Physical Sciences and Mathematics Commons^™

What Is Answer Set Programming To Propositional Satisfiability, Yuliya Lierler

Yuliya Lierler

Constraint Cnf: A Sat And Csp Language Under One Roof, Broes De Cat, Yuliya Lierler

Yuliya Lierler

Performance Tuning In Answer Set Programming, Matt Buddenhagen, Yuliya Lierler

Yuliya Lierler

Constraint Answer Set Programming Versus Satisfiability Modulo Theories Or Constraints Versus Theories, Yuliya Lierler, Benjamin Susman

Yuliya Lierler

Abstract Disjunctive Answer Set Solvers, Remi Brochenin, Yuliya Lierler, Marco Maratea

Yuliya Lierler

A fundamental task in answer set programming is to compute answer sets of logic programs. Answer set solvers are the programs that perform this task. The problem of deciding whether a disjunctive program has an answer set isΣP2 -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 and CLASP. 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. In particular, we present transition systems for CMODELS (without backjumping …

Asp-Based Problem Solving With Cutting-Edge Tools, Marcello Balduccini, Yuliya Lierler

Yuliya Lierler

In the development of practical applications of answer set programming (ASP), encodings that use well-established solvers such as CLASP and DLV are sometimes affected by scalability issues. In those situations, one can resort to more sophisticated ASP tools exploiting, for instance, incremental and constraint ASP. However, today there is no specific methodology for the selection or use of such tools. In this paper we describe how we used such cutting-edge ASP tools on challenging problems from the Third Answer Set Programming Competition, and outline the methodology we followed. We view this paper as a first step in the development of …

Representing Synonymity In Causal Logic And In Logic Programming, Joohyung Lee, Yuliya Lierler, Vladimir Lifschitz, Fangkai Yang

Yuliya Lierler

We investigate the relationship between rules representing synonymity in nonmonotonic causal logic and in answer set programming. This question is of interest in connection with current work on modular languages for describing actions.

A Sat-Based Polynomial Space Algorithm For Answer Set Programming, Enrico Giunchiglia, Marco Maratea, Yuliya Lierler

Yuliya Lierler

The relation between answer set programming (ASP) and propositional satisfiability (SAT) is at the center of many research papers, partly because of the tremendous performance boost of SAT solvers during last years. Various translations from ASP to SAT are known but the resulting SAT formula either includes many new variables or may have an unpractical size. There are also well known results showing a one-to-one correspondence between the answer sets of a logic program and the models of its completion. Unfortunately, these results only work for specific classes of problems. In this paper we present a SAT-Based decision procedure for …

Fages' Theorem And Answer Set Programming, Yuliya Lierler, Esta Erdem, Vladimir Lifschitz

Yuliya Lierler

We generalize a theorem by François Fages that describes the relationship between the completion semantics and the answer set semantics for logic programs with negotiation as failure. The study of this relationship is important in connection with the emergence of answer set programming. Whenever the two semantics are equivalent, answer sets can be computed by a satisfiability solver, and the use of answer set solvers such as SMODELS and DLV is unnecessary. A logic programming representation of the blocks world due to Ilkka Niemelä is discussed as an example.

Answer Set Programming Based On Propositional Satisfiability, Enrico Giunchiglia, Yuliya Lierler, Marco Maratea

Yuliya Lierler

Answer set programming (ASP) emerged in the late 1990s as a new logic programming paradigm that has been successfully applied in various application domains. Also motivated by the availability of efficient solvers for propositional satisfiability (SAT), various reductions from logic programs to SAT were introduced. All these reductions, however, are limited to a subclass of logic programs or introduce new variables or may produce exponentially bigger propositional formulas. In this paper, we present a SAT-based procedure, called ASPSAT, that (1) deals with any (nondisjunctive) logic program, (2) works on a propositional formula without additional variables (except for those possibly introduced …

Abstract Answer Set Solvers, Yuliya Lierler

Yuliya Lierler

Nieuwenhuis, Oliveras, and Tinelli showed how to describe enhancements of the Davis-Putnam-Logemann-Loveland algorithm using transition systems, instead of pseudocode. We design a similar framework for three algorithms that generate answer sets for logic programs: SMODELS, ASP-SAT with Backtracking, 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.

