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24th International Conference on Logic programming (ICLP)

作者： Fink, Michael Vienna Univ Technol Inst Informat Syst A-1040 Vienna Austria

ISBN: (纸本)9783540899815

In answer-set programming different notions of equivalence, Such as the prominent notions of strong and uniform equivalence, have been studied and characterized by various selections of models in the logic of Here-and-There (HT). For uniform equivalence however, Correct characterizations in terms of HT-models can only be obtained for finite theories, respectively programs. In this paper, we show that a selection of countermodels in HT captures uniform equivalence also for infinite theories. This result is turned into coherent characterizations of the different notions of equivalence by countermodels, as well as by a mixture of HT-models and countermodels (so-called equivalence interpretations), which are lifted to first-order theories Under a very general semantics given in terms of a quantified version of HT. We show that countermodels exhibit expedient properties like I simplified treatment of extended signatures, and provide further results for non-ground logic programs. In particular, uniform equivalence coincides under open and ordinary answer-set semantics, and for finite non-ground programs Under these semantics, also the usual characterization of uniform equivalence in terms of maximal and total HT-models of the grounding is correct, even for infinite domains, when corresponding ground programs are infinite.

关键词： answer-set programming uniform equivalence knowledge representation program optimization

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A general framework for equivalences in answer-set programming by countermodels in the logic of Here-and-There

A general framework for equivalences in Answer-Set Programmi...

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24th International Conference on Logic programming (ICLP)

作者： Fink, Michael Vienna Univ Technol Inst Informat Syst A-1040 Vienna Austria

Different notions of equivalence, such as the prominent notions of strong and uniform equivalence, have been studied in answer-set programming, mainly for the purpose of identifying programs that can serve as substitutes without altering the semantics, for instance in program optimization. Such semantic comparisons are usually characterized by various selections of models in the logic of Here-and- There (HT). For uniform equivalence however, correct characterizations in terms of HT-models can only be obtained for finite theories, respectively programs. In this paper, we show that a selection of countermodels in HT captures uniform equivalence also for infinite theories. This result is turned into coherent characterizations of the different notions of equivalence by countermodels, as well as by a mixture of HT-models and countermodels (so-called equivalence interpretations). Moreover, we generalize the so-called notion of relativized hyperequivalence for programs to propositional theories, and apply the same methodology in order to obtain a semantic characterization which is amenable to infinite settings. This allows for a lifting of the results to first-order theories under a very general semantics given in terms of a quantified version of HT. We thus obtain a general framework for the study of various notions of equivalence for theories under answer-set semantics. Moreover, we prove an expedient property that allows for a simplified treatment of extended signatures, and provide further results for non-ground logic programs. In particular, uniform equivalence coincides under open and ordinary answer-set semantics, and for finite non-ground programs under these semantics, also the usual characterization of uniform equivalence in terms of maximal and total HT-models of the grounding is correct, even for infinite domains, when corresponding ground programs are infinite.

关键词： answer-set programming Uniform equivalence Relativized equivalence Knowledge representation

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Model-based recasting in answer-set programming

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Journal of Applied Non-Classical Logics 2013年第1-2期23卷 75-104页

As is well known, answer-set programs do not satisfy the replacement property in general, i.e., programsandthat are equivalent may cease to be so when they are put in the context of some other program, i.e.,andmay have different (sets of) answer sets. Lifschitz, Pearce, and Valverde (2001Lifschitz,V,Pearce,DandValverde,*** equivalent logic *** Transactions on Computational Logic, 2:526–541.[Crossref],[Google Scholar]) thus introducedstrong equivalencefor context-independent equivalence, and proved that such equivalence holds between given programsandiffandare equivalent theories in the monotoniclogic of here-and-there. In this article, we consider a related question: given a program,does there exist some programfrom a certain classof programs such thatandare equivalent under a given notion of equivalence? Furthermore, if the answer to this question is positive, how can we recastas an equivalent program from(i.e., construct such a)? In particular, we consider classes of programs that emerge by (dis)allowing disjunction and/or negation, and as equivalence notions we consider strong, uniform, and ordinary equivalence. Based on general model-theoretic properties and a novel form of canonical programs, we develop semantic characterisations for the existence of such a program, determine the computational complexity of checking existence, and provide (local) rewriting rules for recasting.

