The ASP(Q) language extends Answer Set Programming (ASP) with Quantifiers that operate over answer sets. Thus, ASP(Q) facilitates a more natural encoding of problems whose complexity exceeds NP within the ASP framework. In this paper we focus on ASP(Q) programs with two quantifiers, i.e., 2-ASP(Q) programs, which can be used to model problems in the second level of the Polynomial Hierarchy. In particular, we propose an approach for evaluating 2-ASP(Q) programs that is inspired by Counterexample Guided Abstraction Refinement (CEGAR). Unlike existing state-of-the-art ASP(Q) solvers, which are typically based on QBF solvers, our new approach leverages ASP solvers, and suffers no overhead due to the effects of translating ASP(Q) in QBF. Experimental results demonstrate that our technique consistently outperforms state-of-the-art ASP(Q) solvers, across benchmark problems located at the second level of the polynomial hierarchy.

Linear Temporal Logic on Finite Traces (LTLf) is a popular logic to express declarative specifications in Artificial Intelligence (AI). The recent call for explainable AI tools has made relevant the problem of computing efficiently minimal unsatisfiable cores (MUCs) and minimal correction sets (MCSes) of LTLf formulas. Recent work has focused on the extraction of MUCs on formulas in conjunctive form. In this paper, we present a method that operates on arbitrary formulas and computes a more refined notion of MUCs, as introduced by Schuppan, along with the corresponding notion of MCSes. Experiments show that our system, based on Answer Set Programming, outperforms available tools.

Linear Temporal Logic over finite traces (LTLf) is a widely used formalism with applications in AI, process mining, model checking, and more. The primary reasoning task for LTLf is satisfiability checking; yet, the recent focus on explainable AI has increased interest in analyzing inconsistent formulae, making the enumeration of minimal explanations for unsatisfiability a relevant task also for LTLf. We introduce a novel technique for enumerating minimal unsatisfiable cores (MUCs) of an LTLf specification. The main idea is to encode an LTLf formula into an Answer Set Programming (ASP) specification, such that the minimal unsatisfiable subsets (MUSes) of the ASP program directly correspond to the MUCs of the original LTLf specification. Leveraging recent advancements in ASP solving yields an MUC enumerator achieving good performance in experiments conducted on established benchmarks from the literature.

Answer Set Programming with Quantifiers (ASP(Q)) extends Answer Set Programming (ASP) by allowing quantification over answer sets. Although probabilistic extensions to ASP exist, there is no such counterpart for ASP(Q). In this paper, we close this gap by introducing Inferential Quantified Answer Set Programming (ASP(Q)Inf), an extension of ASP(Q) that supports probabilistic inference over programs with alternating quantifiers, allowing uncertainty at the innermost level. We demonstrate the modeling capabilities of ASP(Q)Inf, analyze its computational complexity, and present an implementation based on Algebraic Model Counting. An experimental evaluation confirms its effectiveness and practical applicability.

Large Language Models (LLMs) have demonstrated impressive capabilities across a wide range of natural language processing tasks, including code generation. While substantial progress has been made in adapting LLMs to generate code for various imperative programming languages, their effectiveness in handling declarative paradigms, such as Answer Set Programming (ASP), remains largely underexplored. This paper takes a step toward bridging that gap by investigating the potential of LLMs for ASP code generation. We begin with a systematic evaluation of several foundational LLMs, moving towards state-of-the-art models. We show that, despite their extensive training, large parameter counts, and significant computational backing, older models exhibit poor performance in generating syntactically and semantically correct ASP programs, while most recent ones mainly achieve impressive results. However, to overcome the need for huge computational power, we introduce LLASP, a fine-tuned, lightweight model specifically trained to encode ASP programs. In this regard, we extensively explore the effectiveness of fine-tuning by curating several dedicated datasets suitable for ASP encoding with increasing levels of complexity. First, we show that LLASP is effective in encoding template-based core problems in ASP; second, that the training strategy can be pushed forward to disregard the need for templating and make the generation prompt-invariant; and lastly, we show that even complex problems can be effectively encoded, beyond core tasks. Experimental results also show that LLASP significantly outperforms both its non-fine-tuned counterparts and most general-purpose LLMs, particularly in terms of semantic correctness, achieving a good trade-off between accuracy and resource-efficiency. Experimental code is publicly available at: https://github.com/EricaCoppolillo/LLASP .