Cmodels For Tight Disjunctive Logic Programs, Yuliya Lierler

Yuliya Lierler

Disjunctive logic programming under the stable model semantics [GL91] is a new answer set programming (ASP) methodology for solving combinatorial search problems. It is a form of declarative programming related to logic programming languages, such as Prolog, where the solutions to a problem are represented by answer sets, and not by answer substitutions produced in response to a query as in convential logic programming. Instead of Prolog systems, this programming method uses answer set solvers, such as smodels1, smodelscc2, cmodels3, dlv4, and gnt1. These systems made it possible for ASP to be successfully applied in such areas as planning, bounded …

Practical And Methodological Aspects Of The Use Of Cutting-Edge Asp Tools, Marcello Balduccini, Yuliya Lierler

Yuliya Lierler

In the development of practical applications of answer set programming (ASP), encodings that use well-established solvers such as CLASP and DLV are sometimes affected by scalability issues. In those situations, one can resort to more sophisticated ASP tools exploiting, for instance, incremental and constraint ASP. However, today there is no specific methodology for the selection or use of such tools. In this paper we describe how we used such cutting-edge ASP tools on challenging problems from the Third Answer Set Programming Competition. We view this paper as a first step in the development of a general methodology for the use …

Experiments With Sat-Based Answer Set Programming, Enrico Giunchiglia, Yuliya Lierler, Marco Maratea, A. Tacchella

Yuliya Lierler

Answer Set Programming (ASP) emerged in the late 1990s as a new logic programming paradigm which has been successfully applied in various application domains. Propositional satisfiability (SAT) is one of the most studied problems in Computer Science. ASP and SAT are closely related: Recent works have studied their relation, and efficient SAT-based ASP solvers (like assat and Cmodels) exist. In this paper we report about (i) the extension of the basic procedures in Cmodels in order to incorporate the most popular SAT reasoning strategies, and (ii) an extensive comparative analysis involving also other state-of-the-art answer set solvers. The experimental analysis …

Cmodels – Sat-Based Disjunctive Answer Set Solver, Yuliya Lierler

Yuliya Lierler

Disjunctive logic programming under the stable model semantics [GL91] is a new methodology called answer set programming (ASP) for solving combinatorial search problems. This programming method uses answer set solvers, such as DLV [Lea05], GNT [Jea05], SMODELS [SS05], ASSAT [LZ02], CMODELS [Lie05a]. Systems DLV and GNT are more general as they work with the class of disjunctive logic programs, while other systems cover only normal programs. DLV is uniquely designed to find the answer sets for disjunctive logic programs. On the other hand, GNT first generates possible stable model candidates and then tests the candidate on the minimality using system …

Sat-Based Answer Set Programming, Yuliya Lierler

Yuliya Lierler

Answer set programming (ASP) is a declarative programming paradigm oriented towards difficult combinatorial search problems. Syntactically, ASP programs look like Prolog programs, but solutions are represented in ASP by sets of atoms, and not by substitutions, as in Prolog. Answer set systems, such as SMODELS, SMODELSCC, and DLV, compute answer sets of a given program in the sense of the answer set (stable model) semantics. This is different from the functionality of Prolog systems, which determine when a given query is true relative to a given logic program. ASP has been applied to many areas of science and technology, from …

Computing Answer Sets Of A Logic Program Via-Enumeration Of Sat Certificates, Yuliya Lierler, Marco Maratea

Yuliya Lierler

Answer set programming is a new programming paradigm proposed based on the answer set semantics of Prolog. It is well known that an answer set for a logic program is also a model of the program's completion. The converse is true when the logic program is "tight". Lin and Zhao showed that for non-tight programs the models of completion which do not correspond to answer sets can be eliminated by adding to the completion what they called "loop formulas". Nevertheless, their solver ASSAT 1 has some disadvantages: it can work only with basic rules, and it can compute only one …

Cmodels: Sat-Based Answer Set Programming System, Yuliya Lierler, Marco Maratea

Yuliya Lierler

CMODELS [1, 2] is an answer set programming [3] system that uses the same frontend LPARSE as answer set solver SMODELS (http://www.tcs.hut.fi/Software/smodels/). CMODELS main computational characteristics is that it computes answer sets using a SAT solver for search. The use of SAT solvers for generating answer sets is based on the fact that for logic programs satisfying syntactic condition, tightness, the answer set semantics is equivalent to the Clark’s completion semantics. In addition, [4] introduced concept of a loop formula, and demonstrated that the answer sets of a logic program are exactly the models of its completion that satisfy the …

Abstract Answer Set Solvers With Backjumping And Learning, Yuliya Lierler

Yuliya Lierler

Nieuwenhuis et al. (2006. Solving SAT and SAT modulo theories: From an abstract Davis-Putnam-Logemann-Loveland procedure to DPLL(T). Journal of the ACM 53(6), 937977 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 describe answer set solvers makes it easier to prove their correctness, to compare them, and to design new systems.

