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This note presents a historical survey of informal semantics that are associated with logic programming under answer set semantics. We review these in uniform terms and align them with two paradigms: Answer Set Programming and ASP-Prolog -- two prominent Knowledge Representation and Reasoning Paradigms in Artificial Intelligence. Under consideration in Theory and Practice of Logic Programming (TPLP)., Comment: Under consideration in Theory and Practice of Logic Programming (TPLP)

By introducing the concepts of a loop and a loop formula, Lin and Zhao showed that the answer sets of a nondisjunctive logic program are exactly the models of its Clark's completion that satisfy the loop formulas of all loops. Recently, Gebser and Schaub showed that the Lin-Zhao theorem remains correct even if we restrict loop formulas to a special class of loops called ``elementary loops.'' In this paper, we simplify and generalize the notion of an elementary loop, and clarify its role. We propose the notion of an elementary set, which is almost equivalent to the notion of an elementary loop for nondisjunctive programs, but is simpler, and, unlike elementary loops, can be extended to disjunctive programs without producing unintuitive results. We show that the maximal unfounded elementary sets for the ``relevant'' part of a program are exactly the minimal sets among the nonempty unfounded sets. We also present a graph-theoretic characterization of elementary sets for nondisjunctive programs, which is simpler than the one proposed in (Gebser & Schaub 2005). Unlike the case of nondisjunctive programs, we show that the problem of deciding an elementary set is coNP-complete for disjunctive programs., Comment: 6 pages. AAAI 2006, 244-249. arXiv admin note: substantial text overlap with arXiv:1012.5847

Refactoring is modifying a program without changing its external behavior. In this paper, we make the concept of external behavior precise for a simple answer set programming language. Then we describe a proof assistant for the task of verifying that refactoring a program in that language is performed correctly., Comment: Accepted to Theory and Practice of Logic Programming (ICLP 2023)

Answer set programming is a declarative logic programming paradigm geared towards solving difficult combinatorial search problems. While different logic programs can encode the same problem, their performance may vary significantly. It is not always easy to identify which version of the program performs the best. We present the system Predictor (and its algorithmic backend) for estimating the grounding size of programs, a metric that can influence a performance of a system processing a program. We evaluate the impact of Predictor when used as a guide for rewritings produced by the answer set programming rewriting tools Projector and Lpopt. The results demonstrate potential to this approach., Comment: Under consideration in Theory and Practice of Logic Programming (TPLP)

ICLP is the premier international event for presenting research in logic programming. Contributions to ICLP 2022 were sought in all areas of logic programming, including but not limited to: Foundations: Semantics, Formalisms, Nonmonotonic reasoning, Knowledge representation. Languages issues: Concurrency, Objects, Coordination, Mobility, Higher order, Types, Modes, Assertions, Modules, Meta-programming, Logic-based domain-specific languages, Programming techniques. Programming support: Program analysis, Transformation, Validation, Verification, Debugging, Profiling, Testing, Execution visualization. Implementation: Compilation, Virtual machines, Memory management, Parallel and Distributed execution, Constraint handling rules, Tabling, Foreign interfaces, User interfaces. Related Paradigms and Synergies: Inductive and coinductive logic programming, Constraint logic programming, Answer set programming, Interaction with SAT, SMT and CSP solvers, Theorem proving, Argumentation, Probabilistic programming, Machine learning. Applications: Databases, Big data, Data integration and federation, Software engineering, Natural language processing, Web and semantic web, Agents, Artificial intelligence, Computational life sciences, Cyber-security, Robotics, Education.

Search-optimization problems are plentiful in scientific and engineering domains. Artificial intelligence has long contributed to the development of search algorithms and declarative programming languages geared towards solving and modeling search-optimization problems. Automated reasoning and knowledge representation are the subfields of AI that are particularly vested in these developments. Many popular automated reasoning paradigms provide users with languages supporting optimization statements. Recall integer linear programming, MaxSAT, optimization satisfiability modulo theory, and (constraint) answer set programming. These paradigms vary significantly in their languages in ways they express quality conditions on computed solutions. Here we propose a unifying framework of so called extended weight systems that eliminates syntactic distinctions between paradigms. They allow us to see essential similarities and differences between optimization statements provided by distinct automated reasoning languages. We also study formal properties of the proposed systems that immediately translate into formal properties of paradigms that can be captured within our framework. Under consideration in Theory and Practice of Logic Programming (TPLP)., Comment: Under consideration in Theory and Practice of Logic Programming (TPLP). arXiv admin note: text overlap with arXiv:2206.06440

