David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
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)|
|Through your library||Only published papers are available at libraries|
References found in this work BETA
No references found.
Citations of this work BETA
Nicholas J. J. Smith (forthcoming). Vagueness, Uncertainty and Degrees of Belief: Two Kinds of Indeterminacy—One Kind of Credence. Erkenntnis:1-18.
Similar books and articles
Michael Kohlhase (1999). Higher-Order Multi-Valued Resolution. Journal of Applied Non-Classical Logics 9 (4):455-477.
Yaroslav Shramko & Heinrich Wansing (2006). Hyper-Contradictions, Generalized Truth Values and Logics of Truth and Falsehood. Journal of Logic, Language and Information 15 (4):403-424.
J. Michael Dunn (2000). Partiality and its Dual. Studia Logica 66 (1):5-40.
Josep Maria Font (2009). Taking Degrees of Truth Seriously. Studia Logica 91 (3):383 - 406.
Jean-Yves Béziau (2006). Many-Valued and Kripke Semantics. In. In Johan van Benthem, Gerhard Heinzman, M. Rebushi & H. Visser (eds.), The Age of Alternative Logics. Springer. 89--101.
A. Avron (2009). Multi-Valued Semantics: Why and How. Studia Logica 92 (2):163 - 182.
Yaroslav Shramko & Heinrich Wansing (2005). Some Useful 16-Valued Logics: How a Computer Network Should Think. [REVIEW] Journal of Philosophical Logic 34 (2):121 - 153.
João Marcos (2009). What is a Non-Truth-Functional Logic? Studia Logica 92 (2):215 - 240.
Added to index2010-02-18
Total downloads41 ( #34,844 of 1,088,372 )
Recent downloads (6 months)1 ( #69,449 of 1,088,372 )
How can I increase my downloads?