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

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Authors:
Carles Noguera
Francesc Esteva
Joan Gispert
Title: On triangular norm based axiomatic extensions of the weak nilpotent minimum logic
Journal: Mathematical Logic Quarterly
Volume 54
Number 4
Pages: 387 - 409
Year: 2008
Preprint




Abstract

In 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 this logic, the variety of WNM-algebras (WNM) and we 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 study their standard completeness properties. We also characterize the generic WNM-chains, i.e. those that generate the variety WNM, and we give finite axiomatizations for some t-norm based extensions of WNM.