关键词： answer-set programming logic of here-and-there strong equivalence uniform equivalence

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Resource Allocation with answer-set programming 09

Resource Allocation with Answer-Set Programming

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International Conference on Autonomous Agents and Multiagent Systems

作者： Joao Leite Jose Alferes Belopeta Mito Universidade Nova de Lisboa

ISBN: (纸本)9781615673346

Multi-agent resource allocation is a growing area of research at the frontier between Economics and Computer Science. Despite the extensive theoretical work and raising number of practical applications, many fundamental problems in multi-agent resource allocation still require adequate attention to its computational aspects. This paper addresses computational aspects of multi-agent resource allocation through the use of a fully declarative and highly expressive logic programming paradigm - answer set programming - to provide uniform, general and flexible solutions to many multi-agent resource allocation problems in a compact and declarative manner.

关键词： Algorithms Economics Resource Allocation answer-set programming Preference Representation Resource utilization management of resources economics algorithms programming computer science

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A Generalisation of Epistemic Splitting Property 17th

A Generalisation of Epistemic Splitting Property

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17th International Conference on Logic programming and Non-monotonic Reasoning

作者： Su, Ezgi Iraz Sinop Univ Dept Comp Engn Sinop Turkiye Univ Milano Bicocca Milan Italy

ISBN: (纸本)9783031742088;9783031742095

answer-set programming (ASP) is a declarative logic programming paradigm that provides an efficient problem-solving approach in logic-based artificial intelligence (AI). While it has proven successful, ASP encounters specific situations where its language falls short of accurately representing and reasoning about incomplete information. Researchers now widely agree that ASP requires powerful introspective reasoning with the use of epistemic modal operators;yet, despite long-lasting debates on how to extend ASP with such operators, they cannot reach a consensus on satisfactory semantics. Cabalar et al. argue that such research should be grounded in formal robustness. Thus, inspired by ASP's foundational properties, they introduce a structural principle called epistemic splitting and designate it as one of the compulsory criteria for epistemic ASP. This paper generalises their approach to a more comprehensive, meticulous, and conservative extension of ASP-splitting, thereby enhancing its applicability and efficiency.

关键词： answer-set programming Equilibrium logic Epistemic logic programs Epistemic splitting property Subjective constraint monotonicity

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Relativized hyperequivalence of logic programs for modular programming

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THEORY AND PRACTICE OF LOGIC programming 2009年第6期9卷 781-819页

作者： Truszczynski, Miroslaw Woltran, Stefan Univ Kentucky Dept Comp Sci Lexington KY 40506 USA Vienna Univ Technol Inst Informat Syst 184 2 A-1040 Vienna Austria

A recent framework of relativized hyperequivalence of programs offers a unifying generalization of strong and uniform equivalence. It seems to be especially well suited for applications in program optimization and modular programming due to its flexibility that allows us to restrict, independently of each other, the head and body alphabets in context programs. We study relativized hyperequivalence for the three semantics of logic programs given by stable, supported, and supported minimal models. For each semantics, we identify four types of contexts, depending on whether the head and body alphabets are given directly or as the complement of a given set. Hyperequivalence relative to contexts where the head and body alphabets are specified directly has been studied before. In this paper, we establish the complexity of deciding relativized hyperequivalence with respect to the three other types of context programs.

关键词： answer-set programming strong equivalence uniform equivalence relativized equivalence stable models supported models minimal models complexity

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Stage semantics and the SCC-recursive schema for argumentation semantics

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JOURNAL OF LOGIC AND COMPUTATION 2016年第4期26卷 1149-1202页

作者： Dvorak, Wolfgang Gaggl, Sarah Alice Univ Vienna Fac Comp Sci Vienna Austria Tech Univ Dresden Inst Artificial Intelligence Computat Log Grp Dresden Germany

Recently, stage and cf2 semantics for abstract argumentation attracted specific attention. By distancing from the notion of defence, they are capable to select arguments out of odd-length cycles. In case of cf2 semantics, the SCC-recursive schema guarantees that important evaluation criteria for argumentation semantics, like directionality, weak- and reinstatement, are fulfilled. Beside several desirable properties, both stage and cf2 semantics still have some drawbacks. The stage semantics does not satisfy the above mentioned evaluation criteria, whereas cf2 semantics produces some questionable results on frameworks with cycles of length a parts per thousand yen 6. Therefore, we suggest to combine stage semantics with the SCC-recursive schema of cf2 semantics. The resulting stage2 semantics overcomes the problems regarding cf2 and stage semantics. We study properties of stage2 semantics and its relations to existing semantics, show that it fulfills the mentioned evaluation criteria, study strong equivalence for stage2 semantics and provide a comprehensive complexity analysis of the associated reasoning problems. Besides the analysis of stage2 semantics, we also complement existing complexity results for cf2 by an analysis of tractable fragments and fixed parameter tractability. Furthermore, we provide answer-set programming (ASP) encodings for stage2 semantics and labelling-based algorithms for cf2 and stage2 semantics.

