On reduction rules, meaning-as-use, and proof-theoretic semantics

Studia Logica 90 (2):211-247 (2008)
The intention here is that of giving a formal underpinning to the idea of ‘meaning-is-use’ which, even if based on proofs, it is rather different from proof-theoretic semantics as in the Dummett–Prawitz tradition. Instead, it is based on the idea that the meaning of logical constants are given by the explanation of immediate consequences, which in formalistic terms means the effect of elimination rules on the result of introduction rules, i.e. the so-called reduction rules. For that we suggest an extension to the Curry– Howard interpretation which draws on the idea of labelled deduction, and brings back Frege’s device of variable-abstraction to operate on the labels (i.e., proof-terms) alongside formulas of predicate logic.
Keywords Philosophy   Computational Linguistics   Mathematical Logic and Foundations   Logic
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DOI 10.1007/s11225-008-9150-5
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Ian Hacking (1979). What is Logic? Journal of Philosophy 76 (6):285-319.

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