Proof theory of epistemic logic of programs

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

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Author Profiles

Paolo Maffezioli
Universitat de Barcelona
Alberto Naibo
University of Paris 1 Panthéon-Sorbonne

References found in this work

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.
What is a theory of meaning?Michael A. E. Dummett - 1975 - In Samuel Guttenplan (ed.), Mind and Language. Oxford University Press.
Proof Analysis in Modal Logic.Sara Negri - 2005 - Journal of Philosophical Logic 34 (5-6):507-544.
[Omnibus Review].Robert Goldblatt - 1986 - Journal of Symbolic Logic 51 (1):225-227.
.Joe Salerno - 2009 - In New Essays on the Knowability Paradox. Oxford University Press.

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