Zoom Talk: Will Stafford (Irvine)
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Proof-Theoretic Validity and Inquisitive Logic
It isn't known what logic is defined by proof-theoretic validity as proposed by Prawitz (1971). It is known that it will be an intermediate logic and may not be closed under substitution. Inquisitive Semantics offers a uniform semantics for questions and assertions. It is axiomatized by inquisitive logic, which is an intermediate logic not closed under substitution. In this talk, I will define a notion of quasi-proof-theoretic validity by restricting proof-theoretic validity to allow double negation elimination for atomic formulas. Using this the extensional alignment of quasi-proof-Theoretic validity and inquisitive logic, as well as proof-theoretic validity and a generalised inquisitive logic, will be shown.