# Many-Valued Logics

In Gillian Russell & Delia Graff Fara (eds.), The Routledge Companion to Philosophy of Language. Routledge 636--51 (2012)
Abstract
A many-valued (aka multiple- or multi-valued) semantics, in the strict sense, is one which employs more than two truth values; in the loose sense it is one which countenances more than two truth statuses. So if, for example, we say that there are only two truth values—True and False—but allow that as well as possessing the value True and possessing the value False, propositions may also have a third truth status—possessing neither truth value—then we have a many-valued semantics in the loose but not the strict sense. A many-valued logic is one which arises from a many-valued semantics and does not also arise from any two-valued semantics [Malinowski, 1993, 30]. By a ‘logic’ here we mean either a set of tautologies, or a consequence relation. We can best explain these ideas by considering the case of classical propositional logic. The language contains the usual basic symbols (propositional constants p, q, r, . . .; connectives ¬, ∧, ∨, →, ↔; and parentheses) and well-formed formulas are defined in the standard way. With the language thus specified—as a set of well-formed formulas—its semantics is then given in three parts. (i) A model of a logical language consists in a free assignment of semantic values to basic items of the non-logical vocabulary. Here the basic items of the non-logical vocabulary are the propositional constants. The appropriate kind of semantic value for a proposition is a truth value, and so a model of the language consists in a free assignment of truth values to basic propositions. Two truth values are countenanced: 1 (representing truth) and 0 (representing falsity). (ii) Rules are presented which determine a truth value for every proposition of the language, given a model. The most common way of presenting these rules is via truth tables (Figure 1). Another way of stating such rules—which will be useful below—is first to introduce functions on the truth values themselves: a unary function ¬ and four binary functions ∧, ∨, → and ↔ (Figure 2)..
Keywords No keywords specified (fix it)
Categories (categorize this paper)
Options
 Save to my reading list Follow the author(s) My bibliography Export citation Find it on Scholar Edit this record Mark as duplicate Revision history Request removal from index

 PhilPapers Archive Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 23,316 External links Setup an account with your affiliations in order to access resources via your University's proxy server Configure custom proxy (use this if your affiliation does not provide a proxy) Through your library Sign in / register to customize your OpenURL resolver.Configure custom resolver
References found in this work BETA

No references found.

Citations of this work BETA
Similar books and articles

### Added to index

2010-02-18

58 ( #82,833 of 1,926,182 )