Formalized Soundness and Completeness of Epistemic Logic

In Alexandra Silva, Renata Wassermann & Ruy de Queiroz (eds.), Logic, Language, Information, and Computation: 27th International Workshop, Wollic 2021, Virtual Event, October 5–8, 2021, Proceedings. Springer Verlag. pp. 1-15 (2021)
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Abstract

We strengthen the foundations of epistemic logic by formalizing the family of normal modal logics in the proof assistant Isabelle/HOL. We define an abstract canonical model and prove a truth lemma for any logic in the family. We then instantiate it with logics based on various epistemic principles to obtain completeness results for systems from K to S5. Our work gives a disciplined treatment of completeness-via-canonicity arguments and demonstrates their compositionality.

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10.1007/978-3-030-88853-4_1

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