A Tableau Algorithm for Description Logics with Concrete Domains and GCIs

Lutz, Carsten; Miličić, Maja

doi:10.1007/11554554_16

Cited by 19 publications

(33 citation statements)

References 14 publications

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“…Indeed, LTL({x = y}) with the freeze operator is shown Σ 1 1 -complete in [DLN05,LP05] The pspace-completeness of PLTL mod leaves open for which constraint system D (not necessarily fragment of Presburger arithmetic), LTL over D is decidable in pspace. Necessary conditions are provided in [DD03] to guarantee the polynomial space upper bound (completion property and frame checking in pspace) and similar conditions are also introduced in [BC02,LM05]. The question is however open in full generality.…”

Section: Discussionmentioning

confidence: 99%

LTL over Integer Periodicity Constraints

Demri

2004

Lecture Notes in Computer Science

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Abstract. Periodicity constraints are used in many logical formalisms, in fragments of Presburger LTL, in calendar logics, and in logics for access control, to quote a few examples. In the paper, we introduce the logic PLTL mod , an extension of Linear-Time Temporal Logic LTL with past-time operators whose atomic formulae are defined from a first-order constraint language dealing with periodicity. Although the underlying constraint language is a fragment of Presburger arithmetic shown to admit a pspace-complete satisfiability problem, we establish that PLTL mod model-checking and satisfiability problems remain in pspace as plain LTL (full Presburger LTL is known to be highly undecidable). This is particularly interesting for dealing with periodicity constraints since the language of PLTL mod has a language more concise than existing languages and the temporalization of our first-order language of periodicity constraints has the same worst case complexity as the underlying constraint language. Finally, we show examples of introduction the quantification in the logical language that provide to PLTL mod , expspacecomplete problems. As another application, we establish that the equivalence problem for extended single-string automata, known to express the equality of time granularities, is pspace-complete by designing a reduction from QBF and by using our results for PLTL mod .

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Section: Discussionmentioning

confidence: 99%

LTL over Integer Periodicity Constraints

Demri

2004

Lecture Notes in Computer Science

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“…The reasoning is for checking concept and role instances and for query answering over a satisfiable ontology [9,11]. Ontology satisfiability is to verify whether ontology O admits at least one model where consistency properties should be verified.…”

Section: Reasoning Over Imprecise Ontologiesmentioning

confidence: 99%

“…For reasoning over vague ontologies using the proposed vagueness theory, we have added the following two expansion rules that should be applied after every expansion by a classical Tableau rule (the reader can be referred to [4,5,9] for the classical Tableau rules). We will get a clash (contradiction) if any new set of truth gaps assertions is not acceptable (Lemma 1 and Equation 4).…”

Section: Reasoning Over Imprecise Ontologiesmentioning

confidence: 99%

Exact Reasoning over Imprecise Ontologies

Bourahla¹

2015

IFIP Advances in Information and Communication Technology

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“…The translated query is then evaluated for subsumption relationship with previously stored query in the cache by using the sound and complete subsumption algorithm given in (Baader et al,91b) (Lutz et al, 2005).…”

Section: Subsumption Analysis Reasoningmentioning

confidence: 99%