Stable models of logic programs have been studied and characterized in relation with other formalisms by many researchers. As already argued in previous papers, such characterizations are interesting for diverse reasons, including theoretical investigations and the possibility of leading to new algorithms for computing stable models of logic programs. At the theoretical level, complexity and expressiveness comparisons have brought about fundamental insights. Beyond that, practical implementations of the developed reductions enable the use of existing solvers for other logical formalisms to compute stable models. In this paper, we first provide a simple characterization of stable models that can be viewed as a proof-theoretic counterpart of the standard model-theoretic definition. We further show how it can be naturally encoded in difference logic. Such an encoding, compared to the existing reductions to classical logics, does not require Boolean variables. Then, we implement our novel translation to a Satisfiability Modulo Theories (SMT) formula. We finally compare our approach, employing the SMT solver yices, to the translation-based ASP solver lp2diff and to clingo on domains from the “Basic Decision” track of the 2017 Answer Set Programming competition. The results show that our approach is competitive to and often better than lp2diff, and that it can also be faster than clingo on non-tight domains.

The grounding bottleneck in Answer Set Programming prohibits large instances from being solved. This is caused by a combinatorial explosion in the grounding phase of standard ground&solve systems. A promising alternative is Body-Decoupled Grounding (BDG), which grounds each body predicate on its own. However, BDG faces challenges in terms of worst-case grounding size and limited interoperability with other systems. This paper addresses shortcomings of BDG by introducing FastFound: an alternative foundedness check that significantly reduces grounding sizes, by grounding each predicate on its own. FastFound’s foundedness check is done implicitly, which leads to a quadratic reduction in grounding size. We start by introducing FastFound for tight normal rules, where we observe that this cannot be substantially improved. Then we extend FastFound to head-cycle-free programs and give novel interoperability results for full disjunctive programs. An experimental evaluation on our prototype shows promising results, as we solve more grounding-heavy tasks than both standard ground&solve systems and BDG.

Stable models of logic programs have been studied and characterized in relation with other formalisms by many researchers. As already argued in previous papers, such characterizations are interesting for diverse reasons, including theoretical investigations and the possibility of leading to new algorithms for computing stable models of logic programs. At the theoretical level, complexity and expressiveness comparisons have brought about fundamental insights. Beyond that, practical implementations of the developed reductions enable the use of existing solvers for other logical formalisms to compute stable models. In this paper, we first provide a simple characterization of stable models that can be viewed as a proof-theoretic counterpart of the standard model-theoretic definition. We further show how it can be naturally encoded in difference logic. Such an encoding, compared to the existing reductions to classical logics, does not require Boolean variables. Then, we implement our novel translation to a Satisfiability Modulo Theories (SMT) formula. We finally compare our approach, employing the SMT solver yices , to the translation-based ASP solver lp2diff and to clingo on domains from the “Basic Decision” track of the 2017 Answer Set Programming competition. The results show that our approach is competitive to and often better than lp2diff , and that it can also be faster than clingo on non-tight domains.

The Job-shop Scheduling Problem (JSP) is a well-known and challenging combinatorial optimization problem in which tasks sharing a machine are to be arranged in a sequence such that encompassing jobs can be completed as early as possible. In this paper, we investigate problem decomposition into time windows whose operations can be successively scheduled and optimized by means of multi-shot Answer Set Programming (ASP) solving. From a computational perspective, decomposition aims to split highly complex scheduling tasks into better manageable subproblems with a balanced number of operations such that good-quality or even optimal partial solutions can be reliably found in a small fraction of runtime. We devise and investigate a variety of decomposition strategies in terms of the number and size of time windows as well as heuristics for choosing their operations. Moreover, we incorporate time window overlapping and compression techniques into the iterative scheduling process to counteract optimization limitations due to the restriction to window-wise partial schedules. Our experiments on different JSP benchmark sets show that successive optimization by multi-shot ASP solving leads to substantially better schedules within tight runtime limits than single-shot optimization on the full problem. In particular, we find that decomposing initial solutions obtained with proficient heuristic methods into time windows leads to improved solution quality.