Search-optimization problems are plentiful in scientific and engineering domains. Artificial intelligence has long contributed to the development of search algorithms and declarative programming languages geared toward solving and modeling search-optimization problems. Automated reasoning and knowledge representation are the subfields of AI that are particularly vested in these developments. Many popular automated reasoning paradigms provide users with languages supporting optimization statements: answer set programming or MaxSAT on minone, to name a few. These paradigms vary significantly in their languages and in the ways they express quality conditions on computed solutions. Here we propose a unifying framework of so-called weight systems that eliminates syntactic distinctions between paradigms and allows us to see essential similarities and differences between optimization statements provided by paradigms. This unifying outlook has significant simplifying and explanatory potential in the studies of optimization and modularity in automated reasoning and knowledge representation. It also supplies researchers with a convenient tool for proving the formal properties of distinct frameworks; bridging these frameworks; and facilitating the development of translational solvers.

Constraint answer set programming or CASP, for short, is a hybrid approach in automated reasoning putting together the advances of distinct research areas such as answer set programming, constraint processing, and satisfiability modulo theories. Constraint answer set programming demonstrates promising results, including the development of a multitude of solvers: acsolver, clingcon, ezcsp, idp, inca, dingo, mingo, aspmt, clingo[l,dl], and ezsmt. It opens new horizons for declarative programming applications such as solving complex train scheduling problems. Systems designed to find solutions to constraint answer set programs can be grouped according to their construction into, what we call, integrational or translational approaches. The focus of this paper is an overview of the key ingredients of the design of constraint answer set solvers drawing distinctions and parallels between integrational and translational approaches. The paper also provides a glimpse at the kind of programs its users develop by utilizing a CASP encoding of Travelling Salesman problem for illustration. In addition, we place the CASP technology on the map among its automated reasoning peers as well as discuss future possibilities for the development of CASP., Comment: Under consideration in Theory and Practice of Logic Programming (TPLP)

In this paper, we study the problem of formal verification for Answer Set Programming (ASP), namely, obtaining a formal proof showing that the answer sets of a given (non-ground) logic program P correctly correspond to the solutions to the problem encoded by P, regardless of the problem instance. To this aim, we use a formal specification language based on ASP modules, so that each module can be proved to capture some informal aspect of the problem in an isolated way. This specification language relies on a novel definition of (possibly nested, first order) program modules that may incorporate local hidden atoms at different levels. Then, verifying the logic program P amounts to prove some kind of equivalence between P and its modular specification. Under consideration for acceptance in TPLP., Comment: Paper presented at the 36th International Conference on Logic Programming (ICLP 2019), University Of Calabria, Rende (CS), Italy, September 2020, 16 pages

In this work we design a narrative understanding tool Text2ALM. This tool uses an action language ALM to perform inferences on complex interactions of events described in narratives. The methodology used to implement the Text2ALM system was originally outlined by Lierler, Inclezan, and Gelfond (2017) via a manual process of converting a narrative to an ALM model. It relies on a conglomeration of resources and techniques from two distinct fields of artificial intelligence, namely, natural language processing and knowledge representation and reasoning. The effectiveness of system Text2ALM is measured by its ability to correctly answer questions from the bAbI tasks published by Facebook Research in 2015. This tool matched or exceeded the performance of state-of-the-art machine learning methods in six of the seven tested tasks. We also illustrate that the Text2ALM approach generalizes to a broader spectrum of narratives., Comment: In Proceedings ICLP 2019, arXiv:1909.07646

Constraint answer set programming integrates answer set programming with constraint processing. System EZSMT+ is a constraint answer set programming tool that utilizes satisfiability modulo theory solvers for search. Its theoretical foundation lies on generalizations of Niemela's characterization of answer sets of a logic program via so called level rankings., Comment: This is an extended abstract submitted to LPNMR-DC 2019

In Knowledge Representation, it is crucial that knowledge engineers have a good understanding of the formal expressions that they write. What formal expressions state intuitively about the domain of discourse is studied in the theory of the informal semantics of a logic. In this paper we study the informal semantics of Answer Set Programming. The roots of answer set programming lie in the language of Extended Logic Programming, which was introduced initially as an epistemic logic for default and autoepistemic reasoning. In 1999, the seminal papers on answer set programming proposed to use this logic for a different purpose, namely, to model and solve search problems. Currently, the language is used primarily in this new role. However, the original epistemic intuitions lose their explanatory relevance in this new context. How answer set programs are connected to the specifications of problems they model is more easily explained in a classical Tarskian semantics, in which models correspond to possible worlds, rather than to belief states of an epistemic agent. In this paper, we develop a new theory of the informal semantics of answer set programming, which is formulated in the Tarskian setting and based on Frege's compositionality principle. It differs substantially from the earlier epistemic theory of informal semantics, providing a different view on the meaning of the connectives in answer set programming and on its relation to other logics, in particular classical logic.

