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On triangular norm based axiomatic extensions of the weak nilpotent minimum logic

AuthorsNoguera, Carles CSIC ORCID; Esteva, Francesc CSIC ORCID ; Gispert, Joan
KeywordsWeak nilpotent minimum logic
Substructural logic
Residuated lattice
Non-classical logic
Algebraic logic
Fuzzy logic
Left-continuous t-norm
Mathematical fuzzy logic
Monoidal triangular norm based logic
Nilpotent minimum logic
Issue Date2008
PublisherJohn Wiley & Sons
CitationMathematical Logic Quarterly 54: 387- 409 (2008)
AbstractIn this paper we carry out an algebraic investigation of the weak nilpotent minimum logic (WNM) and its t-norm based axiomatic extensions. We consider the algebraic counterpart of WNM, the variety of WNM-algebras (double-struck Wdouble-struck Ndouble-struck M) and prove that it is locally finite, so all its subvarieties are generated by finite chains. We give criteria to compare varieties generated by finite families of WNM-chains, in particular varieties generated by standard WNM-chains, or equivalently t-norm based axiomatic extensions of WNM, and we study their standard completeness properties. We also characterize the generic WNM-chains, i. e. those that generate the variety double-struck Wdouble-struck Ndouble-struck M, and we give finite axiomatizations for some t-norm based extensions of WNM. © 2008 Wiley-VCH Verlag GmbH & Co. KGaA.
Identifiersdoi: 10.1002/malq.200710054
issn: 0942-5616
Appears in Collections:(IIIA) Artículos
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