Proof-theoretic semantic values for logical operators

Review of Symbolic Logic 4 (3):466-478 (2011)

Authors
Nissim Francez
Technion, Israel Institute of Technology
Abstract
The paper proposes a semantic value for the logical constants (connectives and quantifiers) within the framework of proof-theoretic semantics, basic meaning on the introduction rules of a meaning conferring natural deduction proof system. The semantic value is defined based on Fregecontributions” to sentential meanings as determined by the function-argument structure as induced by a type-logical grammar. In doing so, the paper proposes a novel proof-theoretic interpretation of the semantic types, traditionally interpreted in Henkin models. The compositionality of the resulting attribution of semantic values is discussed. Elsewhere, the same method was used for defining proof-theoretic meaning of subsentential phrases in a fragment of natural language. Doing the same for (the simpler and clearer case of) logic sheds more light on the proposal.
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DOI 10.1017/s1755020311000098
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References found in this work BETA

Grundlagen der Arithmetik.Gottlob Frege - 1884 - Breslau: Wilhelm Koebner.
Formal Features of Compositionality.Wilfrid Hodges - 2001 - Journal of Logic, Language and Information 10 (1):7-28.
Rules for Subatomic Derivation.Bartosz Więckowski - 2011 - Review of Symbolic Logic 4 (2):219-236.

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Citations of this work BETA

Bilateralism in Proof-Theoretic Semantics.Nissim Francez - 2013 - Journal of Philosophical Logic (2-3):1-21.
Reprint Of: A More General General Proof Theory.Heinrich Wansing - 2017 - Journal of Applied Logic 25:23-46.
Bilateralism in Proof-Theoretic Semantics.Nissim Francez - 2014 - Journal of Philosophical Logic 43 (2-3):239-259.

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