This issue of TPLP contains the regular papers of the 41 st

In view of the high total cost of semiconductor manufacturing assets, respective equipment needs to be as productive as possible. To avoid needless idling and unnecessary downtime, scheduling and maintenance strategies are important in practice. This paper presents a novel approach to reduce the substantial setup costs inherent to ion implantation by deriving scheduling constraints based on current equipment conditions. Consequently, a supervised learning pipeline is established that utilizes built-in sensors and process target data to accurately predict setup costs. The derived constraints are integrated into scheduling, thereby enhancing its efficiency through dynamic dispatching adaptations. The application of our method is projected to significantly improve equipment availability by avoiding more than 100 hours of potential downtime annually.

Answer set programming is a popular declarative paradigm with countless applications for modeling and solving combinatorial problems. We can view a program as a knowledge database compactly representing conditions for solutions. Often we are interested in reasoning about solutions of filtering answer sets. At the heart of these questions is brave and cautious reasoning. For browsing answer sets, we combine both as restricting atoms of answer sets is only meaningful for atoms called facets that belong to some (brave) but not to all answer sets (cautious). Surprisingly, the precise computational complexity of facet problems remained widely open so far. In this paper, we study the complexity of answer set facets. We establish tight results for reasoning with facets, deciding upper and lower bounds as well as the exact number of facets, and comparing facets. Facet reasoning seems to be a natural problem formalism, residing in complexity families Σᴾ, Πᴾ, Dᴾ, and Θᴾ, up to the third level. Moreover, our study considers quantitative importance questions on facets and generalizing from facets to conjunctions, disjunctions, and arbitrary queries. We complete our results by an experimental evaluation.

Abstract The Operating Room Scheduling (ORS) problem deals with the optimization of daily operating room surgery schedules. It is a challenging problem subject to many constraints, like to determine the starting time of different surgeries and allocating the required resources, including the availability of beds in different units. In the past years, Answer Set Programming (ASP) has been successfully employed for addressing and solving the ORS problem. Despite its importance, due to the inherent difficulty of retrieving real data, all the analyses on ORS ASP encodings have been performed on synthetic data so far. In this paper, first we present a new, improved ASP encoding for the ORS problem. Then, we deal with the real case of ASL1 Liguria, an Italian health authority operating through three hospitals, and present adaptations of the ASP encodings to deal with the real-world data. Further, we analyse the resulting encodings on hospital scheduling data by ASL1 Liguria. Results on some scenarios show that the ASP solutions produce satisfying schedules also when applied to such challenging, real data.1

The ability to efficiently solve hard combinatorial optimization problems is a key prerequisite to various applications of declarative programming paradigms. Symmetries in solution candidates pose a significant challenge to modern optimization algorithms since the enumeration of such candidates might substantially reduce their performance. This paper proposes a novel approach using Inductive Logic Programming (ILP) to lift symmetry-breaking constraints for optimization problems modeled in Answer Set Programming (ASP). Given an ASP encoding with optimization statements and a set of small representative instances, our method augments ground ASP programs with auxiliary normal rules enabling the identification of symmetries using existing tools, like SBASS. Then, the obtained symmetries are lifted to first-order constraints with ILP. We prove the correctness of our method and evaluate it on real-world optimization problems from the domain of automated configuration. Our experiments show significant improvements of optimization performance due to the learned first-order constraints.