关键词： Abstract argumentation cf2 semantics stage2 semantics odd-length cycles computational complexity strong equivalence answer-set programming labellings

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Beyond Uniform Equivalence between answer-set Programs

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ACM TRANSACTIONS ON COMPUTATIONAL LOGIC 2021年第1期22卷 1–46页

作者： Oetsch, Johannes Seidl, Martina Tompits, Hans Woltran, Stefan Bosch Ctr Artificial Intelligence Robert Bosch Campus 1 D-71272 Berlin Germany Tech Univ Wien Inst Log & Computat Favoritenstr 9-11 A-1040 Vienna Austria Johannes Kepler Univ Linz Inst Formal Models & Verificat Altenbergerstr 69 A-4040 Linz Austria

This article deals with advanced notions of equivalence between nonmonotonic logic programs under the answer-set semantics, a topic of considerable interest, because such notions form the basis for program verification and are useful for program optimisation, debugging, and modular programming. In fact, there is extensive research in answer-set programming (ASP) dealing with different notions of equivalence between programs. Prominent among these notions is uniform equivalence, which checks whether two programs have the same semantics when joined with an arbitrary set of facts. In this article, we study a family of more fine-grained versions of uniform equivalence, viz. relativised uniform equivalence with projection, which extends standard uniform equivalence in terms of two additional parameters: one for specifying the input alphabet and one for specifying the output alphabet for programs. In particular, the second parameter is used for projecting answer sets to a set of designated output atoms. answer-set projection, in particular, allows to compare programs that make use of different auxiliary atoms, which is important for practical programming aspects. We introduce novel semantic characterisations for the program correspondence problems under consideration and analyse their computational complexity. In the general case, deciding these problems lies on the third level of the polynomial hierarchy. Therefore, this task cannot be efficiently reduced to propositional answer-set programs itself (under the usual complexity-theoretic assumptions). However, reductions to quantified Boolean formulas (QBFs) are feasible. Indeed, we provide efficient (in fact, linear-time constructible) reductions to QBFs and discuss simplifications for certain special cases. These QBF reductions yield the basis for a prototype implementation, the system ccT, for deciding correspondence problems by using off-the-shelf QBF solvers. We discuss an application of cc T for verifying the correct

关键词： answer-set programming disjunctive logic programs nonmonotonic reasoning program equivalence quantified Boolean logic

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A Brief History of Updates of answer-set Programs

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THEORY AND PRACTICE OF LOGIC programming 2023年第1期23卷 57-110页

作者： Leite, Joao Slota, Martin Univ Nova Lisboa Fac Ciencias & Tecnol NOVA LINCS Dept Informat Lisbon Portugal

Over the last couple of decades, there has been a considerable effort devoted to the problem of updating logic programs under the stable model semantics (a.k.a. answer-set programs) or, in other words, the problem of characterising the result of bringing up-to-date a logic program when the world it describes changes. Whereas the state-of-the-art approaches are guided by the same basic intuitions and aspirations as belief updates in the context of classical logic, they build upon fundamentally different principles and methods, which have prevented a unifying framework that could embrace both belief and rule updates. In this paper, we will overview some of the main approaches and results related to answer-set programming updates, while pointing out some of the main challenges that research in this topic has faced.

关键词： belief update belief change logic programming answer-set programming

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Declarative Approaches to Counterfactual Explanations for Classification

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THEORY AND PRACTICE OF LOGIC programming 2023年第3期23卷 559-593页

作者： Bertossi, Leopoldo Univ Adolfo Ibanez Fac Engn & Sci Santiago Chile Millennium Inst Fdn Res Data IMFD Santiago Chile

We propose answer-set programs that specify and compute counterfactual interventions on entities that are input on a classification model. In relation to the outcome of the model, the resulting counterfactual entities serve as a basis for the definition and computation of causality-based explanation scores for the feature values in the entity under classification, namely responsibility scores. The approach and the programs can be applied with black-box models, and also with models that can be specified as logic programs, such as rule-based classifiers. The main focus of this study is on the specification and computation of best counterfactual entities, that is, those that lead to maximum responsibility scores. From them one can read off the explanations as maximum responsibility feature values in the original entity. We also extend the programs to bring into the picture semantic or domain knowledge. We show how the approach could be extended by means of probabilistic methods, and how the underlying probability distributions could be modified through the use of constraints. Several examples of programs written in the syntax of the DLV ASP-solver, and run with it, are shown.

关键词： classification explanations counterfactuals causality answer-set programming constraints

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