A new fixpoint semantics for general logic programs compared with the well-founded and the stable model semantics

Large logic programs are normally designed by teams of individuals, each of whom designs a subprogram. While each of these subprograms may have consistent completions, the logic program obtained by taking the union of these subprograms may not. However, the resulting program still serves a useful purpose, for a (possibly) very large subset of it still has a consistent completion. We argue that “small” inconsistencies may cause a logic program to have no models (in the traditional sense), even though it still serves some useful purpose. A semantics is developed in this paper for general logic programs which ascribes a very reasonable meaning to general logic programs irrespective of whether they have consistent (in the classical logic sense) completions.

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Query Answering with Guarded Existential Rules under Stable Model Semantics

Proceedings of the AAAI Conference on Artificial Intelligence ◽

10.1609/aaai.v34i03.5695 ◽

2020 ◽

Vol 34 (03) ◽

pp. 3017-3024

Author(s):

Hai Wan ◽

Guohui Xiao ◽

Chenglin Wang ◽

Xianqiao Liu ◽

Junhong Chen ◽

...

Keyword(s):

Answer Set Programming ◽

Query Answering ◽

Prototype System ◽

Stable Model ◽

Logic Programs ◽

Termination Problem ◽

Answer Set

In this paper, we study the problem of query answering with guarded existential rules (also called GNTGDs) under stable model semantics. Our goal is to use existing answer set programming (ASP) solvers. However, ASP solvers handle only finitely-ground logic programs while the program translated from GNTGDs by Skolemization is not in general. To address this challenge, we introduce two novel notions of (1) guarded instantiation forest to describe the instantiation of GNTGDs and (2) prime block to characterize the repeated infinitely-ground program translated from GNTGDs. Using these notions, we prove that the ground termination problem for GNTGDs is decidable. We also devise an algorithm for query answering with GNTGDs using ASP solvers. We have implemented our approach in a prototype system. The evaluation over a set of benchmarks shows encouraging results.

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Uniform Equivalence of Logic Programs under the Stable Model Semantics

Logic Programming - Lecture Notes in Computer Science ◽

10.1007/978-3-540-24599-5_16 ◽

2003 ◽

pp. 224-238 ◽

Cited By ~ 40

Author(s):

Thomas Eiter ◽

Michael Fink

Keyword(s):

Stable Model ◽

Logic Programs

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Negation as Failure Using Tight Derivations for General Logic Programs

Foundations of Deductive Databases and Logic Programming ◽

10.1016/b978-0-934613-40-8.50007-5 ◽

1988 ◽

pp. 149-176 ◽

Cited By ~ 59

Author(s):

Allen Van Gelder

Keyword(s):

Logic Programs ◽

Negation As Failure ◽

General Logic

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A decidable subclass of finitary programs

Theory and Practice of Logic Programming ◽

10.1017/s1471068410000232 ◽

2010 ◽

Vol 10 (4-6) ◽

pp. 481-496 ◽

Cited By ~ 8

Author(s):

SABRINA BASELICE ◽

PIERO A. BONATTI

Keyword(s):

Problem Solving ◽

Answer Set Programming ◽

Stable Model ◽

Unique Combination ◽

Logic Programs ◽

Trade Off ◽

Full Support ◽

Odd Cycles ◽

Answer Set

AbstractAnswer set programming—the most popular problem solving paradigm based on logic programs—has been recently extended to support uninterpreted function symbols (Syrjänen 2001, Bonatti 2004; Simkus and Eiter 2007; Gebseret al. 2007; Baseliceet al. 2009; Calimeriet al. 2008). All of these approaches have some limitation. In this paper we propose a class of programs called FP2 that enjoys a different trade-off between expressiveness and complexity. FP2 is inspired by the extension of finitary normal programs with local variables introduced in (Bonatti 2004, Section 5). FP2 programs enjoy the following unique combination of properties: (i) the ability of expressing predicates with infinite extensions; (ii) full support for predicates with arbitrary arity; (iii) decidability of FP2 membership checking; (iv) decidability of skeptical and credulous stable model reasoning for call-safe queries. Odd cycles are supported by composing FP2 programs with argument restricted programs.

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Interdefinability of defeasible logic and logic programming under the well-founded semantics

Theory and Practice of Logic Programming ◽

10.1017/s147106841100041x ◽

2011 ◽

Vol 13 (1) ◽

pp. 107-142 ◽

Cited By ~ 1

Author(s):

FREDERICK MAIER

Keyword(s):

Logic Programming ◽

Opposite Direction ◽

Stable Model ◽

Logic Programs ◽

Defeasible Logic ◽

Normal Logic

AbstractWe provide a method of translating theories of Nute's defeasible logic into logic programs, and a corresponding translation in the opposite direction. Under certain natural restrictions, the conclusions of defeasible theories under the ambiguity propagating defeasible logic ADL correspond to those of the well-founded semantics for normal logic programs, and so it turns out that the two formalisms are closely related. Using the same translation of logic programs into defeasible theories, the semantics for the ambiguity blocking defeasible logic NDL can be seen as indirectly providing an ambiguity blocking semantics for logic programs. We also provide antimonotone operators for both ADL and NDL, each based on the Gelfond–Lifschitz (GL) operator for logic programs. For defeasible theories without defeaters or priorities on rules, the operator for ADL corresponds to the GL operator and so can be seen as partially capturing the consequences according to ADL. Similarly, the operator for NDL captures the consequences according to NDL, though in this case no restrictions on theories apply. Both operators can be used to define stable model semantics for defeasible theories.

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