Abstract Inferring linear temporal logic over finite traces ($\text{LTL}_{\text{f}}$) formulas from a set of example traces, known as passive learning, presents significant challenges due to its combinatorial nature. In this paper, we introduce a novel approach to $\text{LTL}_{\text{f}}$ passive learning based on inductive logic programming (ILP), leveraging the inductive learning of answer set programs framework. Our ILP-based method effectively exploits the set of example traces to guide the learning process, and experimental results demonstrate that it o ffers a more efficient solution compared to traditional techniques based on propositional satisfiability.

Maximum-a-Posteriori (MAP) inference is a crucial problem in Artificial Intelligence, which requires both marginalization and maximization, and asks for the most probable value for a given set of variables such that an evidence holds. Several languages within the Statistical Relational Artificial Intelligence landscape support the encoding of MAP. Here, we focus on Probabilistic Answer Set Programming, consider the credal and smProbLog semantics, and introduce a three-level algebraic model counting representation for MAP. We implemented our approach on top of a state-of-the-art solver and compared it with existing solutions, showing the competitive performance of our proposal, even against less general tools.

Most Probable Explanation (MPE) is a fundamental problem in statistical relational artificial intelligence. In the context of Probabilistic Answer Set Programming (PASP), solving MPE is still an open research problem. In this paper, we present three novel approaches for solving the MPE task in PASP that are based on: i) Algebraic Model Counting, ii) Answer Set Programming (ASP), and iii) ASP with quantifiers (ASP(Q)). These approaches are implemented and evaluated against existing solvers across different datasets and configurations. Empirical results demonstrate that the novel solutions consistently outperform existing alternatives for non-stratified programs.

Recent advancements in AI have made LLMs valuable tools for automating the interpretation of textual descriptions of business processes and for converting formal process specifications into natural language. However, there are no practical methodologies or systematic assessments to ensure these automatic translations are faithful. This paper proposes a novel approach, based on an auxiliary bidirectional translation task, to assess LLMs performance quantitatively; also, it also empirically evaluates the performance of state-of-the-art LLMs for bidirectional translations between natural language and declarative formal process specifications. The results reveal substantial variability in performance among the LLMs, highlighting the importance of LLM selection and confirming the need for a robust method for assessing LLMs' outputs.

Probabilistic logic-based languages offer an expressive framework for encoding uncertain information in a human-interpretable way. Among existing formalisms, Probabilistic Answer Set Programming (PASP) stands out for its ease of modeling complex scenarios. The current definition of PASP is limited to programs consisting of disjunctive rules and probabilistic facts only. To enhance the expressivity of the framework, we introduce Optimal Probabilistic Answer Set Programming, which extends the language by allowing the inclusion of weak constraints within PASP specifications. We motivate this extension through some real-world application scenarios and present a detailed computational complexity analysis for both the inference and Most Probable Explanation (MPE) tasks.

Abstract Answer set programming (ASP), a well-known declarative logic programming paradigm, has recently found practical application in Process Mining. In particular, ASP has been used to model tasks involving declarative specifications of business processes. In this area, Declare stands out as the most widely adopted declarative process modeling language, offering a means to model processes through sets of constraints valid traces must satisfy, that can be expressed in linear temporal logic over finite traces (LTL $_{\text {f}}$ ). Existing ASP-based solutions encode Declare constraints by modeling the corresponding LTL $_{\text {f}}$ formula or its equivalent automaton which can be obtained using established techniques. In this paper, we introduce a novel encoding for Declare constraints that directly models their semantics as ASP rules, eliminating the need for intermediate representations. We assess the effectiveness of this novel approach on two Process Mining tasks by comparing it with alternative ASP encodings and a Python library for Declare.

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

Recently, Large Language Models (LLMs) have showcased their potential in various natural language processing tasks, including code generation. However, while significant progress has been made in adapting LLMs to generate code for several imperative programming languages and tasks, there remains a notable gap in their application to declarative formalisms, such as Answer Set Programming (ASP). In this paper, we move a step towards exploring the capabilities of LLMs for ASP code generation. First, we perform a systematic evaluation of several state-of-the-art LLMs. Despite their power in terms of number of parameters, training data and computational resources, empirical results demonstrate inadequate performances in generating correct ASP programs. Therefore, we propose LLASP, a fine-tuned lightweight model specifically trained to encode fundamental ASP program patterns. To this aim, we create an ad-hoc dataset covering a wide variety of fundamental problem specifications that can be encoded in ASP. Our experiments demonstrate that the quality of ASP programs generated by LLASP is remarkable. This holds true not only when compared to the non-fine-tuned counterpart but also when compared to the majority of eager LLM candidates, particularly from a semantic perspective. All the code and data used to perform the experiments are publicly available: https://github.com/EricaCoppolillo/LLASP.