Optimizing operations in semiconductor manufacturing facilities is challenging. The production line can be modeled as an NP-hard constrained flexible job-shop scheduling problem, intractable with mathematical optimization due to its scale. Therefore, decision-making in factories is dominated by handcrafted heuristics. Though machine learning-based approaches proved efficient in solving such problems, their applications are limited due to the lack of trust in the underlying black-box models, and issues with scalability for larger instances. This work presents a genetic programming-based method to generate explainable, improved dispatching heuristics. Our method outputs a set of human-readable dispatching strategies, verifiable by scheduling experts before deployment. In case of minor changes in the environment or the optimization objectives, the continued evolution of the candidate solutions is possible without starting the training process from scratch. The introduced method is evaluated on a simulator executing real-world scale instances. The resulting heuristics improve the key performance indicators of the generated schedules. Furthermore, the generated dispatchers are easy to integrate into existing industrial systems. These favorable properties make the method applicable to various large-scale, dynamic, practical scheduling scenarios, where adaptions to different environments go along with modest human effort limited to the design of a fitness function.

Abstract Answer set programming (ASP) emerged in the late 1990s as a paradigm for knowledge representation and reasoning. The attractiveness of ASP builds on an expressive high-level modeling language along with the availability of powerful off-the-shelf solving systems. While the utility of incorporating aggregate expressions in the modeling language has been realized almost simultaneously with the inception of the first ASP solving systems, a general semantics of aggregates and its efficient implementation have been long-standing challenges. Aggregates have been proposed and widely used in database systems, and also in the deductive database language Datalog, which is one of the main precursors of ASP. The use of aggregates was, however, still restricted in Datalog (by either disallowing recursion or only allowing monotone aggregates), while several ways to integrate unrestricted aggregates evolved in the context of ASP. In this survey, we pick up at this point of development by presenting and comparing the main aggregate semantics that have been proposed for propositional ASP programs. We highlight crucial properties such as computational complexity and expressive power, and outline the capabilities and limitations of different approaches by illustrative examples.

Abstract Efficient omission of symmetric solution candidates is essential for combinatorial problem-solving. Most of the existing approaches are instance-specific and focus on the automatic computation of Symmetry Breaking Constraints (SBCs) for each given problem instance. However, the application of such approaches to large-scale instances or advanced problem encodings might be problematic since the computed SBCs are propositional and, therefore, can neither be meaningfully interpreted nor transferred to other instances. As a result, a time-consuming recomputation of SBCs must be done before every invocation of a solver. To overcome these limitations, we introduce a new model-oriented approach for Answer Set Programming that lifts the SBCs of small problem instances into a set of interpretable first-order constraints using the Inductive Logic Programming paradigm. Experiments demonstrate the ability of our framework to learn general constraints from instance-specific SBCs for a collection of combinatorial problems. The obtained results indicate that our approach significantly outperforms a state-of-the-art instance-specific method as well as the direct application of a solver.

Abstract Scheduling methods are important for effective production and logistics management, where tasks need to be allocated and performed with limited resources. In particular, the Job-shop Scheduling Problem (JSP) is a well known and challenging combinatorial optimization problem in which tasks sharing a machine are to be arranged in a sequence such that encompassing jobs can be completed as early as possible. Given that already moderately sized JSP instances can be highly combinatorial, and neither optimal schedules nor the runtime to termination of complete optimization methods is known, efficient approaches to approximate good-quality schedules are of interest. In this paper, we propose problem decomposition into time windows whose operations can be successively scheduled and optimized by means of multi-shot Answer Set Programming (ASP) solving. From a computational perspective, decomposition aims to split highly complex scheduling tasks into better manageable subproblems with a balanced number of operations so that good-quality or even optimal partial solutions can be reliably found in a small fraction of runtime. Regarding the feasibility and quality of solutions, problem decomposition must respect the precedence of operations within their jobs and partial schedules optimized by time windows should yield better global solutions than obtainable in similar runtime on the entire instance. We devise and investigate a variety of decomposition strategies in terms of the number and size of time windows as well as heuristics for choosing their operations. Moreover, we incorporate time window overlapping and compression techniques into the iterative scheduling process to counteract window-wise optimization limitations restricted to partial schedules. Our experiments on JSP benchmark sets of several sizes show that successive optimization by multi-shot ASP solving leads to substantially better schedules within the runtime limit than global optimization on the full problem, where the gap increases with the number of operations to schedule. While the obtained solution quality still remains behind a state-of-the-art Constraint Programming system, our multi-shot solving approach comes closer the larger the instance size, demonstrating good scalability by problem decomposition.

