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FOLASP: FO(.) as Input Language for answer set Solvers

THEORY AND PRACTICE OF LOGIC programming 2021年第6期21卷 785-801页

作者： Van Dessel, Kylian Devriendt, Jo Vennekens, Joost Katholieke Univ Leuven Dept Comp Sci De Nayer Campus St Katelijne Waver Belgium Katholieke Univ Leuven Inst AI Leuven AI Leuven Belgium

Technological progress in answer set programming (ASP) has been stimulated by the use of common standards, such as the ASP-Core-2 language. While ASP has its roots in nonmonotonic reasoning, efforts have also been made to reconcile ASP with classical first-order (FO) logic. This has resulted in the development of FO(.), an expressive extension of FO, which allows ASP-like problem solving in a purely classical setting. This language may be more accessible to domain experts already familiar with FO and may be easier to combine with other formalisms that are based on classical logic. It is supported by the IDP inference system, which has successfully competed in a number of ASP competitions. Here, however, technological progress has been hampered by the limited number of systems that are available for FO(.). In this paper, we aim to address this gap by means of a translation tool that transforms an FO(.) specification into ASP-Core-2, thereby allowing ASP-Core-2 solvers to be used as solvers for FO(.) as well. We present experimental results to show that the resulting combination of our translation with an off-the-shelf ASP solver is competitive with the IDP system as a way of solving problems formulated in FO(.).

关键词： declarative programming first order logic answer set programming

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Semi-equilibrium models for paracoherent answer set programs

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ARTIFICIAL INTELLIGENCE 2016年 234卷 219-271页

作者： Amendola, Giovanni Eiter, Thomas Fink, Michael Leone, Nicola Moura, Joao Univ Calabria Dept Math & Comp Sci Via P BucciCubo 30b I-87036 Arcavacata Di Rende CS Italy Vienna Univ Technol Inst Informat Syst Favoritenstr 9-11 A-1040 Vienna Austria Univ Nova Lisboa Dept Informat NOVA LINCS P-2829516 Caparica Portugal

The answer set semantics may assign a logic program to model, due to logical contradiction or unstable negation, which is caused by cyclic dependency of an atom on its negation. While logical contradictions can be handled with traditional techniques from paraconsistent reasoning, instability requires other methods. We consider resorting to a paracoherent semantics, in which 3-valued interpretations are used where a third truth value besides true and false expresses that an atom is believed true. This is at the basis of the semi-stable model semantics, which was defined using a program transformation. In this paper, we give a model-theoretic characterization of semi-stable models, which makes the semantics more accessible. Motivated by some anomalies of semi-stable model semantics with respect to basic epistemic properties, we propose an amendment that satisfies these properties. The latter has both a transformational and a model-theoretic characterization that reveals it as a relaxation of equilibrium logic, the logical reconstruction of answer set semantics, and is thus called the semi-equilibrium model semantics. We consider refinements of this semantics to respect modularity in the rules, based on splitting sets, the major tool for modularity in modeling and evaluating answer set programs. In that, we single out classes of canonical models that are amenable for customary bottom-up evaluation of answer set programs, with an option to switch to a paracoherent mode when lack of an answer set is detected. A complexity analysis of major reasoning tasks shows that semi-equilibrium models are harder than answer sets (i.e., equilibrium models), due to a global minimization step for keeping the gap between true and believed true atoms as small as possible. Our results contribute to the logical foundations of paracoherent answer set programming, which gains increasing importance in inconsistency management, and at the same time provide a basis for algorithm development and

关键词： answer set programming Equilibrium logic Paracoherent reasoning Splitting sequences Inconsistency management

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Unfolding partiality and disjunctions in stable model semantics

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ACM TRANSACTIONS ON COMPUTATIONAL LOGIC 2006年第1期7卷 1-37页