Answer Set Programming (ASP) is a widely recognized formalism for Knowledge Representation and Reasoning. Traditional ASP systems, that employ the ground and solve architecture, are subject to the grounding bottleneck (i.e., variable-elimination can exhaust all computational resources). Compilation-based approaches have recently demonstrated how grounding can be effectively bypassed by compiling rules into propagators that simulate them. However, compiling an entire ASP program is not always advantageous. In this paper, we present both a program rewriting technique and an algorithm for the compilation of grounding that allow for unrestricted blending of grounding and compilation. We implement these techniques in a hybrid ASP system that compares favourably with state-of-the-art ASP solvers on established benchmarks.

Abstract Unit testing frameworks are nowadays considered a best practice, included in almost all modern software development processes, to achieve rapid development of correct specifications. Knowledge representation and reasoning paradigms such as Answer Set Programming (ASP), that have been used in industry-level applications, are not an exception. Indeed, the first unit testing specification language for ASP was proposed in 2011 as a feature of the ASPIDE development environment. Later, a more portable unit testing language was included in the LANA annotation language. In this paper we revisit both languages and tools for unit testing in ASP. We propose a new unit test specification language that allows one to inline tests within ASP programs, and we identify the computational complexity of the tasks associated with checking the various program-correctness assertions. Test-case specifications are transparent to the traditional evaluation, but can be interpreted by a specific testing tool. Thus, we present a novel environment supporting test-driven development of ASP programs.

Abstract Answer Set Programming with Quantifiers (ASP(Q)) has been introduced to provide a natural extension of ASP modeling to problems in the polynomial hierarchy (PH). However, ASP(Q) lacks a method for encoding in an elegant and compact way problems requiring a polynomial number of calls to an oracle in $\Sigma _n^p$ (that is, problems in $\Delta _{n+1}^p$ ). Such problems include, in particular, optimization problems. In this paper, we propose an extension of ASP(Q), in which component programs may contain weak constraints. Weak constraints can be used both for expressing local optimization within quantified component programs and for modeling global optimization criteria. We showcase the modeling capabilities of the new formalism through various application scenarios. Further, we study its computational properties obtaining complexity results and unveiling non-obvious characteristics of ASP(Q) programs with weak constraints.

Answer Set Programming (ASP) is a well-known AI formalism. Traditional ASP systems, that follow the “ground&solve” approach, are intrinsically limited by the so-called grounding bottleneck. Basically, the grounding step (i.e., variable-elimination) can be computationally expensive, and even unfeasible in several cases of practical interest. Recent work demonstrated that the grounding bottleneck can be partially overcome by compiling in external propagators subprograms acting as constraints. In this paper a novel compilation technique is presented that can be applied to tight normal programs; thus, the class of ASP programs that can be compiled is extended beyond constraints. The approach is implemented in the new system PROASP. PROASP skips entirely the grounding phase and performs solving by injecting custom propagators in GLUCOSE. An experiment, conducted on grounding-intensive ASP benchmarks, shows that PROASP is capable of solving instances that are out of reach for state-of-the-art ASP systems.

Process Mining is a family of techniques that exploit data collected from process execution to analyze and improve process efficiency, quality, and security. Over the years, many modeling languages have been proposed for process model specification, with different expressiveness, features, and computational properties. We propose a new logic-based declarative formalism, called Constraint Formulae, to compose process specifications, expressed in heterogeneous process modeling languages, without altering their original semantics. We formalize common process mining tasks for Constraint Formulae, study their computational properties, and provide an implementation in Answer Set Programming.