Abstract Many industrial applications require finding solutions to challenging combinatorial problems. Efficient elimination of symmetric solution candidates is one of the key enablers for high-performance solving. However, existing model-based approaches for symmetry breaking are limited to problems for which a set of representative and easily solvable instances is available, which is often not the case in practical applications. This work extends the learning framework and implementation of a model-based approach for Answer Set Programming to overcome these limitations and address challenging problems, such as the Partner Units Problem. In particular, we incorporate a new conflict analysis algorithm in the Inductive Logic Programming system ILASP, redefine the learning task, and suggest a new example generation method to scale up the approach. The experiments conducted for different kinds of Partner Units Problem instances demonstrate the applicability of our approach and the computational benefits due to the first-order constraints learned.

Efficient production scheduling is an important application area of constraint-based optimization techniques. Problem domains like flow- and job-shop scheduling have been extensive study targets, and solving approaches range from complete and local search to machine learning methods. In this paper, we devise and compare constraint-based optimization techniques for scheduling specialized manufacturing processes in the build-to-print business. The goal is to allocate production equipment such that customer orders are completed in time as good as possible, while respecting machine capacities and minimizing extra shifts required to resolve bottlenecks. To this end, we furnish several approaches for scheduling pending production tasks to one or more workdays for performing them. First, we propose a greedy custom algorithm that allows for quickly screening the effects of altering resource demands and availabilities. Moreover, we take advantage of such greedy solutions to parameterize and warm-start the optimization performed by integer linear programming (ILP) and constraint programming (CP) solvers on corresponding problem formulations. Our empirical evaluation is based on production data by Kostwein Holding GmbH, a worldwide supplier in the build-to-print business, and thus demonstrates the industrial applicability of our scheduling methods. We also present a user-friendly web interface for feeding the underlying solvers with customer order and equipment data, graphically displaying computed schedules, and facilitating the investigation of changed resource demands and availabilities, e.g., due to updating orders or including extra shifts.

Efficient omission of symmetric solution candidates is essential for combinatorial problem solving. Most of the existing approaches are instance-specific and focus on the automatic computation of Symmetry Breaking Constraints (SBCs) for each given problem instance. However, the application of such approaches to large-scale instances or advanced problem encodings might be problematic. Moreover, the computed SBCs are propositional and, therefore, can neither be meaningfully interpreted nor transferred to other instances. To overcome these limitations, we introduce a new model-oriented approach for Answer Set Programming that lifts the SBCs of small problem instances into a set of interpretable first-order constraints using the Inductive Logic Programming paradigm. Experiments demonstrate the ability of our framework to learn general constraints from instance-specific SBCs for a collection of combinatorial problems. The obtained results indicate that our approach significantly outperforms a state-of-the-art instance-specific method as well as the direct application of a solver.

Abstract Many knowledge representation tasks involve trees or similar structures as abstract datatypes. However, devising compact and efficient declarative representations of such structural properties is non-obvious and can be challenging indeed. In this article, we take a number of acyclicity properties into consideration and investigate various logic-based approaches to encode them. We use answer set programming as the primary representation language but also consider mappings to related formalisms, such as propositional logic, difference logic and linear programming. We study the compactness of encodings and the resulting computational performance on benchmarks involving acyclic or tree structures.

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 Answer Set Programming (ASP) is a prominent knowledge representation language with roots in logic programming and non-monotonic reasoning. Biennial ASP competitions are organized in order to furnish challenging benchmark collections and assess the advancement of the state of the art in ASP solving. In this paper, we report on the design and results of the Seventh ASP Competition, jointly organized by the University of Calabria (Italy), the University of Genova (Italy), and the University of Potsdam (Germany), in affiliation with the 14th International Conference on Logic Programming and Non-Monotonic Reasoning (LPNMR 2017).

