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

1991 ◽  
Vol 9 (3-4) ◽  
pp. 425-443 ◽  
Author(s):  
François Fages
Keyword(s):  
Stable Model ◽  
Logic Programs ◽  
General Logic ◽  
Fixpoint Semantics

ON THE PARALLEL COMPLEXITY OF ACYCLIC LOGIC PROGRAMS

1996 ◽  
Vol 06 (02) ◽  
pp. 223-230
Author(s):  
SHIVA CHAUDHURI ◽  
YANNIS DIMOPOULOS ◽  
CHRISTOS D. ZAROLIAGIS
Keyword(s):  
Related Problem ◽  
Directed Acyclic Graph ◽  
Stable Model ◽  
Logic Programs ◽  
Parallel Complexity ◽  
Acyclic Graph ◽  
General Logic

In this paper we investigate the parallel complexity of computing the stable model of acyclic general logic programs. Within this class of logic programs, we consider the cases of negative and definite logic programs. Both cases are proved to be [Formula: see text]-complete. We prove the same for a related problem, namely that of computing the kernel of a directed acyclic graph.

Y-Logic: A Framework for Reasoning About Chameleonic Programs with Inconsistent Completions

1990 ◽  
Vol 13 (4) ◽  
pp. 465-483
Author(s):  
V.S. Subrahmanian
Keyword(s):  
Classical Logic ◽  
Logic Program ◽  
Logic Programs ◽  
Large Subset ◽  
General Logic ◽  
Traditional Sense

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.

scholarly journals Query Answering with Guarded Existential Rules under Stable Model Semantics

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.

scholarly journals A decidable subclass of finitary programs

2010 ◽  
Vol 10 (4-6) ◽  
pp. 481-496 ◽  
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.

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

2011 ◽  
Vol 13 (1) ◽  
pp. 107-142 ◽  
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.

scholarly journals Unfolding and fixpoint semantics of concurrent constraint logic programs

1992 ◽  
Vol 105 (1) ◽  
pp. 85-128 ◽  
Author(s):  
Maurizio Gabbrielli ◽  
Giorgio Levi
Keyword(s):  
Logic Programs ◽  
Fixpoint Semantics ◽  
Constraint Logic Programs

Tabled evaluation with delaying for general logic programs

1996 ◽  
Vol 43 (1) ◽  
pp. 20-74 ◽  
Author(s):  
Weidong Chen ◽  
David S. Warren
Keyword(s):  
Logic Programs ◽  
General Logic
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