Answer Set Programming (ASP) is a well-known logic-based formalism that has been used to model and solve a variety of AI problems. For several years, ASP implementations primarily focused on the main computational task: the computation of one answer set of a (logic) program. Nonetheless, several AI problems, that can be conveniently modelled in ASP, require to enumerate solutions characterized by an optimality property that can be expressed in terms of subset-minimality with respect to some objective atoms. In this context, solutions are often either (i) answer sets that are subset-minimal w.r.t. the objective atoms or (ii) atoms that are contained in all subset-minimal answer sets, or (iii) sets of atoms that enforce the absence of answer sets on the ASP program at hand — such sets are referred to as minimal unsatisfiable subsets (MUSes). In all the above-mentioned cases, the corresponding computational task is currently not supported by plain state-of-the-art ASP solvers. In this paper, we study formally these tasks and fill the gap in current implementations by proposing several algorithms to enumerate MUSes and subset-minimal answer sets, as well as perform cautious reasoning on subset-minimal answer sets. We implement our algorithms on top of wasp and perform an experimental analysis on several hard benchmarks showing the good performance of our implementation.

Abstract Artificial Intelligence plays a main role in supporting and improving smart manufacturing and Industry 4.0, by enabling the automation of different types of tasks manually performed by domain experts. In particular, assessing the compliance of a product with the relative schematic is a time-consuming and prone-to-error process. In this paper, we address this problem in a specific industrial scenario. In particular, we define a Neuro-Symbolic approach for automating the compliance verification of the electrical control panels. Our approach is based on the combination of Deep Learning techniques with Answer Set Programming (ASP), and allows for identifying possible anomalies and errors in the final product even when a very limited amount of training data is available. The experiments conducted on a real test case provided by an Italian Company operating in electrical control panel production demonstrate the effectiveness of the proposed approach.

Abstract Answer Set Programming with Quantifiers ASP(Q) extends Answer Set Programming (ASP) to allow for declarative and modular modeling of problems from the entire polynomial hierarchy. The first implementation of ASP(Q), called QASP, was based on a translation to Quantified Boolean Formulae (QBF) with the aim of exploiting the well-developed and mature QBF-solving technology. However, the implementation of the QBF encoding employed in qasp is very general and might produce formulas that are hard to evaluate for existing QBF solvers because of the large number of symbols and subclauses. In this paper, we present a new implementation that builds on the ideas of QASP and features both a more efficient encoding procedure and new optimized encodings of ASP(Q) programs in QBF. The new encodings produce smaller formulas (in terms of the number of quantifiers, variables, and clauses) and result in a more efficient evaluation process. An algorithm selection strategy automatically combines several QBF-solving back-ends to further increase performance. An experimental analysis, conducted on known benchmarks, shows that the new system outperforms QASP.

Answer Set Programming (ASP) is a well-known declarative AI formalism for knowledge representation and reasoning. State-of-the-art ASP implementations employ the ground&solve approach, and they were successfully applied to industrial and academic problems. Nonetheless there are classes of ASP programs whose evaluation is not efficient (sometimes not feasible) due to the combinatorial blow-up of the program produced by the grounding step. Recent researches suggest that compilation-based techniques can mitigate the grounding bottleneck problem. However, no compilation-based technique has been developed for ASP programs that contain aggregates, which are one of the most relevant and commonly-employed constructs of ASP. In this paper, we propose a compilation-based approach for ASP programs with aggregates. We implement it on top of a state-of-the-art ASP system, and evaluate the performance on publicly-available benchmarks. Experiments show our approach is effective on ground-intensive ASP programs.

Answer Set Programming (ASP) is a well-known formalism for Knowledge Representation and Reasoning, successfully employed to solve many AI problems, also thanks to the availability of efficient implementations. Traditionally, ASP systems are based on the ground&solve approach, where the grounding transforms a general input program into its propositional counterpart, whose stable models are then computed by the solver using the CDCL algorithm. This approach suffers an intrinsic limitation: the grounding of one or few constraints may be unaffordable from a computational point of view; a problem known as grounding bottleneck. In this paper, we develop an innovative approach for evaluating ASP programs, where some of the constraints of the input program are not grounded but automatically translated into propagators of the CDCL algorithm that work on partial interpretations. We implemented the new approach on top of the solver WASP and carried out an experimental analysis on different benchmarks. Results show that our approach consistently outperforms state-of-the-art ASP systems by overcoming the grounding bottleneck.

Abstract Answer Set Programming (ASP) is a well-known declarative problem solving paradigm developed in the field of nonmonotonic reasoning and logic programming. The usual target of ASP is the solution of combinatorial search problems, nonetheless the language of ASP was extended with weak constraints for concise modelling of optimization problems. In the case of ASP programs with weak constraints, the main computational task of an ASP solver is optimum stable model search . In this article, we present and compare several algorithms for optimum stable model search. We consider solutions traditionally adopted by ASP solvers, and we introduce new solving strategies obtained by porting to the ASP setting some algorithms that were introduced for Maximum Satisfiability solving. The article also reports on the implementation of these algorithms in the ASP solver wasp . An empirical analysis highlights pros and cons of different strategies for computing optimum stable models.

