Plurivalent Logics

  • Graham Priest Graduate Center, CUNY

Abstract

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.

Author Biography

Graham Priest, Graduate Center, CUNY
Distinguished Professor, Philosophy Department
Published
2014-04-08
How to Cite
PRIEST, Graham. Plurivalent Logics. The Australasian Journal of Logic, [S.l.], v. 11, n. 1, apr. 2014. ISSN 1448-5052. Available at: <https://ojs.victoria.ac.nz/ajl/article/view/1830>. Date accessed: 17 nov. 2018. doi: https://doi.org/10.26686/ajl.v11i1.1830.