Open AccessPlurivalent Logics
Author(s) -
Graham Priest
Publication year - 2014
Publication title -
australasian journal of logic
Language(s) - English
Resource type - Journals
ISSN - 1448-5052
DOI - 10.26686/ajl.v11i1.1830
Subject(s) - semantics (computer science) , proof theoretic semantics , relation (database) , computer science , well founded semantics , programming language , contrast (vision) , propositional calculus , operational semantics , mathematics , algebra over a field , theoretical computer science , computational semantics , denotational semantics , calculus (dental) , artificial intelligence , pure mathematics , database , medicine , dentistry
In this paper, I will describe a technique for generating a novel kind of semantics for a logic, and explore some of its consequences. It would be natural to call the semantics produced by the technique in question ‘many-valued'; but that name is, of course, already taken. I call them, instead, ‘plurivalent'. In standard logical semantics, formulas take exactly one of a bunch of semantic values. I call such semantics ‘univalent'. In a plurivalent semantics, by contrast, formulas may take one or more such values (maybe even less than one). The construction I shall describe can be applied to any univalent semantics to produce a corresponding plurivalent one. In the paper I will be concerned with the application of the technique to propositional many-valued (including two-valued) logics. Sometimes going plurivalent does not change the consequence relation; sometimes it does. I investigate the possibilities in detail with respect to small family of many-valued logics.