Substitutional Validity for Modal Logic

Notre Dame Journal of Formal Logic 64 (3):291-316 (2023)
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Abstract

In the substitutional framework, validity is truth under all substitutions of the nonlogical vocabulary. I develop a theory where □ is interpreted as substitutional validity. I show how to prove soundness and completeness for common modal calculi using this definition.

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Marco Grossi
University of Oxford

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