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Semantics of structured normal logic programs

JOURNAL OF logic AND ALGEBRAIC PROGRAMMING 2012年第5期81卷 559-584页

作者： Pasarella, Edelmira Orejas, Fernando Pino, Elvira Navarro, Marisa Univ Politecn Cataluna Dept LSI ES-08034 Barcelona Spain Univ Basque Country Dept LSI San Sebastian 20080 Spain

In this paper we provide semantics for normal logic programs enriched with structuring mechanisms and scoping rules. Specifically, we consider constructive negation and expressions of the form Q D G in goals, where Q is a program unit. G is a goal and D stands for the so-called embedded implication. Allowing the use of these expressions can be seen as adding block structuring to logic programs. In this context, we consider static and dynamic rules for visibility in blocks. In particular, we provide new semantic definitions for the class of normal logic programs with both visibility rules. For the dynamic case we follow a standard approach. We first propose an operational semantics. Then, we define a model-theoretic semantics in terms of ordered structures which are a kind of intuitionistic Beth structures. Finally, an (effective) fixpoint semantics is provided and we prove the equivalence of these three definitions. In order to deal with the static case, we first define an operational semantics and then we present an alternative semantics in terms of a transformation of the given structured programs into flat ones. We finish by showing that this transformation preserves the computed answers of the given static program. (C) 2012 Elsevier Inc. All rights reserved.

关键词： Semantics normal logic programs Embedded implication Visibility rules Structuring mechanism Intuitionistic structures

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On the Equivalence Between Abstract Dialectical Frameworks and logic programs

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THEORY AND PRACTICE OF logic PROGRAMMING 2019年第5-6期19卷 941-956页

作者： Alcantara, Joao Sa, Samy Acosta-Guadarrama, Juan Univ Fed Ceara Fortaleza Ceara Brazil Autonomous Univ Juarez Ciudad Juarez Mexico

A Abstract Dialectical Frameworks (ADFs) are argumentation frameworks where each node is associated with an acceptance condition. This allows us to model different types of dependencies as supports and attacks. Previous studies provided a translation from normal logic programs (NLPs) to ADFs and proved the stable models semantics for a normal logic program has an equivalent semantics to that of the corresponding ADF. However, these studies failed in identifying a semantics for ADFs equivalent to a three-valued semantics (as partial stable models and well-founded models) for NLPs. In this work, we focus on a fragment of ADFs, called Attacking Dialectical Frameworks (ADF(+) s), and provide a translation from NLPs to ADF(+) s robust enough to guarantee the equivalence between partial stable models, well-founded models, regular models, stable models semantics for NLPs and respectively complete models, grounded models, preferred models, stable models for ADFs. In addition, we define a new semantics for ADF(+) s, called L-stable, and show it is equivalent to the L-stable semantics for NLPs.

关键词： Abstract Dialectical Frameworks normal logic programs Argumentation Instantiations of Argumentation Frameworks

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Computing Loops with at Most One External Support Rule

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ACM TRANSACTIONS ON COMPUTATIONAL logic 2013年第1期14卷 3-3页

作者： Chen, Xiaoping Ji, Jianmin Lin, Fangzhen Univ Sci & Technol China Sch Comp Sci & Technol Hefei 230026 Anhui Peoples R China Hong Kong Univ Sci & Technol Dept Comp Sci & Engn Kowloon Hong Kong Peoples R China

A consequence of a logic program under answer set semantics is one that is true for all answer sets. This article considers using loop formulas to compute some of these consequences in order to increase the efficiency of answer set solvers. Since computing loop formulas are in general intractable, we consider only loops with either no external support or at most one external support, as their loop formulas are either unit or binary clauses. We show that for disjunctive logic programs, loop formulas of loops with no external support can be computed in polynomial time, and that an iterative procedure using unit propagation on these formulas and the program completion computes the well-founded models in the case of normal logic programs and the least fixed point of a simplification operator used by DLV for disjunctive logic programs. For loops with at most one external support, their loop formulas can be computed in polynomial time for normal logic programs, but are NP-hard for disjunctive programs. So for normal logic programs, we have a procedure similar to the iterative one for loops without any external support, but for disjunctive logic programs, we present a polynomial approximation algorithm. All these algorithms have been implemented, and our experiments show that for certain logic programs, the consequences computed by our algorithms can significantly speed up current ASP solvers cmodels, clasp, and DLV.

关键词： Algorithms Experimentation Answer set semantics normal logic programs disjunctive logic programs loop formulas well-founded semantics answer set solvers

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Extending the Grounded Semantics by logic Programming Semantics

Extending the Grounded Semantics by Logic Programming Semant...

