In this paper we study Weak Nilpotent Minimum t-norms and their associated algebraic structures, the standard WNM-chains. We classify all the varieties generated by one standard WNM-chain, obtaining all the axiomatic extensions of WNM logic that are complete with respect to the semantics given by a left-continuous t-norm. To this end, we define a set of canonical standard WNM-chains and we prove that they generate pairwise different varieties and there are no other varieties generated by a standard WNM-chain.
Noguera, C., Esteva, F., Gispert, J. (2005). On varieties generated by weak nilpotent minimum t-norms. In Proceedings - 4th Conference of the European Society for Fuzzy Logic and Technology and 11th French Days on Fuzzy Logic and Applications, EUSFLAT-LFA 2005 Joint Conference (pp.866-871).
On varieties generated by weak nilpotent minimum t-norms
Noguera C.
;
2005-01-01
Abstract
In this paper we study Weak Nilpotent Minimum t-norms and their associated algebraic structures, the standard WNM-chains. We classify all the varieties generated by one standard WNM-chain, obtaining all the axiomatic extensions of WNM logic that are complete with respect to the semantics given by a left-continuous t-norm. To this end, we define a set of canonical standard WNM-chains and we prove that they generate pairwise different varieties and there are no other varieties generated by a standard WNM-chain.
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https://hdl.handle.net/11365/1200779