insight into means of classifying the expressive power of default logic variants; specifically we suggest that the property of semi-monotonicity represents a division with respect to expressibility, whereas regularity and cumulativity do not.

MOTIVATION: Continued development of analytical techniques based on gas chromatography and mass spectrometry now facilitates the generation of larger sets of metabolite concentration data. An important step towards the understanding of metabolite dynamics is the recognition of stable states where metabolite concentrations exhibit a simple behaviour. Such states can be characterized through the identification of significant thresholds in the concentrations. But general techniques for finding discretization thresholds in continuous data prove to be practically insufficient for detecting states due to the weak conditional dependences in concentration data. RESULTS: We introduce a method of recognizing states in the framework of decision tree induction. It is based upon a global analysis of decision forests where stability and quality are evaluated. It leads to the detection of thresholds that are both comprehensible and robust. Applied to metabolite concentration data, this method has led to the discovery of hidden states in the corresponding variables. Some of these reflect known properties of the biological experiments, and others point to putative new states. AVAILABILITY: An implementation of this approach can be obtained from the authors upon request.

We present a general approach for representing and reasoning with sets of defaults in default logic, focusing on reasoning about preferences among sets of defaults. First, we consider how to control the application of a set of defaults so that either all apply (if possible) or none do (if not). From this, an approach to dealing with preferences among sets of default rules is developed. We begin with an ordered default theory, consisting of a standard default theory, but with possible preferences on sets of rules. This theory is transformed into a second, standard default theory wherein the preferences are respected. The approach differs from other work, in that we obtain standard default theories and do not rely on prioritized versions of default logic. In practical terms this means we can immediately use existing default logic theorem provers for an implementation. Also, we directly generate just those extensions containing the most preferred applied rules; in contrast, most previous approaches generate all extensions, then select the most preferred. In a major application of the approach, we show how semimonotonic default theories can be encoded so that reasoning can be carried out at the object level. With this, we can reason about default extensions from within the framework of a standard default logic. Hence one can encode notions such as skeptical and credulous conclusions, and can reason about such conclusions within a single extension.

In recent years, there has been a large amount of disparate work concerning the representation and reasoning with qualitative preferential information by means of approaches to nonmonotonic reasoning. Given the variety of underlying systems, assumptions, motivations, and intuitions, it is difficult to compare or relate one approach with another. Here, we present an overview and classification for approaches to dealing with preference. A set of criteria for classifying approaches is given, followed by a set of desiderata that an approach might be expected to satisfy. A comprehensive set of approaches is subsequently given and classified with respect to these sets of underlying principles.

In this paper, we show how an approach to belief revision and belief contraction can be axiomatized by means of quantified Boolean formulas. Specifically, we consider the approach of belief change scenarios, a general framework that has been introduced for expressing different forms of belief change. The essential idea is that for a belief change scenario (K, R, C), the set of formulas K, representing the knowledge base, is modified so that the sets of formulas R and C are respectively true in, and consistent with the result. By restricting the form of a belief change scenario, one obtains specific belief change operators including belief revision, contraction, update, and merging. For both the general approach and for specific operators, we give a quantified Boolean formula such that satisfying truth assignments to the free variables correspond to belief change extensions in the original approach. Hence, we reduce the problem of determining the results of a belief change operation to that of satisfiability. This approach has several benefits. First, it furnishes an axiomatic specification of belief change with respect to belief change scenarios. This then leads to further insight into the belief change framework. Second, this axiomatization allows us to identify strict complexity bounds for the considered reasoning tasks. Third, we have implemented these different forms of belief change by means of existing solvers for quantified Boolean formulas. As well, it appears that this approach may be straightforwardly applied to other specific approaches to belief change.

We introduce a methodology and framework for expressing general preference information in logic programming under the answer set semantics. An ordered logic program is an extended logic program in which rules are named by unique terms, and in which preferences among rules are given by a set of atoms of form s [pr ] t where s and t are names. An ordered logic program is transformed into a second, regular, extended logic program wherein the preferences are respected, in that the answer sets obtained in the transformed program correspond with the preferred answer sets of the original program. Our approach allows the specification of dynamic orderings, in which preferences can appear arbitrarily within a program. Static orderings (in which preferences are external to a logic program) are a trivial restriction of the general dynamic case. First, we develop a specific approach to reasoning with preferences, wherein the preference ordering specifies the order in which rules are to be applied. We then demonstrate the wide range of applicability of our framework by showing how other approaches, among them that of Brewka and Eiter, can be captured within our framework. Since the result of each of these transformations is an extended logic program, we can make use of existing implementations, such as dlv and smodels. To this end, we have developed a publicly available compiler as a front-end for these programming systems.

We provide a semantic framework for preference handling in answer set programming. To this end, we introduce preference preserving consequence operators. The resulting fixpoint characterizations provide us with a uniform semantic framework for characterizing preference handling in existing approaches. Although our approach is extensible to other semantics by means of an alternating fixpoint theory, we focus here on the elaboration of preferences under answer set semantics. Alternatively, we show how these approaches can be characterized by the concept of order preservation. These uniform semantic characterizations provide us with new insights about inter-relationships and moreover about ways of implementation.

In this paper, we elaborate the idea that contexts provide an important and meaningful notion in default reasoning. We demonstrate this by looking at Reiter's default logic that has been the prime candidate for formalizing consistency-based default reasoning ever since its introduction in 1980. This results in a new context-based approach to default logic, called contextual default logic. The approach extends the notion of a default rule and supplies each default extension with a context. In particular, contextual default logic provides a unified framework for default logics. That is, it allows for embedding existing variants of default logic along with more traditional approaches like the closed world assumption. Since this is accomplished in a homogeneous way, we gain additional expressiveness by combining the diverse approaches. A key advantage of contextual default logic is that it provides a syntactical instrument for comparing existing default logics in a unified setting. In particular, the approach reveals that existing default logics mainly differ in the way they deal with an explicit or implicit underlying context.

We introduce a uniform semantical framework for various default logics in terms of Kripke structures. This possible worlds approach provides a simple but meaningful instrument for comparing existing default logics in a unified setting. The possible w