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.

Answer set programming (ASP) is a successful declarative formalism for knowledge representation and reasoning. The evaluation of ASP programs is nowadays based on the conflict-driven clause learning (CDCL) backtracking search algorithm. Recent work suggested that the performance of CDCL-based implementations can be considerably improved on specific benchmarks by extending their solving capabilities with custom heuristics and propagators. However, embedding such algorithms into existing systems requires expert knowledge of the internals of ASP implementations. The development of effective solver extensions can be made easier by providing suitable programming interfaces. In this paper, we present the interface for extending the CDCL-based ASP solver wasp. The interface is both general, that is, it can be used for providing either new branching heuristics or propagators, and external, that is, the implementation of new algorithms requires no internal modifications of wasp. Moreover, we review the applications of the interface witnessing it can be successfully used to extend wasp for solving effectively hard instances of both real-world and synthetic problems.

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).

Three kinds of submissions were accepted:• Technical papers for technically sound, innovative ideas that can advance the state of logic programming.• Application papers that impact interesting application domains.• System and tool papers which emphasize novelty, practicality, usability, and availability of the systems and tools described.

Abstract Answer Set Programming (ASP) is a well-established formalism for logic programming. Problem solving in ASP requires to write an ASP program whose answers sets correspond to solutions. Albeit the non-existence of answer sets for some ASP programs can be considered as a modeling feature, it turns out to be a weakness in many other cases, and especially for query answering. Paracoherent answer set semantics extend the classical semantics of ASP to draw meaningful conclusions also from incoherent programs, with the result of increasing the range of applications of ASP. State of the art implementations of paracoherent ASP adopt the semi-equilibrium semantics, but cannot be lifted straightforwardly to compute efficiently the (better) split semi-equilibrium semantics that discards undesirable semi-equilibrium models. In this paper an efficient evaluation technique for computing a split semi-equilibrium model is presented. An experiment on hard benchmarks shows that better paracoherent answer sets can be computed consuming less computational resources than existing methods.

Abstract In the last years, abstract argumentation has met with great success in AI, since it has served to capture several non-monotonic logics for AI. Relations between argumentation framework (AF) semantics and logic programming ones are investigating more and more. In particular, great attention has been given to the well-known stable extensions of an AF, that are closely related to the answer sets of a logic program. However, if a framework admits a small incoherent part, no stable extension can be provided. To overcome this shortcoming, two semantics generalizing stable extensions have been studied, namely semi-stable and stage. In this paper, we show that another perspective is possible on incoherent AFs, called paracoherent extensions, as they have a counterpart in paracoherent answer set semantics. We compare this perspective with semi-stable and stage semantics, by showing that computational costs remain unchanged, and moreover an interesting symmetric behaviour is maintained.

Abstract Answer Set Programming (ASP) is a logic programming paradigm featuring a purely declarative language with comparatively high modeling capabilities. Indeed, ASP can model problems in NP in a compact and elegant way. However, modeling problems beyond NP with ASP is known to be complicated, on the one hand, and limited to problems in $\[\Sigma _2^P\]$ on the other. Inspired by the way Quantified Boolean Formulas extend SAT formulas to model problems beyond NP, we propose an extension of ASP that introduces quantifiers over stable models of programs. We name the new language ASP with Quantifiers (ASP(Q)). In the paper we identify computational properties of ASP(Q); we highlight its modeling capabilities by reporting natural encodings of several complex problems with applications in artificial intelligence and number theory; and we compare ASP(Q) with related languages. Arguably, ASP(Q) allows one to model problems in the Polynomial Hierarchy in a direct way, providing an elegant expansion of ASP beyond the class NP.

Abstract Answer Set Programming (ASP) is a well-known declarative formalism in logic programming. Efficient implementations made it possible to apply ASP in many scenarios, ranging from deductive databases applications to the solution of hard combinatorial problems. State-of-the-art ASP systems are based on the traditional ground&solve approach and are general-purpose implementations, i.e., they are essentially built once for any kind of input program. In this paper, we propose an extended architecture for ASP systems, in which parts of the input program are compiled into an ad-hoc evaluation algorithm (i.e., we obtain a specific binary for a given program), and might not be subject to the grounding step. To this end, we identify a condition that allows the compilation of a sub-program, and present the related partial compilation technique. Importantly, we have implemented the new approach on top of a well-known ASP solver and conducted an experimental analysis on publicly-available benchmarks. Results show that our compilation-based approach improves on the state of the art in various scenarios, including cases in which the input program is stratified or the grounding blow-up makes the evaluation unpractical with traditional ASP systems.