Answer set programming is a prominent declarative programming paradigm used in formulating combinatorial search problems and implementing different knowledge representation formalisms. Frequently, several related and yet substantially different answer set programs exist for a given problem. Sometimes these encodings may display significantly different performance. Uncovering precise formal links between these programs is often important and yet far from trivial. This paper presents formal results carefully relating a number of interesting program rewritings. It also provides the proof of correctness of system Projector concerned with automatic program rewritings for the sake of efficiency. Under consideration in Theory and Practice of Logic Programming (TPLP)., Comment: Under consideration in Theory and Practice of Logic Programming (TPLP)

Constraint answer set programming is a promising research direction that integrates answer set programming with constraint processing. It is often informally related to the field of satisfiability modulo theories. Yet, the exact formal link is obscured as the terminology and concepts used in these two research areas differ. In this paper, we connect these two research areas by uncovering the precise formal relation between them. We believe that this work will booster the cross-fertilization of the theoretical foundations and the existing solving methods in both areas. As a step in this direction we provide a translation from constraint answer set programs with integer linear constraints to satisfiability modulo linear integer arithmetic that paves the way to utilizing modern satisfiability modulo theories solvers for computing answer sets of constraint answer set programs., Comment: Under consideration in Theory and Practice of Logic Programming (TPLP)

Researchers in answer set programming and constraint programming have spent significant efforts in the development of hybrid languages and solving algorithms combining the strengths of these traditionally separate fields. These efforts resulted in a new research area: constraint answer set programming. Constraint answer set programming languages and systems proved to be successful at providing declarative, yet efficient solutions to problems involving hybrid reasoning tasks. One of the main contributions of this paper is the first comprehensive account of the constraint answer set language and solver EZCSP, a mainstream representative of this research area that has been used in various successful applications. We also develop an extension of the transition systems proposed by Nieuwenhuis et al. in 2006 to capture Boolean satisfiability solvers. We use this extension to describe the EZCSP algorithm and prove formal claims about it. The design and algorithmic details behind EZCSP clearly demonstrate that the development of the hybrid systems of this kind is challenging. Many questions arise when one faces various design choices in an attempt to maximize system's benefits. One of the key decisions that a developer of a hybrid solver makes is settling on a particular integration schema within its implementation. Thus, another important contribution of this paper is a thorough case study based on EZCSP, focused on the various integration schemas that it provides. Under consideration in Theory and Practice of Logic Programming (TPLP)., Comment: Under consideration in Theory and Practice of Logic Programming (TPLP)

Modular logic programs provide a way of viewing logic programs as consisting of many independent, meaningful modules. This paper introduces first-order modular logic programs, which can capture the meaning of many answer set programs. We also introduce conservative extensions of such programs. This concept helps to identify strong relationships between modular programs as well as between traditional programs. We show how the notion of a conservative extension can be used to justify the common projection rewriting. This note is under consideration for publication in Theory and Practice of Logic Programming., Comment: Paper presented at the 32nd International Conference on Logic Programming (ICLP 2016), New York City, USA, 16-21 October 2016, 15 pages, LaTeX, 3 PDF figures

Answer set programming is a declarative programming paradigm oriented towards difficult combinatorial search problems. A fundamental task in answer set programming is to compute stable models, i.e., solutions of logic programs. Answer set solvers are the programs that perform this task. The problem of deciding whether a disjunctive program has a stable model is $\Sigma^P_2$-complete. The high complexity of reasoning within disjunctive logic programming is responsible for few solvers capable of dealing with such programs, namely DLV, GnT, Cmodels, CLASP and WASP. In this paper we show that transition systems introduced by Nieuwenhuis, Oliveras, and Tinelli to model and analyze satisfiability solvers can be adapted for disjunctive answer set solvers. Transition systems give a unifying perspective and bring clarity in the description and comparison of solvers. They can be effectively used for analyzing, comparing and proving correctness of search algorithms as well as inspiring new ideas in the design of disjunctive answer set solvers. In this light, we introduce a general template, which accounts for major techniques implemented in disjunctive solvers. We then illustrate how this general template captures solvers DLV, GnT and Cmodels. We also show how this framework provides a convenient tool for designing new solving algorithms by means of combinations of techniques employed in different solvers., Comment: To appear in Theory and Practice of Logic Programming (TPLP)

