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Proof-Theoretic Semantics and Inquisitive Logic

Will Stafford

Journal of Philosophical Logic 50 (5):1199-1229 (2021)

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Proof-Theoretic Validity isn’t Intuitionistic; So What?Will Stafford - forthcoming - Australasian Journal of Philosophy.details Several recent results bring into focus the superintuitionistic nature of most notions of proof-theoretic validity, but little work has been done evaluating the consequences of these results. Proof-theoretic validity claims to offer a formal explication of how inferences follow from the definitions of logic connectives (which are defined by their introduction rules). This paper explores whether the new results undermine this claim. It is argued that, while the formal results are worrying, superintuitionistic inferences are valid because the treatments of atomic (...) Download Export citation Bookmark
Constructive Validity of a Generalized Kreisel–Putnam Rule.Ivo Pezlar - forthcoming - Studia Logica.details In this paper, we propose a computational interpretation of the generalized Kreisel–Putnam rule, also known as the generalized Harrop rule or simply the Split rule, in the style of BHK semantics. We will achieve this by exploiting the Curry–Howard correspondence between formulas and types. First, we inspect the inferential behavior of the Split rule in the setting of a natural deduction system for intuitionistic propositional logic. This will guide our process of formulating an appropriate program that would capture the corresponding (...) Download Export citation Bookmark
Prawitz's completeness conjecture: A reassessment.Peter Schroeder-Heister - 2024 - Theoria 90 (5):492-514.details In 1973, Dag Prawitz conjectured that the calculus of intuitionistic logic is complete with respect to his notion of validity of arguments. On the background of the recent disproof of this conjecture by Piecha, de Campos Sanz and Schroeder-Heister, we discuss possible strategies of saving Prawitz's intentions. We argue that Prawitz's original semantics, which is based on the principal frame of all atomic systems, should be replaced with a general semantics, which also takes into account restricted frames of atomic systems. (...) Download Export citation Bookmark
The proof-theoretic square.Antonio Piccolomini D’Aragona - 2023 - Synthese 201 (6):1-34.details In Prawitz’s semantics, the validity of an argument may be defined, either relatively to an atomic base which determines the meaning of the non-logical terminology, or relatively to the whole class of atomic bases, namely as logical validity. In the first case, which may be qualified as local, one has to choose whether validity of arguments is or not monotonic over expansions of bases, while in the second case, which may be qualified as global, one has to choose whether the (...) Download Export citation Bookmark

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