作者： Janhunen, Tomi Niemela, Ilkka Seipel, Dietmar Simons, Patrik You, Jia-Huai Aalto Univ FI-02015 Helsinki Finland Univ Wurzburg D-97074 Wurzburg Germany Neotide Oy FI-65200 Vaasa Finland Univ Alberta Edmonton AB T6G 2H1 Canada

This article studies an implementation methodology for partial and disjunctive stable models where partiality and disjunctions are unfolded from a logic program so that an implementation of stable models for normal (disjunction-free) programs can be used as the core inference engine. The unfolding is done in two separate steps. First, it is shown that partial stable models can be captured by total stable models using a simple linear and modular program transformation. Hence, reasoning tasks concerning partial stable models can be solved using an implementation of total stable models. Disjunctive partial stable models have been lacking implementations which now become available as the translation handles also the disjunctive case. Second, it is shown how total stable models of disjunctive programs can be determined by computing stable models for normal programs. Thus an implementation of stable models of normal programs can be used as a core engine for implementing disjunctive programs. The feasibility of the approach is demonstrated by constructing a system for computing stable models of disjunctive programs using the SMODELS system as the core engine. The performance of the resulting system is compared to that of DLV, which is a state-of-the-art system for disjunctive programs.

关键词： algorithms performance theory answer set programming disjunctive stable models partial models inference engine minimal models quantified Boolean formulas

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Preferred answer sets for ordered logic programs

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THEORY AND PRACTICE OF LOGIC programming 2006年第1-2期6卷 107-167页

作者： Van Nieuwenborgh, D Vermeir, D Vrije Univ Brussel Dept Comp Sci B-1050 Brussels Belgium

We extend answer set semantics to deal with inconsistent programs (containing classical negation), by finding a "best" answer set. Within the context of inconsistent programs, it is natural to have a partial order on rules, representing a preference for satisfying certain rules, possibly at the cost of violating less important ones. We show that such a rule order induces a natural order on extended answer sets, the minimal elements of which we call preferred answer sets. We characterize the expressiveness of the resulting semantics and show that it can simulate negation as failure, disjunction and some other formalisms such as logic programs with ordered disjunction. The approach is shown to be useful in several application areas, e.g. repairing database, where minimal repairs correspond to preferred answer sets.

关键词： nonmonotonic reasoning knowledge representation answer set programming preference

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ASSAT: computing answer sets of a logic program by SAT solvers

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ARTIFICIAL INTELLIGENCE 2004年第1-2期157卷 115-137页

作者： Lin, FZ Zhao, YT Hong Kong Univ Sci & Technol Dept Comp Sci Kowloon Hong Kong Peoples R China

We propose a new translation from normal logic programs with constraints under the answer set semantics to propositional logic. Given a normal logic program, we show that by adding, for each loop in the program, a corresponding loop formula to the program's completion, we obtain a one-to-one correspondence between the answer sets of the program and the models of the resulting propositional theory. In the worst case, there may be an exponential number of loops in a logic program. To address this problem, we propose an approach that adds loop formulas a few at a time, selectively. Based on these results, we implement a system called ASSAT(X), depending on the SAT solver X used, for computing one answer set of a normal logic program with constraints. We test the system on a variety of benchmarks including the graph coloring, the blocks world planning, and Hamiltonian Circuit domains. Our experimental results show that in these domains, for the task of generating one answer set of a normal logic program, our system has a clear edge over the state-of-art answer set programming systems Smodels and DLU. (C) 2004 Elsevier B.V. All rights reserved.

关键词： answer set programming answer set semantics stable model semantics logic programming SAT SAT solvers

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Action-Centered Information Retrieval

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THEORY AND PRACTICE OF LOGIC programming 2020年第2期20卷 249-272页

作者： Balduccini, Marcello Leblanc, Emily C. St Josephs Univ Philadelphia PA 19131 USA Drexel Univ Philadelphia PA 19104 USA

Information retrieval (IR) aims at retrieving documents that are most relevant to a query provided by a user. Traditional techniques rely mostly on syntactic methods. In some cases, however, links at a deeper semantic level must be considered. In this paper, we explore a type of IR task in which documents describe sequences of events, and queries are about the state of the world after such events. In this context, successfully matching documents and query requires considering the events' possibly implicit uncertain effects and side effects. We begin by analyzing the problem, then propose an action language-based formalization, and finally automate the corresponding IR task using answer set programming.

