Logic and Logical Philosophy 23 (3):301--328 (2014)

Authors
Paolo Maffezioli
University of Barcelona
Abstract
A combination of epistemic logic and dynamic logic of programs is presented. Although rich enough to formalize some simple game-theoretic scenarios, its axiomatization is problematic as it leads to the paradoxical conclusion that agents are omniscient. A cut-free labelled Gentzen-style proof system is then introduced where knowledge and action, as well as their combinations, are formulated as rules of inference, rather than axioms. This provides a logical framework for reasoning about games in a modular and systematic way, and to give a step-by-step reconstruction of agents omniscience. In particular, its semantic assumptions are made explicit and a possible solution can be found in weakening the properties of the knowledge operator.
Keywords labelled sequent calculus  dynamic propositional logic  epistemic paradox  structural proof theory  epistemic logic
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DOI 10.12775/LLP.2013.026
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Proof Analysis in Modal Logic.Sara Negri - 2005 - Journal of Philosophical Logic 34 (5-6):507-544.
What is a Theory of Meaning? (II).Michael Dummett - 1976 - In Gareth Evans & John McDowell (eds.), Truth and Meaning: Essays in Semantics. Oxford: Clarendon Press.
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