Categorical Semantics

  • James W. Garson
Chapter

Abstract

In “Tonk, Plonk and Plink” Belnap [1962] defended the claim that natural deduction rules define the meaning of a connective, provided at least that those rules form a conservative extension of the structural rules of deduction. In this paper we will investigate a stronger criterion of success for defining the meaning of a connective. Each connective comes with an intended interpretation, (for example, the intended interpretation of & is recorded by the truth table for &). For a set of rules to define the meaning of a connective, we would expect it to be categorical, i.e., we expect (roughly) that it force the intended interpretation of the connective on all its “models”. To put it another way, rules define a connective when they are strong enough to eliminate any non-standard interpretations.1

Keywords

Modal Logic Categorical Semantic Ontological Commitment Canonical Model Semantical Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bibliography

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Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • James W. Garson

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