关键词： reasoning about actions and change answer set programming information retrieval

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Look-back Techniques for ASP Programs with Aggregates

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FUNDAMENTA INFORMATICAE 2011年第4期107卷 379-413页

作者： Faber, Wolfgang Maratea, Marco Leone, Nicola Ricca, Francesco Univ Calabria Dept Math I-87036 Arcavacata Di Rende CS Italy Univ Genoa DIST Genoa Italy

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.

关键词： Knowledge Representation and Reasoning Nonmonotonic Reasoning answer set programming Heuristics Aggregates

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Capturing (Optimal) Relaxed Plans with Stable and Supported Models of Logic Programs

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THEORY AND PRACTICE OF LOGIC programming 2023年第4期23卷 782-796页

作者： Rankooh, Masood Feyzbakhsh Janhunen, Tomi Tampere Univ Tampere Finland

We establish a novel relation between delete-free planning, an important task for the AI planning community also known as relaxed planning, and logic programming. We show that given a planning problem, all subsets of actions that could be ordered to produce relaxed plans for the problem can be bijectively captured with stable models of a logic program describing the corresponding relaxed planning problem. We also consider the supported model semantics of logic programs, and introduce one causal and one diagnostic encoding of the relaxed planning problem as logic programs, both capturing relaxed plans with their supported models. Our experimental results show that these new encodings can provide major performance gain when computing optimal relaxed plans, with our diagnostic encoding outperforming state-of-the-art approaches to relaxed planning regardless of the given time limit when measured on a wide collection of STRIPS planning benchmarks.

关键词： planning heuristics answer set programming optimal delete-free planning supported models acyclicity constraint dependency graph vertex elimination

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First-Order Logic with Inductive Definitions for Model-Based Problem Solving

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AI MAGAZINE 2016年第3期37卷 69-80页

作者： Bruynooghe, Maurice Denecker, Marc Truszczynski, Mirosiaw Katholieke Univ Leuven Dept Comp Sci Leuven Belgium Declarat Languages & Artificial Intelligence Res Leuven Belgium Katholieke Univ Leuven Comp Sci Leuven Belgium Res Grp Knowledge Representat & Reasoning Leuven Belgium Univ Kentucky Comp Sci Lexington KY 40506 USA

In answer set programming (ASP), programs can be viewed as specifications of finite Herbrand structures. Other logics can be (and, in fact, were) used toward the same end and can be taken as the basis of declarative programming systems of similar functionality as ASP. We discuss here one such logic, the logic FO(ID), and its implementation IDP3. The choice is motivated by notable similarities between ASP and FO(ID), even if both approaches trace back to different origins.

关键词： Declarative programming Problem Solving Stable model semantics answer set programming First-order logic

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ASP-Core-2 Input Language Format

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THEORY AND PRACTICE OF LOGIC programming 2020年第2期20卷 294-309页

作者： Calimeri, Francesco Faber, Wolfgang Gebser, Martin Ianni, Giovambattista Kaminski, Roland Krennwallner, Thomas Leone, Nicola Maratea, Marco Ricca, Francesco Schaub, Torsten Univ Calabria DeMaCS Arcavacata Di Rende Italy Alpen Adria Univ Inst Angew Informat Klagenfurt Austria Univ Potsdam Inst Comp Sci Potsdam Germany XIMES GmbH Vienna Austria Univ Genoa DIBRIS Genoa Italy

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 theASP-CORE-2standard input language for answer set programming, which has been adopted in ASP Competition events since 2013.

关键词： answer set programming standard language knowledge representation and reasoning standardization

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