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THE FUNDAMENTAL THEOREM OF ULTRAPRODUCT IN PAVELKA'S LOGIC
Author(s) -
Ying Mingsheng
Publication year - 1992
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.19920380115
Subject(s) - ultraproduct , mathematics , zeroth order logic , discrete mathematics , computer science , multimodal logic , artificial intelligence , description logic
In [This Zeitschrift 25 (1979), 45‐52, 119‐134, 447‐464], Pavelka systematically discussed propositional calculi with values in enriched residuated lattices and developed a general framework for approximate reasoning. In the first part of this paper we introduce the concept of generalized quantifiers into Pavelka's logic and establish the fundamental theorem of ultraproduct in first order Pavelka's logic with generalized quantifiers. In the second part of this paper we show that the fundamental theorem of ultraproduct in first order Pavelka's logic is preserved under some direct product of lattices of truth values.