Indicative Conditionals and Dynamic Epistemic Logic

Proceedings of the Sixteenth Conference on Theoretical Aspects of Rationality and Knowledge (TARK 2017), Liverpool, UK, 24-26 July 2017 (2017)

Authors
Wesley H. Holliday
University of California, Berkeley
Abstract
Recent ideas about epistemic modals and indicative conditionals in formal semantics have significant overlap with ideas in modal logic and dynamic epistemic logic. The purpose of this paper is to show how greater interaction between formal semantics and dynamic epistemic logic in this area can be of mutual benefit. In one direction, we show how concepts and tools from modal logic and dynamic epistemic logic can be used to give a simple, complete axiomatization of Yalcin's [16] semantic consequence relation for a language with epistemic modals and indicative conditionals. In the other direction, the formal semantics for indicative conditionals due to Kolodny and MacFarlane [9] gives rise to a new dynamic operator that is very natural from the point of view of dynamic epistemic logic, allowing succinct expression of dependence (as in dependence logic) or supervenience statements. We prove decidability for the logic with epistemic modals and Kolodny and MacFarlane's indicative conditional via a full and faithful computable translation from their logic to the modal logic K45.
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References found in this work BETA

Epistemic Modals.Seth Yalcin - 2007 - Mind 116 (464):983-1026.
Ifs and Oughts.Niko Kolodny & John MacFarlane - 2010 - Journal of Philosophy 107 (3):115-143.
A Counterexample to Modus Tollens.Seth Yalcin - 2012 - Journal of Philosophical Logic 41 (6):1001-1024.

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