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On witnessed models in fuzzy logic II
Author(s) -
Hájek Petr
Publication year - 2007
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200710019
Subject(s) - unary operation , predicate variable , propositional calculus , mathematics , predicate logic , predicate (mathematical logic) , łukasiewicz logic , fuzzy logic , many valued logic , predicate functor logic , discrete mathematics , zeroth order logic , calculus (dental) , arithmetic , algebra over a field , autoepistemic logic , artificial intelligence , computer science , pure mathematics , substructural logic , programming language , description logic , multimodal logic , medicine , dentistry
First the expansion of the Łukasiewicz (propositional and predicate) logic by the unary connectives of dividing by any natural number (Rational Łukasiewicz logic) is studied; it is shown that in the predicate case the expansion is conservative w.r.t. witnessed standard 1‐tautologies. This result is used to prove that the set of witnessed standard 1‐tautologies of the predicate product logic is Π 2 ‐hard. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)