What difference does it make: Three truth-values or two plus gaps?
type: Item
instance of: scholarly article
title: What difference does it make: Three truth-values or two plus gaps?
zbMATH Open document ID: 1013.03008
DOI: 10.1023/A:1014772016276
author: Katarzyna Kijania-Placek
published in: Erkenntnis
publication date: 2002-10-08T00:00:00Z
review text: A 3-valued logic is called strongly 3-valued iff the equivalence connective (primitive or defined in the classical way) satisfies the property \(v(\alpha \equiv \beta) = 1\) iff \(v(\alpha) = v(\beta)\). A table is called regular if a given column (row) contains a 1 at the \(\square\)-row (column) only if the column (row) consists entirely of 1's, and likewise for 0 (where \(\square\) denotes the third value or gap). A logic is called regular if the tables of all its primitive connectives are regular. The author concludes that Łukasiewicz's logics are strongly 3-valued but lack the feature of monotonicity, which disqualifies them from epistemological applications. However, since the sets of tautologies are never identical to the set of classical tautologies, this provides a promising basis for ontological applications. Kleene's logics are weakly 3-valued logics, but are regular and thus monotonic and as such well suited for epistemological applications.
reviewed by: Albert Hoogewijs
Mathematics Subject Classification ID: 03A05
Mathematics Subject Classification ID: 03B50
zbMATH DE Number: 1812442
zbMATH Keywords: three-valued logic
zbMATH Keywords: Łukasiewicz logic
zbMATH Keywords: Kleene logic
MaRDI profile type: Publication
full work available at URL: a:1014772016276
OpenAlex ID: W223759234
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description: scientific article; zbMATH DE number 1812442