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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.


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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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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.


About the Project

The project has started on July 1st, 2004 and is planned for 4.5 years.

It is oriented toward semantic web topics, namely: inteligent models, algorithms, methods and tools.

The team of researchers is formally divided into 8 working groups, each working in a specific area.

 

A part of Brno project results, namely Vit Novacek's part, can be found at OLE Ontology Acquisition Project site.

About People

The project is centered around key researchers and includes Ph. D. students.

On the project colaborate people from the following 3 institutions:


Institute of Computer Science
Academy of Sciences of the Czech Republic

Faculty of Mathematics and Physics
Charles University in Prague

Faculty of Informatics
Masaryk University Brno

Project Characteristic

The project aims at integration of progresive theoretical disciplines of Computer Science with their practical applications.

Its goal is to examine and develop theoretical backgrounds of the semantic web, mainly from the point of view of modern AI methods and methods of computing by nature, as e.i.  artificial neural nets, evolutionary algorithms, datamining, special (e.i. description) logics, etc., and to apply and verify selected methods of intelligent data and knowledge processing in that field.

The results of the project are expected to be mainly:

  • theoretical treatises, published in international journals and presented at international conferences
  • new algorithms for knowledge extraction from data, based on neural, cognitive, fuzzy and evolutionary approaches
  • prototypical implementations of these algorithms within a multiagent systems.

The project is founded by the Program of the Information Socienty (of the Thematic Program II of the National Research Program of the Czech Republic).

Thanks

We thank the government of the Czech Republic for sponsoring this project.

This page was last modified 01.12.2006 00:00.