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On strong standard completeness in some MTL Δ expansions

AuthorsVidal, Amanda; Bou, Felix; Esteva, Francesc ; Godo, Lluis
KeywordsMonoidal t-norm logic
Standard completeness
Infinitary rules
Left-continuous t-norms
Mathematical fuzzy logic
Issue Date2017
CitationSoft Computing 21: 125- 147 (2017)
AbstractIn this paper, inspired by the previous work of Franco Montagna on infinitary axiomatizations for standard BL-algebras, we focus on a uniform approach to the following problem: given a left-continuous t-norm ∗ , find an axiomatic system (possibly with infinitary rules) which is strongly complete with respect to the standard algebra [InlineEquation not available: see fulltext.] This system will be an expansion of Monoidal t-norm-based logic. First, we introduce an infinitary axiomatic system L∗∞, expanding the language with Δ and countably many truth constants, and with only one infinitary inference rule, that is inspired in Takeuti–Titani density rule. Then we show that L∗∞ is indeed strongly complete with respect to the standard algebra [InlineEquation not available: see fulltext.]. Moreover, the approach is generalized to axiomatize expansions of these logics with additional operators whose intended semantics over [0, 1] satisfy some regularity conditions. © 2016, Springer-Verlag Berlin Heidelberg.
Identifiersdoi: 10.1007/s00500-016-2338-0
issn: 1432-7643
e-issn: 1433-7479
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