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Blocking mechanisms in description logics, a general approach

Dmitry Tishkovsky - 11.6.2008

We will take a close look on various standard mechanism of blocking in tableaux for various description logics and attemt to simulate these mechanisms by a general blocking rule - the unrestricted blocking rule. In particular, we will consider static and dynamic, subset and equality, and successor and anywhere blocking mechanisms.

Reasoning about actions and knowlege: Multi-agent dynamic logics with informational test

Dmitry Tishkovsky - 9.6.2008

The logics are based on a new formalisation and semantics of the test operator of propositional dynamic logic and a representation of actions which distinguishes abstract actions from concrete actions. The new test operator, called informational test, can be used to formalise the beliefs and knowledge of particular agents as dynamic modalities. This approach is consistent with the formalisation of the agents` beliefs and knowledge as K(D)45 and S5 modalities. Properties concerning informativeness, truthfulness and preservation of beliefs were proved for a derivative of the informational test operator. It was shown that common belief and common knowledge can be expressed in the considered logics. This means, the logics are more expressive than propositional dynamic logic with an extra modality for belief or knowledge. The logics remain decidable and belong to 2EXPTIME. Versions of the considered logics express natural additional properties of beliefs or knowledge and interaction of beliefs or knowledge with actions. It was shown that a simulation of PDL can be constructed in one of these extensions.

A General Tableau Method for Deciding Description Logics, Modal Logics and Related First-Order Fragments

Dmitry Tishkovsky - 11.6.2008

A general method for proving termination of tableaux-based procedures for modal-type logics and related first-order fragments will be presented. The method is based on connections between filtration arguments and a general blocking technique. The method provides a general framework for developing tableau-based decision procedures for a large class of logics. In particular, the method can be applied to many well-known description and modal logics. The class includes traditional modal logics such as S4 and modal logics with the universal modality, as well as description logics such as ALC with nominals and general TBoxes. Also contained in the class are harder and less well-studied modal logics with complex modalities and description logics with complex role operators such as Boolean modal logic, and the description logic ALBO. In addition, the techniques allow us to specify tableau-based decision procedures for related solvable fragments of first-order logic, including the two-variable fragment of first-order logic. This solves a long-standing open problem.

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Results - Publications

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Sojka Petr, Choi Key-Sun, Fellbaum Christiane, Vossen Piek
Proceedings of the Third International WordNet Conference, GWC 2006
In: Proceedings of the Third International Wordnet Conference, 2006.
Sojka Petr, Kopeček Ivan, Pala Karel
Text, Speech and Dialogue - Proceedings of the 9th International Conference, TSD 2006
In: Text, Speech and Dialogue - Proceedings of the 9th International Conference, TSD 2006, LNCS 4188, Springer-Verlag, Berlin / Heidelberg, 2006. ISBN: 978-3-540-39090-9
Paper in pdf format
Štuller Július, Linková Zdeňka
Inteligentní modely, algoritmy, metody a nástroje pro vytváření sémantického webu
In: Inteligentní modely, algoritmy, metody a nástroje pro vytváření sémantického webu, Ústav informatiky AV ČR, Prague, 2006. ISBN: 80-903298-7-X
Vojtáš Peter
Information Technologies - Applications and Theory
In: Proceedings of ITAT 2006, Information Technologies - Applications and Theory, 2006. ISBN: 80-969184-4-3
Wiedermann Jiří, Tel Gerard, Pokorný Jaroslav, Bieliková Mária, Štuller Július
Proceedings of SOFSEM 2006
In: Proceedings of SOFSEM 2006, Volume: II, ICS AS CR, Prague, 2006. ISBN: 80-903298-4-5
Wiedermann Jiří, Tel Gerard, Pokorný Jaroslav, Bieliková Mária, Štuller Július
Proceedings of SOFSEM 2006: Theory and Practice of Computer Science
In: Proceedings of SOFSEM 2006: Theory and Practice of Computer Science, LNCS 3831, Springer-Verlag, Berlin, 2006. ISBN: 3-540-31198-X
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