Abstract Answer set programming (ASP) is one of the major declarative programming paradigms in the area of logic programming and non-monotonic reasoning. Despite that ASP features a simple syntax and an intuitive semantics, errors are common during the development of ASP programs. In this paper we propose a novel debugging approach allowing for interactive localization of bugs in non-ground programs. The new approach points the user directly to a set of non-ground rules involved in the bug, which might be refined (up to the point in which the bug is easily identified) by asking the programmer a sequence of questions on an expected answer set. The approach has been implemented on top of the ASP solver wasp. The resulting debugger has been complemented by a user-friendly graphical interface, and integrated in aspide, a rich integrated development environment (IDE) for answer set programs. In addition, an empirical analysis shows that the new debugger is not affected by the grounding blowup limiting the application of previous approaches based on meta-programming.

Answer Set Programming (ASP) is a well-established formalism for nonmonotonic reasoning.While incoherence, the non-existence of answer sets for some programs, is an important feature of ASP, it has frequently been criticised and indeed has some disadvantages, especially for query answering.Paracoherent semantics have been suggested as a remedy, which extend the classical notion of answer sets to draw meaningful conclusions also from incoherent programs. In this paper we present an alternative characterization of the two major paracoherent semantics in terms of (extended) externally supported models. This definition uses a transformation of ASP programs that is more parsimonious than the classic epistemic transformation used in recent implementations.A performance comparison carried out on benchmarks from ASP competitions shows that the usage of the new transformation brings about performance improvements that are independent of the underlying algorithms.

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.

Answer Set Programming (ASP) is a well-established formalism for nonmonotonic reasoning. An ASP program can have no answer set due to cyclic default negation. In this case, it is not possible to draw any conclusion, even if this is not intended. Recently, several paracoherent semantics have been proposed that address this issue,and several potential applications for these semantics have been identified. However, paracoherent semantics have essentially been inapplicable in practice, due to the lack of efficient algorithms and implementations. In this paper, this lack is addressed, and several different algorithms to compute semi-stable and semi-equilibrium models are proposed and implemented into an answer set solving framework. An empirical performance comparison among the new algorithms on benchmarks from ASP competitions is given as well.

We propose a model of random quantified boolean formulas and their natural random disjunctive logic program counterparts. The model extends the standard models for random SAT and 2QBF. We provide theoretical bounds for the phase transition region in the new model, and show experimentally the presence of the easy-hard-easy pattern. Importantly, we show that the model is well suited for assessing solvers tuned to real-world instances. Moreover, to the best of our knowledge, our model and results on random disjunctive logic programs are the first of their kind.

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.

Abstract Answer set programming (ASP) is a well-established declarative paradigm. One of the successes of ASP is the availability of efficient systems. State-of-the-art systems are based on the ground+solve approach. In some applications, this approach is infeasible because the grounding of one or a few constraints is expensive. In this paper, we systematically compare alternative strategies to avoid the instantiation of problematic constraints, which are based on custom extensions of the solver. Results on real and synthetic benchmarks highlight some strengths and weaknesses of the different strategies.

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.

Abstract Answer Set Programming (ASP) is a popular logic programming paradigm that has been applied for solving a variety of complex problems. Among the most challenging real-world applications of ASP are two industrial problems defined by Siemens: the Partner Units Problem (PUP) and the Combined Configuration Problem (CCP). The hardest instances of PUP and CCP are out of reach for state-of-the-art ASP solvers. Experiments show that the performance of ASP solvers could be significantly improved by embedding domain-specific heuristics, but a proper effective integration of such criteria in off-the-shelf ASP implementations is not obvious. In this paper the combination of ASP and domain-specific heuristics is studied with the goal of effectively solving real-world problem instances of PUP and CCP. As a byproduct of this activity, the ASP solverwaspwas extended with an interface that eases embedding new external heuristics in the solver. The evaluation shows that our domain-heuristic-driven ASP solver finds solutions for all the real-world instances of PUP and CCP ever provided by Siemens.

