Issues of Decidability for Description Logics in the Framework of Resolution

Hustadt, Ullrich; Schmidt, Renate A.

doi:10.1007/3-540-46508-1_13

Cited by 45 publications

(58 citation statements)

References 12 publications

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“…The following result is a consequence of decidability results in [26] and also of the decidability of the two-variable fragment of first-order logic.…”

Section: Dynamic Modal Logicsmentioning

confidence: 86%

“…It follows from [26,33] that the result remains true when we allow negation as a relational operator [26], or relational composition and identity [33]. However, adding both relational negation and relational composition leads to undecidability.…”

Section: Theorem 3 Let L Be a Dynamic Modal Logic With Any Subset Of mentioning

confidence: 99%

“…The translation is similar to the one used in [46,48]; other structural translations have been used in [10,25,26,28], for instance.…”

Section: Theorem 3 Let L Be a Dynamic Modal Logic With Any Subset Of mentioning

confidence: 99%

“…In this paper we discuss and extend an approach of developing tableaux calculi for modal logics that has been suggested and followed in our previous work [10,19,25,26,28,46,48]. Although resolution calculi apparently operate considerably differently from tableau calculi, we have shown that it is possible to linearly simulate many forms of modal logic or description logic tableau calculi with standard techniques of first-order resolution theorem proving.…”

Section: Introductionmentioning

confidence: 98%

“…Although resolution calculi apparently operate considerably differently from tableau calculi, we have shown that it is possible to linearly simulate many forms of modal logic or description logic tableau calculi with standard techniques of first-order resolution theorem proving. In [26] we have shown how derivations and search in standard tableau algorithms of the description logic A L C can be linearly simulated by resolution. This corresponds to local satisfiability testing in the basic multi-modal logic K (m) .…”

Section: Introductionmentioning

confidence: 99%

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A new methodology for developing deduction methods

Schmidt

2009

Ann Math Artif Intell

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This paper explores the use of resolution as a meta-framework for developing various, different deduction calculi. In this work the focus is on developing deduction calculi for modal dynamic logics. Dynamic modal logics are PDL-like extended modal logics which are closely related to description logics. We show how tableau systems, modal resolution systems and Rasiowa-Sikorski systems can be developed and studied by using standard principles and methods of first-order theorem proving. The approach is based on the translation of reasoning problems in modal logic to first-order clausal form and using a suitable refinement of resolution to construct and mimic derivations of the desired proof method. The inference rules of the calculus can then be read off from the clausal form. We show how this approach can be used to generate new proof calculi and prove soundness, completeness and decidability results. This slightly unusual approach allows us to gain new insights and results for familiar and less familiar logics, for different proof methods, and compare them not only theoretically but also empirically in a uniform framework.

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“…The following result is a consequence of decidability results in [26] and also of the decidability of the two-variable fragment of first-order logic.…”

Section: Dynamic Modal Logicsmentioning

confidence: 86%

Section: Theorem 3 Let L Be a Dynamic Modal Logic With Any Subset Of mentioning

confidence: 99%

“…The translation is similar to the one used in [46,48]; other structural translations have been used in [10,25,26,28], for instance.…”

Section: Theorem 3 Let L Be a Dynamic Modal Logic With Any Subset Of mentioning

confidence: 99%