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Logic Journal of IGPL 2005 13(2):201-209; doi:10.1093/jigpal/jzi014
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© The Author, 2005. Published by Oxford University Press. All rights reserved.

Original Articles

Logic of Visibility, Perception, and Knowledge and Admissible Inference Rules

M.I. Golovanov1, A.V. Kosheleva2 and V. Rybakov3

1 Department of Mathematics and Computer Science, Krasnoyarsk University ave. Svobodnyi 79, 660 041, Krasnoyarsk, Russia. E-mail: glvnv{at}lan.krasu.ru, 2 Department of Mathematics and Computer Science, Krasnoyarsk University ave. Svobodnyi 79, 660 041, Krasnoyarsk, Russia. E-mail: kosheleva{at}krasu.ru, 3 Department of Computing and Mathematics, Manchester Metropolitan University, John Dalton Building, Chester Street., Manchester, M1 5GD UK. E-mail: V.Rybakov{at}mmu.ac.uk

We investigate admissible inference rules for the multi-modal logic VSK+ extending the logic VSK – the logic of Visibility, Perception and Knowledge. The logic VSK has been introduced by M.Wooldridge and A. Lomuscio [21]. VSK was intended for reasoning about properties of computational agents situated in some environment. Admissible rules are important for modelling of logical consequence. We consider these rules for VSK+, the logic of a wise agent (one which knows anything visible). The main result of our paper is the construction of an algorithm which determines admissible inference rules in VSK+. The algorithm is based on the proof of existence of computable bounds on the size of special Kripke 3-frames refuting inadmissible rules.

Received 7 October 2003. Revised 25 November 2004.


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