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14th International Conference of the Catalan-Association-for-Artificial-Intelligence (CCIA)

作者： Carlos Nieves, Juan Osorio, Mauricio Cortes, Ulises Univ Politecn Cataluna Software Dept LSI C Jordi Girona 1-3 E-08034 Barcelona Spain Fundac Univ Amer Puebla Mexico

ISBN: (纸本)9781607508427;9781607508410

We introduce a formal argumentation method based on normal programs and rewriting systems which is able to define extensions of the grounded semantics based on specific rewriting rules which perform particular kind of reasoning as in reasoning by cases. These new argumentation semantics are intermediate argumentation semantics between the grounded and the preferred semantics.

关键词： Argumentation Theory normal logic programs Rewriting Systems

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Well-Founded Semantics for Description logic programs in the Semantic Web

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ACM TRANSACTIONS ON COMPUTATIONAL logic 2011年第2期12卷 11-11页

作者： Eiter, Thomas Ianni, Giovambattista Lukasiewicz, Thomas Schindlauer, Roman Vienna Univ Technol Inst Informat Syst A-1040 Vienna Austria Univ Calabria Dip Matemat I-87036 Arcavacata Di Rende Italy Univ Oxford Oxford OX1 2JD England

The realization of the Semantic Web vision, in which computational logic has a prominent role, has stimulated a lot of research on combining rules and ontologies, which are formulated in different formalisms. In particular, combining logic programming with the Web Ontology Language ( OWL), which is a standard based on description logics, emerged as an important issue for linking the Rules and Ontology Layers of the Semantic Web. Nonmonotonic description logic programs (dl-programs) were introduced for such a combination, in which a pair (L, P) of a description logic knowledge base L and a set of rules P with negation as failure is given a model-based semantics that generalizes the answer set semantics of logic programs. In this article, we reconsider dl-programs and present a well-founded semantics for them as an analog for the other main semantics of logic programs. It generalizes the canonical definition of the well-founded semantics based on unfounded sets, and, as we show, lifts many of the well-known properties from ordinary logic programs to dl-programs. Among these properties, our semantics amounts to a partial model approximating the answer set semantics, which yields for positive and stratified dl-programs, a total model coinciding with the answer set semantics;it has polynomial data complexity provided the access to the description logic knowledge base is polynomial;under suitable restrictions, it has lower complexity and even first-order rewritability is achievable. The results add to previous evidence that dl-programs are a versatile and robust combination approach, which moreover is implementable using legacy engines.

关键词： Theory Languages Answer set semantics description logic programs description logics normal logic programs semantic Web well-founded semantic

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A Novel Combination of Answer Set Programming with Description logics for the Semantic Web

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IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING 2010年第11期22卷 1577-1592页

作者： Lukasiewicz, Thomas Univ Oxford Comp Lab Oxford OX1 3QD England Vienna Univ Technol Inst Informat Syst A-1040 Vienna Austria

We present a novel combination of disjunctive programs under the answer set semantics with description logics for the Semantic Web. The combination is based on a well-balanced interface between disjunctive programs and description logics, which guarantees the decidability of the resulting formalism without assuming syntactic restrictions. We show that the new formalism has very nice semantic properties. In particular, it faithfully extends both disjunctive programs and description logics. Furthermore, we describe algorithms for reasoning in the new formalism, and we give a precise picture of its computational complexity. We also define the well-founded semantics for the normal case, where normal programs are combined with tractable description logics, and we explore its semantic and computational properties. In particular, we show that the well-founded semantics approximates the answer set semantics. We also describe algorithms for the problems of consistency checking and literal entailment under the well-founded semantics, and we give a precise picture of their computational complexity. As a crucial property, in the normal case, consistency checking and literal entailment under the well-founded semantics are both tractable in the data complexity, and even first-order rewritable (and thus can be done in LOGSPACE in the data complexity) in a special case that is especially useful for representing mappings between ontologies.

关键词： Description logic programs disjunctive logic programs normal logic programs answer set semantics well-founded semantics description logics Semantic Web algorithms complexity first-order rewritability

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TIGHT SEMANTICS FOR logic programs

TIGHT SEMANTICS FOR LOGIC PROGRAMS

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26th International Conference on logic Programming (ICLP)

作者： Pereira, Luis Moniz Pinto, Alexandre Miguel Univ Nova Lisboa Ctr Inteligencia Artificial CENTRIA Dept Informat Fac Ciencias & Tecnol P-2829516 Caparica Portugal