Problems arising in several areas of computer science have combinatorial nature. Solving these problems with reasonable performance is often both a challenging and crucial task, because feasible or...

The recent application of Machine Learning techniques to the Answer Set Programming (ASP) field proved to be effective. In particular, the multi-engine ASP solver me-asp is efficient: it is able to solve more instances than any other ASP system that participated to the 3rd ASP Competition on the ‘System Track’ benchmarks. In the me-asp approach, classification methods inductively learn offline algorithm selection policies starting from both a set of features of instances in a training set, and the solvers performance on such instances. In this article we present an improvement to the multi-engine framework of me-asp, in which we add the capability of updating the learned policies when the original approach fails to give good predictions. An experimental analysis, conducted on training and test sets of ground instances obtained from the ones submitted to the ‘System Track’ of the 3rd ASP Competition, shows that the policy adaptation improves the performance of me-asp when applied to test sets containing domains of instances that were not considered for training.

Abstract Consistent query answering over a database that violates primary key constraints is a classical hard problem in database research that has been traditionally dealt with logic programming. However, the applicability of existing logic-based solutions is restricted to data sets of moderate size. This paper presents a novel decomposition and pruning strategy that reduces, in polynomial time, the problem of computing the consistent answer to a conjunctive query over a database subject to primary key constraints to a collection of smaller problems of the same sort that can be solved independently. The new strategy is naturally modeled and implemented using Answer Set Programming (ASP). An experiment run on benchmarks from the database world prove the effectiveness and efficiency of our ASP-based approach also on large data sets.

Abstract Query answering in Answer Set Programming (ASP) is usually solved by computing (a subset of) the cautious consequences of a logic program. This task is computationally very hard, and there are programs for which computing cautious consequences is not viable in reasonable time. However, current ASP solvers produce the (whole) set of cautious consequences only at the end of their computation. This paper reports on strategies for computing cautious consequences, also introducing anytime algorithms able to produce sound answers during the computation.

Abstract Answer Set Programming (ASP) is a well-established paradigm of declarative programming in close relationship with other declarative formalisms such as SAT Modulo Theories, Constraint Handling Rules, FO(.), PDDL and many others. Since its first informal editions, ASP systems have been compared in the now well-established ASP Competition. The Third (Open) ASP Competition, as the sequel to the ASP Competitions Series held at the University of Potsdam in Germany (2006–2007) and at the University of Leuven in Belgium in 2009, took place at the University of Calabria (Italy) in the first half of 2011. Participants competed on a pre-selected collection of benchmark problems, taken from a variety of domains as well as real world applications. The Competition ran on two tracks: the Model and Solve (M&S) Track, based on an open problem encoding, and open language, and open to any kind of system based on a declarative specification paradigm; and the System Track, run on the basis of fixed, public problem encodings, written in a standard ASP language. This paper discusses the format of the competition and the rationale behind it, then reports the results for both tracks. Comparison with the second ASP competition and state-of-the-art solutions for some of the benchmark domains is eventually discussed.

Abstract Answer-set programming (ASP) is a truly declarative programming paradigm proposed in the area of non-monotonic reasoning and logic programming, which has been recently employed in many applications. The development of efficient ASP systems is, thus, crucial. Having in mind the task of improving the solving methods for ASP, there are two usual ways to reach this goal: (i) extending state-of-the-art techniques and ASP solvers or (ii) designing a new ASP solver from scratch. An alternative to these trends is to build on top of state-of-the-art solvers, and to apply machine learning techniques for choosing automatically the “best” available solver on a per-instance basis. In this paper, we pursue this latter direction. We first define a set of cheap-to-compute syntactic features that characterize several aspects of ASP programs. Then, we apply classification methods that, given the features of the instances in atrainingset and the solvers' performance on these instances, inductively learn algorithm selection strategies to be applied to atestset. We report the results of a number of experiments considering solvers and different training and test sets of instances taken from the ones submitted to the “System Track” of the Third ASP Competition. Our analysis shows that by applying machine learning techniques to ASP solving, it is possible to obtain very robust performance: our approach can solve more instances compared with any solver that entered the Third ASP Competition.

