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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.
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.
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.
Guido Governatori
Guido Governatori is a lecturer in the School of Information Technology and
Electrical Engineering, The University of Queensland, Brisbane, Australia,
where he is a member of the Data and Knowledge Engineering (DKE) group.
He graduated in Philosophy in 1993 from the University of Bologna
(Department of Philosophy), and in 1997 he received his PhD in Computer
Science and Law from the same university (CIRFID, now
CIRSFID) with a thesis on "A formal model of normative reasoning". In 1997
and 1998 he was an academic visitor at the Department of Computing, Imperial
College, London, where he worked with Dov Gabbay on labelled deductive
systems for fibred logics. From 1998 to 2000 he was a research associate at
Griffith University, where he worked with Grigoris Antoniou, David Billington,
and Michael Maher on an ARC large grant on defeasible logic and regulations.
Currently he is the main chief investigator in two Australian Research
Council Discovery Projects on "Combining modal logic for dynamic and
multi-agents systems" and "A Formal Approach to Resource Allocation in
Service Oriented Marketplaces".
His research interests include modal and non-classical logics, formal model
of argumentation and negotiation, normative reasoning, non-monotonic
reasoning, labelled deductive systems, and intelligent information systems.
