A proof-theoretic approach to formal epistemology

Abstract: (joint work with Edi Pavlovic) Ever since antiquity, attempts have been made to characterize knowledge through belief augmented by additional properties such as truth and justification. These characterizations have been challenged by Gettier counterexamples and their variants. A modern proposal, what is known as defeasibility theory, characterizes knowledge through stability under revisions of beliefs on the basis of true or arbitrary information (Hintikka (1962), Stalnaker (1998)). A formal investigation of such a proposal calls for the methods of dynamic epistemic logic: well-developed semantic approaches to dynamic epistemic logic have been given through plausibility models of Baltag and Smets (2008) and Pacuit (2013), but a corresponding proof theory is still in its beginning. We shall recast plausibility models in terms of the more general neighbourhood models and develop on their basis complete proof systems, following a methodology introduced in Negri (2017) and developed for conditional doxastic notions in Girlando et al. (2018). An inferential treatment of various epistemic and doxastic notions such as safe belief and strong belief will give a new way to study their relationships; among these, the characterization of knowledge as belief stable under arbitrary revision will be grounded through formal labelled sequent calculus derivations.

logic in computer sciencelogic

Audience: researchers in the topic

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