Abstract A data integration system provides transparent access to different data sources by suitably combining their data, and providing the user with a unified view of them, called global schema. However, source data are generally not under the control of the data integration process; thus, integrated data may violate global integrity constraints even in the presence of locally consistent data sources. In this scenario, it may be anyway interesting to retrieve as much consistent information as possible. The process of answering user queries under global constraint violations is called consistent query answering (CQA). Several notions of CQA have been proposed, e.g., depending on whether integrated information is assumed to be sound, complete, exact, or a variant of them. This paper provides a contribution in this setting: it uniforms solutions coming from different perspectives under a common Answer-Set Programming (ASP)-based core, and provides query-driven optimizations designed for isolating and eliminating inefficiencies of the general approach for computing consistent answers. Moreover, the paper introduces some new theoretical results enriching existing knowledge on the decidability and complexity of the considered problems. The effectiveness of the approach is evidenced by experimental results.

Abstract Answer-Set Programming (ASP) is a powerful logic-based programming language, which is enjoying increasing interest within the scientific community and (very recently) in industry. The evaluation of Answer-Set Programs is traditionally carried out in two steps. At the first step, an input program undergoes the so-called instantiation (or grounding) process, which produces a program ′ semantically equivalent to , but not containing any variable; in turn, ′ is evaluated by using a backtracking search algorithm in the second step. It is well-known that instantiation is important for the efficiency of the whole evaluation, might become a bottleneck in common situations, is crucial in several real-world applications, and is particularly relevant when huge input data have to be dealt with. At the time of this writing, the available instantiator modules are not able to exploit satisfactorily the latest hardware, featuring multi-core/multi-processor Symmetric MultiProcessing technologies. This paper presents some parallel instantiation techniques, including load-balancing and granularity control heuristics, which allow for the effective exploitation of the processing power offered by modern Symmetric MultiProcessing machines. This is confirmed by an extensive experimental analysis reported herein.

Abstract The seaport of Gioia Tauro is the largest transshipment terminal of the Mediterranean coast. A crucial management task for the companies operating in the seaport is team-building: the problem of properly allocating the available personnel for serving the incoming ships. Teams have to be carefully arranged in order to meet several constraints, such as allocation of employees with appropriate skills, fair distribution of the working load, and turnover of the heavy/dangerous roles. This makes team-building a hard and expensive task requiring several hours of manual preparation per day. In this paper we present a system based on Answer Set Programming for the automatic generation of the teams of employees in the seaport of Gioia Tauro. The system is currently exploited in the Gioia Tauro seaport by ICO BLG, a company specialized in automobile logistics.

The introduction of aggregates has been one of the most relevant language extensions to Answer Set Programming (ASP). Aggregates are very expressive, they allow to represent many problems in a more succinct and elegant way compared to aggregate-free programs. A significant amount of research work has been devoted to aggregates in the ASP community in the last years, and relevant research results on ASP with aggregates have been published, on both theoretical and practical sides. The high expressiveness of aggregates (eliminating aggregates often causes a quadratic blow-up in program size) requires suitable evaluation methods and optimization techniques for an efficient implementation. Nevertheless, in spite of the above-mentioned research developments, aggregates are treated in a quite straightforward way in most ASP systems. In this paper, we explore the exploitation of look-back techniques for an efficient implementation of aggregates. We define a reason calculus for backjumping in ASP programs with aggregates. Furthermore, we describe how these reasons can be used in order to guide look-back heuristics for programs with aggregates. We have implemented both the new reason calculus and the proposed heuristics in the DLV system, and have carried out an experimental analysis on publicly available benchmarks which shows significant performance benefits.

In this paper we present a successful application of logic programming for e-tourism: the iTravel system. The system exploits two technologies that are based on the state-of-the-art computational logic system DLV: (i) a system for ontology representa

Enterprise/Corporate ontologies are widely adopted to conceptualize business enterprise information. In this area, the semantic peculiarities of Answer Set Programming (ASP), like the Closed World Assumption (CWA) and the Unique Name Assumption (UNA), are more appropriate than the OntologyWeb Language (OWL) assumptions, also because such ontologies frequently stem from relational databases, where both CWA and UNA are adopted. This article presents OntoDLV, a system based on ASP for the specification and reasoning on enterprise ontologies. OntoDLV implements a powerful ontology representation language, called OntoDLP, extending (disjunctive) ASP with all the main ontology features including classes, inheritance, relations and axioms. OntoDLP is strongly typed, and includes also complex type constructors, like lists and sets. Importantly, OntoDLV supports a powerful interoperability mechanism with OWL, allowing the user to retrieve information from OWL ontologies, and build rule-based reasoning on top of OWL ontologies. The system is already used in a number of real-world applications including agent-based systems, information extraction, and text classification.