Default theory for Well Founded Semantics with explicit negation

Alferes, José Júlio; Aparício, Joaquim Nunes

doi:10.1007/bfb0023437

Cited by 35 publications

(55 citation statements)

References 2 publications

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“…Something similar happened for other extensions such as abductive logic programming (e.g., [17,19,26]) and logic programming with a second form of negation in addition to negation by default (e.g., [24,34,38]). …”

Section: Composition Of Normal Programsmentioning

confidence: 66%

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On the Semantics of Logic Program Composition

Brogi

2004

Program Development in Computational Logic

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Abstract. This paper aims at offering an insightful synthesis of different compositional semantics for logic program composition which have been developed in the literature. In particular, we will analyse the notions of program equivalence, compositionality, and full abstraction for logic programs. We will show how the notion of supported interpretation provides a unifying compositional model-theoretic characterisation both of positive programs and of programs containing negation.

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Section: Composition Of Normal Programsmentioning

confidence: 66%

“…-Other forms of negation -such as explicit negation [34], answer set semantics [24], and 3-valued stable semantics [37]; -Abduction -as modeled for instance in [16] and in [26].…”

Section: Discussionmentioning

confidence: 99%

On the Semantics of Logic Program Composition

Brogi

2004

Program Development in Computational Logic

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“…This problem is similar to the issue of coherence that arises when adding strong negation to logic programs [6,13,14]: the strong (or classical) negation must imply negation by default. In our case, if the ontology entails that some atom A is false, then perforce the default negation not A must hold in the program.…”

Section: The Gist Of the Approachmentioning

confidence: 99%

Queries to Hybrid MKNF Knowledge Bases through Oracular Tabling

Alferes

Knorr

Swift

2009

Lecture Notes in Computer Science

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Abstract. An important issue for the Semantic Web is how to combine open-world ontology languages with closed-world (non-monotonic) rule paradigms. Several proposals for hybrid languages allow concepts to be simultaneously defined by an ontology and rules, where rules may refer to concepts in the ontology and the ontology may also refer to predicates defined by the rules. Hybrid MKNF knowledge bases are one such proposal, for which both a stable and a well-founded semantics have been defined. The definition of Hybrid MKNF knowledge bases is parametric on the ontology language, in the sense that non-monotonic rules can extend any decidable ontology language. In this paper we define a query-driven procedure for Hybrid MKNF knowledge bases that is sound with respect to the original stable model-based semantics, and is correct with respect to the well-founded semantics. This procedure is able to answer conjunctive queries, and is parametric on an inference engine for reasoning in the ontology language. Our procedure is based on an extension of a tabled rule evaluation to capture reasoning within an ontology by modeling it as an interaction with an external oracle and, with some assumptions on the complexity of the oracle compared to the complexity of the ontology language, maintains the data complexity of the well-founded semantics for hybrid MKNF knowledge bases.

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“…In the case of WFS for ELP, some counterintuitive results have led to the need for a variation called WFSX (WFS with eXplicit negation) [16]. This semantics guarantees the so-called coherence principle: if an atom A ∈ H is founded in the WFM, its complementary atom A must be unfounded.…”

Section: Recall Of Logic Programmingmentioning

confidence: 99%

Logic Programs with Functions and Default Values

Cabalar

Lorenzo

2004

Logics in Artificial Intelligence

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Abstract. In this work we reconsider the replacement of predicate-like notation by functional terms, using a similar syntax to Functional Logic Programming, but under a completely different semantic perspective. Our starting point comes from the use of logic programs for Knowledge Representation and Nonmonotonic Reasoning, especially under three well-known semantics for default negation: Clark's completion, stable models and well-founded semantics. The motivation for introducing functions in this setting arises from the frequent occurrence of functional dependences in the representation of many domains. The use of functions allows us to avoid explicit axiomatization (to ensure the uniqueness of value) and provides a more compact representation by nesting functional terms. This gets rid of a considerable amount of unnecessary variables, what may be exploited for the process of program grounding, something common in this type of applications of Logic Programming. From a representational point of view, the most interesting introduced feature is the possibility of replacing default negation by the concept of default value of a function. In the paper, we explore this idea of functions with default values, providing adapted versions of the three mentioned semantics for the functional case, and equivalent translations into logic programs.

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Default theory for Well Founded Semantics with explicit negation

Cited by 35 publications

References 2 publications

On the Semantics of Logic Program Composition

On the Semantics of Logic Program Composition

Queries to Hybrid MKNF Knowledge Bases through Oracular Tabling

Logic Programs with Functions and Default Values

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