scholarly journals Strong Negation in Well-Founded and Partial Stable Semantics for Logic Programs

2006 ◽  
pp. 592-601 ◽  
Author(s):  
Pedro Cabalar ◽  
Sergei Odintsov ◽  
David Pearce
Keyword(s):  
Logic Programs ◽  
Strong Negation ◽  
Stable Semantics

scholarly journals Ultimate Well-Founded and Stable Semantics for Logic Programs with Aggregates

2001 ◽  
pp. 212-226 ◽  
Author(s):  
Marc Denecker ◽  
Nikolay Pelov ◽  
Maurice Bruynooghe
Keyword(s):  
Logic Programs ◽  
Stable Semantics

scholarly journals Well-founded and stable semantics of logic programs with aggregates

2007 ◽  
Vol 7 (3) ◽  
pp. 301-353 ◽  
Author(s):  
NIKOLAY PELOV ◽  
MARC DENECKER ◽  
MAURICE BRUYNOOGHE
Keyword(s):  
Logic Programming ◽  
Second Order ◽  
Logic Programs ◽  
Consequence Operator ◽  
Trade Offs ◽  
Stable Semantics ◽  
Consequence Operators ◽  
Semantics Of Logic Programs ◽  
Stable Models

AbstractIn this paper, we present a framework for the semantics and the computation of aggregates in the context of logic programming. In our study, an aggregate can be an arbitrary interpreted second order predicate or function. We define extensions of the Kripke-Kleene, the well-founded and the stable semantics for aggregate programs. The semantics is based on the concept of a three-valuedimmediate consequence operatorof an aggregate program. Such an operatorapproximatesthe standard two-valued immediate consequence operator of the program, and induces a unique Kripke-Kleene model, a unique well-founded model and a collection of stable models. We study different ways of defining such operators and thus obtain a framework of semantics, offering different trade-offs betweenprecisionandtractability. In particular, we investigate conditions on the operator that guarantee that the computation of the three types of semantics remains on the same level as for logic programs without aggregates. Other results show that, in practice, even efficient three-valued immediate consequence operators which are very low in the precision hierarchy, still provide optimal precision.

Dempster-Shafer Logic Programs and Stable Semantics

1993 ◽  
pp. 654-704
Author(s):  
Raymond Ng ◽  
V. S. Subrahmanian
Keyword(s):  
Logic Programs ◽  
Stable Semantics

scholarly journals On the Equivalence Between Abstract Dialectical Frameworks and Logic Programs

2019 ◽  
Vol 19 (5-6) ◽  
pp. 941-956
Author(s):  
JOÃO ALCÂNTARA ◽  
SAMY SÁ ◽  
JUAN ACOSTA-GUADARRAMA
Keyword(s):  
Logic Program ◽  
Logic Programs ◽  
Different Types ◽  
Stable Semantics ◽  
Acceptance Condition ◽  
Normal Logic ◽  
Normal Logic Program ◽  
Stable Models

AbstractAbstract 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.

scholarly journals Extending Well-Founded Semantics with Clark’s Completion for Disjunctive Logic Programs

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Juan Carlos Nieves ◽  
Mauricio Osorio
Keyword(s):  
Aggregation Operator ◽  
Stable Model ◽  
Logic Programs ◽  
Complete Lattices ◽  
Transformation Rules ◽  
Disjunctive Program ◽  
Stable Semantics ◽  
Disjunctive Logic Programs ◽  
Disjunctive Programs ◽  
Explicit Negation

In this paper, we introduce new semantics (that we call D3-WFS-DCOMP) and compare it with the stable semantics (STABLE). For normal programs, this semantics is based onsuitableintegration of the well-founded semantics (WFS) and the Clark’s completion. D3-WFS-DCOM has the following appealing properties: First, it agrees with STABLE in the sense that it never defines a nonminimal model or a nonminimal supported model. Second, for normal programs it extends WFS. Third, every stable model of a disjunctive programPis a D3-WFS-DCOM model ofP. Fourth, it is constructed using transformation rules accepted by STABLE. We also introduce second semantics that we call D2-WFS-DCOMP. We show that D2-WFS-DCOMP is equivalent to D3-WFS-DCOMP for normal programs but this is not the case for disjunctive programs. We also introduce third new semantics that supports the use of implicit disjunctions. We illustrate how these semantics can be extended to programs including explicit negation, default negation in the head of a clause, and aluboperator, which is a generalization of the aggregation operatorsetofover arbitrary complete lattices.

scholarly journals Guarded resolution for Answer Set Programming

2010 ◽  
Vol 11 (1) ◽  
pp. 111-123 ◽  
Author(s):  
V. W. MAREK ◽  
J. B. REMMEL
Keyword(s):  
Answer Set Programming ◽  
Proof System ◽  
Logic Programs ◽  
Resolution Rule ◽  
Theoretic Concept ◽  
Stable Semantics ◽  
Normal Logic ◽  
Propositional Theory ◽  
Stable Models ◽  
Answer Set

AbstractWe investigate a proof system based on a guarded resolution rule and show its adequacy for the stable semantics of normal logic programs. As a consequence, we show that Gelfond–Lifschitz operator can be viewed as a proof-theoretic concept. As an application, we find a propositional theory EP whose models are precisely stable models of programs. We also find a class of propositional theories 𝓒P with the following properties. Propositional models of theories in 𝓒P are precisely stable models of P, and the theories in 𝓒T are of the size linear in the size of P.

Well-Founded Semantics Coincides with Three-Valued Stable Semantics1

1990 ◽  
Vol 13 (4) ◽  
pp. 445-463
Author(s):  
Teodor Przymusinski
Keyword(s):  
Logic Program ◽  
Natural Extension ◽  
Natural Generalization ◽  
Stable Model ◽  
Logic Programs ◽  
Default Theory ◽  
Recent Approach ◽  
Stable Semantics ◽  
Disjunctive Logic Programs ◽  
Stable Models

We introduce 3-valued stable models which are a natural generalization of standard (2-valued) stable models. We show that every logic program P has at least one 3-valued stable model and that the well-founded model of any program P [Van Gelder et al., 1990] coincides with the smallest 3-valued stable model of P. We conclude that the well-founded semantics of an arbitrary logic program coincides with the 3-valued stable model semantics. The 3-valued stable semantics is closely related to non-monotonic formalisms in AI. Namely, every program P can be translated into a suitable autoepistemic (resp. default) theory P ˆ so that the 3-valued stable semantics of P coincides with the (3-valued) autoepistemic (resp. default) semantics of P ˆ. Similar results hold for circumscription and CWA. Moreover, it can be shown that the 3-valued stable semantics has a natural extension to the class of all disjunctive logic programs and deductive databases. Finally, following upon the recent approach developed by Gelfond and Lifschitz, we extend all of our results to more general logic programs which, in addition to the use of negation as failure, permit the use of classical negation.

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