This volume contains the papers presented at the sixth workshop on Answer Set Programming and Other Computing Paradigms (ASPOCP 2013) held on August 25th, 2013 in Istanbul, co-located with the 29th International Conference on Logic Programming (ICLP 2013). It thus continues a series of previous events co-located with ICLP, aiming at facilitating the discussion about crossing the boundaries of current ASP techniques in theory, solving, and applications, in combination with or inspired by other computing paradigms., Comment: Proceedings of Answer Set Programming and Other Computing Paradigms (ASPOCP 2013), 6th International Workshop, August 25, 2013, Istanbul, Turkey

Integrating diverse formalisms into modular knowledge representation systems offers increased expressivity, modeling convenience and computational benefits. We introduce concepts of abstract modules and abstract modular systems to study general principles behind the design and analysis of model-finding programs, or solvers, for integrated heterogeneous multi-logic systems. We show how abstract modules and abstract modular systems give rise to transition systems, which are a natural and convenient representation of solvers pioneered by the SAT community. We illustrate our approach by showing how it applies to answer set programming and propositional logic, and to multi-logic systems based on these two formalisms., Comment: Proceedings of Answer Set Programming and Other Computing Paradigms (ASPOCP 2013), 6th International Workshop, August 25, 2013, Istanbul, Turkey

This volume contains the papers presented at the fifth workshop on Answer Set Programming and Other Computing Paradigms (ASPOCP 2012) held on September 4th, 2012 in Budapest, co-located with the 28th International Conference on Logic Programming (ICLP 2012). It thus continues a series of previous events co-located with ICLP, aiming at facilitating the discussion about crossing the boundaries of current ASP techniques in theory, solving, and applications, in combination with or inspired by other computing paradigms.

Combinatory categorial grammar (CCG) is a grammar formalism used for natural language parsing. CCG assigns structured lexical categories to words and uses a small set of combinatory rules to combine these categories to parse a sentence. In this work we propose and implement a new approach to CCG parsing that relies on a prominent knowledge representation formalism, answer set programming (ASP) - a declarative programming paradigm. We formulate the task of CCG parsing as a planning problem and use an ASP computational tool to compute solutions that correspond to valid parses. Compared to other approaches, there is no need to implement a specific parsing algorithm using such a declarative method. Our approach aims at producing all semantically distinct parse trees for a given sentence. From this goal, normalization and efficiency issues arise, and we deal with them by combining and extending existing strategies. We have implemented a CCG parsing tool kit - AspCcgTk - that uses ASP as its main computational means. The C&C supertagger can be used as a preprocessor within AspCcgTk, which allows us to achieve wide-coverage natural language parsing., Comment: 12 pages, 2 figures, Proceedings of the 25th Workshop on Logic Programming (WLP 2011)

A fundamental task for propositional logic is to compute models of propositional formulas. Programs developed for this task are called satisfiability solvers. We show that transition systems introduced by Nieuwenhuis, Oliveras, and Tinelli to model and analyze satisfiability solvers can be adapted for solvers developed for two other propositional formalisms: logic programming under the answer-set semantics, and the logic PC(ID). We show that in each case the task of computing models can be seen as "satisfiability modulo answer-set programming," where the goal is to find a model of a theory that also is an answer set of a certain program. The unifying perspective we develop shows, in particular, that solvers CLASP and MINISATID are closely related despite being developed for different formalisms, one for answer-set programming and the latter for the logic PC(ID)., Comment: 30 pages; Accepted for presentation at ICLP 2011 and for publication in Theory and Practice of Logic Programming; contains the appendix with proofs

Nonmonotonic causal logic, introduced by Norman McCain and Hudson Turner, became a basis for the semantics of several expressive action languages. McCain's embedding of definite propositional causal theories into logic programming paved the way to the use of answer set solvers for answering queries about actions described in such languages. In this paper we extend this embedding to nondefinite theories and to first-order causal logic., Comment: 29 pages. To appear in Theory and Practice of Logic Programming (TPLP); Theory and Practice of Logic Programming, May, 2011

Using the notion of an elementary loop, Gebser and Schaub refined the theorem on loop formulas due to Lin and Zhao by considering loop formulas of elementary loops only. In this article, we reformulate their 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 show that the corresponding problem is {\sf 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 due to Ben-Eliyahu and Dechter. 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., Comment: 36 pages, 2 figures

Nieuwenhuis, Oliveras, and Tinelli (2006) showed how to describe enhancements of the Davis-Putnam-Logemann-Loveland algorithm using transition systems, instead of pseudocode. We design a similar framework for several algorithms that generate answer sets for logic programs: Smodels, Smodels-cc, Asp-Sat with Learning (Cmodels), and a newly designed and implemented algorithm Sup. This approach to describing answer set solvers makes it easier to prove their correctness, to compare them, and to design new systems., Comment: Long version of the paper that will appear in special issue of Theory and Practice of Logic Programming