Partial Logics with Two Kinds of Negation as a Foundation for Knowledge-Based Reasoning

Herre, Heinrich; Jaspars, Jan; Wagner, G.

doi:10.1007/978-94-015-9309-0_7

Cited by 20 publications

(26 citation statements)

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“…Since we allow arbitrary formulas in the body of rules some extra complexity is necessary to obtain an intuitive semantics in the spirit of partial logic [33]. This is not just a technical exercise and will provide extra expressive power, as we will show later on.…”

Section: Definition 5 (Erdf Interpretationmentioning

confidence: 99%

“…In particular, Berners-Lee [12] identifies the following fundamental theoretical problems: negation and contradictions, open-world versus closed-world assumptions, and rule systems for the Semantic Web. Therefore, in [6], the Semantic Web language RDFS [38,32] is extended to accommodate the two negations of Partial Logic [33], namely weak negation ∼ (expressing negation-as-failure or non-truth) and strong negation ¬ (expressing explicit negative information or falsity), as well as derivation rules. In particular, users can now add negative triples to RDF graphs.…”

Section: Introductionmentioning

confidence: 99%

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Extended RDF: Computability and complexity issues

Analyti

Damásio

Antoniou

2015

Ann Math Artif Intell

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Abstract. ERDF stable model semantics is a recently proposed semantics for ERDF ontologies and a faithful extension of RDFS semantics on RDF graphs. In this paper, we elaborate on the computability and complexity issues of the ERDF stable model semantics. Based on the undecidability result of ERDF stable model semantics, decidability under this semantics cannot be achieved, unless ERDF ontologies of restricted syntax are considered. Therefore, we propose a slightly modified semantics for ERDF ontologies, called ERDF #n-stable model semantics. We show that entailment under this semantics is, in general, decidable and also extends RDFS entailment. Equivalence statements between the two semantics are provided. Additionally, we provide algorithms that compute the ERDF #n-stable models of syntax-restricted and general ERDF ontologies. Further, we provide complexity results for the ERDF #n-stable model semantics on syntax-restricted and general ERDF ontologies. Finally, we provide complexity results for the ERDF stable model semantics on syntax-restricted ERDF ontologies.

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Section: Definition 5 (Erdf Interpretationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Extended RDF: Computability and complexity issues

Analyti

Damásio

Antoniou

2015

Ann Math Artif Intell

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“…In [2], we defined the #n-stable models of an ERDF ontology (for an n ∈ IN ), based on the coherent stable models of partial logic [7] (which, on ELPs, are equivalent [7] to Answer Sets [5]). Here, we extend this definition to modular stable models of an r-ERDF ontology w.r.t.…”

Section: Definition 12 (Modular Herbrand Interpretation Ordering)mentioning

confidence: 99%

“…On the other hand, the inclusion of negative information both in the form of negation-as-failure and explicit negative information is also needed to enable various forms of reasoning. In [1], the Semantic Web language RDFS [8,6] is extended to accommodate the two negations of Partial Logic [7], namely weak negation ∼ (expressing negation-as-failure or non-truth) and strong negation ¬ (expressing explicit negative information or falsity), as well as derivation rules. The new language is called Extended RDF (ERDF ).…”

Section: Introductionmentioning

confidence: 99%

A Formal Theory for Modular ERDF Ontologies

Analyti

Antoniou

Damásio

2009

Web Reasoning and Rule Systems

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Abstract. The success of the Semantic Web is impossible without any form of modularity, encapsulation, and access control. In an earlier paper, we extended RDF graphs with weak and strong negation, as well as derivation rules. The ERDF #n-stable model semantics of the extended RDF framework (ERDF) is defined, extending RDF(S) semantics. In this paper, we propose a framework for modular ERDF ontologies, called modular ERDF framework, which enables collaborative reasoning over a set of ERDF ontologies, while support for hidden knowledge is also provided. In particular, the modular ERDF stable model semantics of modular ERDF ontologies is defined, extending the ERDF #n-stable model semantics. Our proposed framework supports local semantics and different points of view, local closed-world and open-world assumptions, and scoped negation-as-failure. Several complexity results are provided.

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“…in extended logic programs) is based on the concept of stable generated partial models (see [HJW99]). Under the preferential semantics of stable generated partial models, weak negation corresponds to negation-asfailure, or, in other words, negation-as-failure implements weak negation when applied to an incomplete predicate, and it implements classical negation when applied to a complete predicate.…”

Section: Two Kinds Of Negation In Knowledge Representationmentioning

confidence: 99%