ISBN: (纸本)9783939897170

We define the Tight Semantics (TS), a new semantics for all NLPs complying with the requirements of: 2-valued semantics;preserving the models of SM;guarantee of model existence, even in face of Odd Loops Over Negation (OLONs) or infinite chains;relevance;cumulativity;and compliance with the Well-Founded Model. When complete models are unnecessary, and top-down querying (a la Prolog) is desired, TS provides the 2-valued option that guarantees model existence, as a result of its relevance property. Top-down querying with abduction by need is rendered available too by TS. The user need not pay the price of computing whole models, nor that of generating all possible abductions, only to filter irrelevant ones subsequently. A TS model of a NLP P is any minimal model (MM) M of P that further satisfies (P) over cap the program remainder of P - in that each loop in (P) over cap has a MM contained in M, whilst respecting the constraints imposed by the MMs of the other loops so-constrained too. The applications afforded by TS are all those of Stable Models, which it generalizes, plus those permitting to solve OLONs for model existence, plus those employing OLONs for productively obtaining problem solutions, not just filtering them (like Integrity Constraints).

关键词： normal logic programs Relevance Cumulat vity Stable Models Well-Founded Semantics Program Remainder

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BEYOND TAMAKI-SATO STYLE UNFOLD/FOLD TRANSFORMATIONS FOR normal logic programs

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International Journal of Foundations of Computer Science 2002年第3期13卷 387-403页

作者： ABHIK ROYCHOUDHURY K. NARAYAN KUMAR C. R. RAMAKRISHNAN I. V. RAMAKRISHNAN Department of Computer Science School of Computing National University of Singapore S16 Level 5 3 Science Drive 2 Singapore 117543 Singapore Chennai Mathematical Institute 92 G.N. Chetty Road Chennai India Department of Computer Science State University of New York at Stony Brook Stony Brook NY 11794 USA

Unfold/fold transformation systems for logic programs have been extensively investigated. Existing unfold/fold transformation systems for normal logic programs typically fold using a single, non-recursive clause i.e. the folding transformation is very restricted. In this paper we present a transformation system that permits folding in the presence of recursion, disjunction, as well as negation. We show that the transformations are correct with respect to various model theoretic semantics of normal logic programs including the well-founded model and stable model semantics.

关键词： logic Programming Program Transformations Unfold/Fold Transformations normal logic programs

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An algebraic framework for the definition of compositional semantics of normal logic programs

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JOURNAL OF logic PROGRAMMING 1999年第1期40卷 89-123页

作者： Lucio, P Orejas, F Pino, E Univ Politecn Cataluna Dept LSI Barcelona 08034 Spain

The aim of our work is the definition of compositional semantics for modular units over the class of normal logic programs. In this sense, we propose a declarative semantics for normal logic programs in terms of model classes that is monotonic in the sense that Mod(P boolean OR P') subset of or equal to Mod(P), for any programs P and P', and we show that in the model class associated to every program there is a least model that can be seen as the semantics of the program, which may be built upwards as the least fix point of a continuous immediate consequence operator. In addition, it is proved that this least model is "typical" for the class of models of Clark-Kunen's completion of the program. This means that our semantics is equivalent to Clark-Kunen's completion. Moreover, following the approach defined in a previous paper, it is shown that our semantics constitutes a "specification frame" equipped with the adequate categorical constructions needed to define compositional and fully abstract (categorical) semantics for a number of program units. In particular, we provide a categorical semantics of arbitrary normal logic program fragments which is compositional and fully abstract with respect to the (standard) union. (C) 1999 Elsevier Science Inc. All rights reserved.

关键词： normal logic programs model-theoretic semantics compositionality institutions monotonic semantics constructive negation modular logic programs

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AN EXTENDED PETRI-NET MODEL FOR normal logic programs

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IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING 1995年第1期7卷 150-162页

作者： SHIMURA, T LOBO, J MURATA, T UNIV ILLINOIS DEPT ELECT ENGN & COMP SCICHICAGOIL 60680

This paper presents an application of the concepts of siphons (deadlocks) and inhibitor arcs in Petri net theory to logic programs with negations. More specifically, an extended Petri net is used to model function-free normal logic programs. In this model, because of the presence of inhibitor arcs, the arbitrary applications of firing rule may cause a contradictory situation. We suggest two directions to avoid contradictions: greedy and secure applications of firing rule. We choose the secure application in this paper and show that this is a direct translation of the well-founded semantics in the net model. Furthermore, we show that the greatest unfounded set corresponds to the greatest siphon in Petri net theory when we delete the transitions disabled by the secure application of firing rule, and that the property of siphon simplifies the computation of well-founded semantics for logic programs. We also propose the reduced-Petri-net method by which we can reduce an extended Petri net to a Petri net without inhibitor arcs and compute the well-founded model by iterative applications of this transformation using conventional application of firing rule.

关键词： logic PROGRAMMING INHIBITOR ARCS NEGATIONS normal logic programs PETRI NETS SIPHONS (DEADLOCKS) WELLFOUNDED SEMANTICS

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