Logic of visibility, perception, and knowledge and admissible inference rules

Golovanov, M. I., Kosheleva, A. V. and Rybakov, Vladimir V. (2005) Logic of visibility, perception, and knowledge and admissible inference rules. Logic journal of IGPL, 13 (2). pp. 201-209. ISSN 1368-9894

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Abstract

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.