# On Reduction Rules, Meaning-as-use, and Proof-theoretic Semantics

@article{Queiroz2008OnRR, title={On Reduction Rules, Meaning-as-use, and Proof-theoretic Semantics}, author={Ruy J. G. B. de Queiroz}, journal={Studia Logica}, year={2008}, volume={90}, pages={211-247} }

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…

## 7 Citations

The original sin of proof-theoretic semantics

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This thesis is that the consequence relation relevant for proof-theoretic semantics is the one given by the sequent-to-sequent derivability relation in Gentzen systems.

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The paper proposes an explicit definition of meaning in terms of rules, appealing to collections of canonical derivations, in contrast to the traditional approach that regards the rules as determining meaning implicitly.

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The intention here is to show that, by considering as sequences of rewrites and substitution, it comes a rather natural fact that two (or more) distinct proofs may be yet canonical and are none to be preferred over one another.

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In proof theory the notion of canonical proof is rather basic, and it is usually taken for granted that a canonical proof of a sentence must be unique up to certain minor syntactical details (such…

Inversion Principles and Introduction Rules

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Following Gentzen’s practice, borrowed from intuitionist logic, Prawitz takes the introduction rule(s) for a connective to show how to prove a formula with the connective dominant. He proposes an…

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