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PROOF-THEORETIC SEMANTIC VALUES FOR LOGICAL OPERATORS

Published online by Cambridge University Press:  07 September 2011

NISSIM FRANCEZ  and
GILAD BEN-AVI
NISSIM FRANCEZ*
Affiliation:
Computer Science Department, The Technion-IIT
GILAD BEN-AVI*
Affiliation:
Computer Science Department, The Technion-IIT
*
*COMPUTER SCIENCE DEPARTMENT, THE TECHNION-IIT, HAIFA, ISRAEL. E-mail:francez@cs.technion.ac.il
†COMPUTER SCIENCE DEPARTMENT, THE TECHNION-IIT, HAIFA, ISRAEL. E-mail:bagilad@cs.technion.ac.il
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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 Frege’s Context Principle, by taking “contributions” 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.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 4 , Issue 3 , September 2011 , pp. 466 - 478
Copyright
Copyright © Association for Symbolic Logic 2011

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References

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