Cmodels-2: Sat-Based Answer Set Solver Enhanced To Non-Tight Programs, Yuliya Lierler, Marco Maratea

Yuliya Lierler

Answer set programming is a new programming paradigm proposed in [1] and [2], and based on the answer set semantics of Prolog [3]. It is well known that an answer set for a logic program is also a model of the program’s completion [4]. The converse is true when the logic program is “tight” [6, 5]. Lin and Zhao [7] showed that for non-tight programs the models of completion which do not correspond to answer sets can be eliminated by adding to the completion what they called “loop formulas”. Nevertheless, their solver ASSAT1 has some disadvantages: it can work only …

On Elementary Loops Of Logic Programs, Martin Gerber, Joohyung Lee, Yuliya Lierler

Yuliya Lierler

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 …

Representing First-Order Causal Theories By Logic Programs, Paolo Ferrarris, Joohyung Lee, Yuliya Lierler, Vladimir Lifschitz, Fangkai Yang

Yuliya Lierler

Nonmonotonic causal logic, introduced by McCain and Turner (McCain, N. and Turner, H. 1997. Causal theories of action and change. In Proceedings of National Conference on Artificial Intelligence (AAAI), Stanford, CA, 460–465) became the 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 the first-order causal logic.

Sat-Based Answer Set Programming, Enrico Giunchiglia, Yuliya Lierler, Marco Maratea

Yuliya Lierler

The relation between answer set programming (ASP) and propositional satisfiability (SAT) is at the center of many research papers, partly because of the tremendous performance boost of SAT solvers during last years. Various translations from ASP to SAT are known but the resulting SAT formula either includes many new variables or may have an unpractical size. There are also well known results showing a one-to-one correspondence between the answer sets of a logic program and the models of its completion. Unfortunately, these results only work for specific classes of problems. In this paper we present a SAT-based decision procedure for …

Disjunctive Answer Set Programming Via Satisfiability, Yuliya Lierler

Yuliya Lierler

Using SAT solvers as inference engines in answer set programming systems showed to be a promising approach in building efficient systems. Nowadays SAT based answer set programming systems successfully work with nondisjunctive programs. This paper proposes a way to use SAT solvers for finding answer sets for disjunctive logic programs. We implement two different ways of SAT solver invocation used in nondisjunctive answer set programming. The algorithms are based on the definition of completion for disjunctive programs and the extension of loop formula to the disjunctive case. We propose the necessary modifications to the algorithms known for nondisjunctive programs in …

Transition Systems For Model Generators — A Unifying Approach, Yuliya Lierler, Miroslaw Truszczyński

Yuliya Lierler

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 answerset 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. …

Elementary Sets For Logic Programs, Martin Gebser, Joohyung Lee, Yuliya Lierler

Yuliya Lierler

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 …

A Tarskian Informal Semantics For Answer Set Programming, Marc Denecker, Yuliya Lierler, Miroslaw Truszczyński, Joost Vennekens

Yuliya Lierler

In their seminal papers on stable model semantics, Gelfond and Lifschitz introduced ASP by casting programs as epistemic theories, in which rules represent statements about the knowledge of a rational agent. To the best of our knowledge, theirs is still the only published systematic account of the intuitive meaning of rules and programs under the stable semantics. In current ASP practice, however, we find numerous applications in which rational agents no longer seem to play any role. Therefore, we propose here an alternative explanation of the intuitive meaning of ASP programs, in which they are not viewed as statements about …

Head-Elementary-Set-Free Logic Programs, Martin Gebser, Joohyung Lee, Yuliya Lierler

Yuliya Lierler

The recently proposed notion of an elementary set yielded a refinement of the theorem on loop formulas, telling us that the stable models of a disjunctive logic program can be characterized by the loop formulas of its elementary sets. Based on the notion of an elementary set, we propose the notion of head-elementary-set-free (HEF) programs, a more general class of disjunctive programs than head-cycle-free (HCF) programs proposed by Ben-Eiiyahu and Dechter. that can still be turned into nondisjunct:ive programs in polynomial time and space by "shifting" the head atoms into the body. We show several properties of HEF programs that …

Termination Of Grounding Is Not Preserved By Strongly Equivalent Transformations, Yuliya Lierler, Vladimir Lifschitz

Yuliya Lierler

The operation of a typical answer set solver begins with grounding—replacing the given program with a program without variables that has the same answer sets. When the given program contains function symbols, the process of grounding may not terminate. In this note we give an example of a pair of consistent, strongly equivalent programs such that one of them can be grounded by LPARSE, DLV, and gringo, and the other cannot.

One More Decidable Class Of Finitely Ground Programs, Yuliya Lierler, Vladimir Lifschitz

Yuliya Lierler

When a logic program is processed by an answer set solver, the first task is to generate its instantiation. In a recent paper, Calimeri et el. made the idea of efficient instantiation precise for the case of disjunctive programs with function symbols, and introduced the class of “finitely ground” programs that can be efficiently instantiated. Since that class is undecidable, it is important to find its large decidable subsets. In this paper, we introduce such a subset—the class of argumentrestricted programs. It includes, in particular, all finite domain programs, ω-restricted programs, and λ-restricted programs.