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 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.

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 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.

Answer Set Programming (ASP) is a well-known paradigm of declarative programming with roots in logic programming and non-monotonic reasoning. Similar to other closely related problem-solving technologies, such as SAT/SMT, QBF, Planning and Scheduling, advancements in ASP solving are assessed in competition events. In this paper, we report about the design and results of the Sixth ASP Competition, which was jointly organized by the University of Calabria (Italy), Aalto University (Finland), and the University of Genoa (Italy), in affiliation with the 13th International Conference on Logic Programming and Non-Monotonic Reasoning. This edition maintained some of the design decisions introduced in 2014, e.g., the conception of sub-tracks, the scoring scheme, and the adherence to a fixed modeling language in order to push the adoption of the ASP-Core-2 standard. On the other hand, it featured also some novelties, like a benchmark selection stage classifying instances according to their empirical hardness, and a "Marathon" track where the top-performing systems are given more time for solving hard benchmarks.

Answer Set Programming (ASP) is a declarative programming paradigm with roots in logic programming, knowledge representation, and non-monotonic reasoning. The ASP competition series aims at assessing and promoting the evolution of ASP systems and applications. Its growing range of challenging application-oriented benchmarks inspires and showcases continuous advancements of the state of the art in ASP.

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.

Abstract Aggregation functions are widely used in answer set programming for representing and reasoning on knowledge involving sets of objects collectively. Current implementations simplify the structure of programs in order to optimize the overall performance. In particular, aggregates are rewritten into simpler forms known as monotone aggregates. Since the evaluation of normal programs with monotone aggregates is in general on a lower complexity level than the evaluation of normal programs with arbitrary aggregates, any faithful translation function must introduce disjunction in rule heads in some cases. However, no function of this kind is known. The paper closes this gap by introducing a polynomial, faithful, and modular translation for rewriting common aggregation functions into the simpler form accepted by current solvers. A prototype system allows for experimenting with arbitrary recursive aggregates, which are also supported in the recent version 4.5 of the groundergringo, using the methods presented in this paper.

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.

Answer set programming (ASP) is a declarative programming paradigm for solving search problems arising in knowledge-intensive domains. One viable way to implement the computation of answer sets corresponding to problem solutions is to recast a logic program as a Boolean satisfiability (SAT) problem and to use existing SAT solver technology for the actual search. Such mappings can be obtained by augmenting Clark's completion with constraints guaranteeing the strong justifiability of answer sets. To this end, we consider an extension of SAT by graphs subject to an acyclicity constraint, called SAT modulo acyclicity. We devise a linear embedding of logic programs and study the performance of answer set computation with SAT modulo acyclicity solvers.

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 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 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.

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 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 Using the notion of an elementary loop, Gebser and Schaub (2005. Proceedings of the Eighth International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR'05), 53–65) refined the theorem on loop formulas attributable to Lin and Zhao (2004) by considering loop formulas of elementary loops only. In this paper, we reformulate the definition of an elementary loop, extend it to disjunctive programs, and study several properties of elementary loops, including how maximal elementary loops are related to minimal unfounded sets. The results provide useful insights into the stable model semantics in terms of elementary loops. For a nondisjunctive program, using a graph-theoretic characterization of an elementary loop, we show that the problem of recognizing an elementary loop is tractable. On the other hand, we also show that the corresponding problem is coNP-complete for a disjunctive program. Based on the notion of an elementary loop, we present the class of Head-Elementary-loop-Free (HEF) programs, which strictly generalizes the class of Head-Cycle-Free (HCF) programs attributable to Ben-Eliyahu and Dechter (1994. Annals of Mathematics and Artificial Intelligence 12, 53–87). Like an HCF program, an HEF program can be turned into an equivalent nondisjunctive program in polynomial time by shifting head atoms into the body.

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.

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.