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On the extension of classical propositional logic by means of a triangular norm
Author(s) -
de Cooman G.,
Kerre E. E.,
Cappelle B.,
Da Ruan,
Vanmassenhove F.
Publication year - 1990
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.4550050307
Subject(s) - monoidal t norm logic , extension (predicate logic) , t norm fuzzy logics , mathematics , intermediate logic , many valued logic , truth function , zeroth order logic , propositional calculus , classical logic , discrete mathematics , łukasiewicz logic , intuitionistic logic , conservative extension , algebra over a field , logical connective , propositional variable , well formed formula , dynamic logic (digital electronics) , substructural logic , pure mathematics , computer science , description logic , multimodal logic , fuzzy logic , theoretical computer science , artificial intelligence , fuzzy number , programming language , transistor , voltage , quantum mechanics , fuzzy set , physics
In this article, we introduce a generalized extension principle by substituting a more general triangular norm T for the min intersection operator in Zadeh's extension principle. We also introduce a family of propositional logics, sup‐ T extension logics, obtained by the extension of classical‐logical functions. A few general properties of these sup‐ T extension logics are derived. It is also shown that classical binary logic and the Kleene ternary logic are special cases of these logics for any choice of T , obtained by a convenient restriction of the truth domain. the very practical decomposability property of classical logic is furthermore shown to hold for the sup‐min extension logic, albeit in a somewhat more limited form.