Name
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 WNM, the variety of WNM-algebras (WNM) 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 WNM, and we give finite axiomatizations for some t-norm based extensions of WNM. (c) 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1002/malq.200710054 | MATHEMATICAL LOGIC QUARTERLY |
Keywords | Field | DocType |
algebraic logic,fuzzy logic,left-continuous t-norm,mathematical fuzzy logic,monoidal triangular norm based logic,MTL-algebra,nilpotent minimum logic,non-classical logic,residuated lattice,substructural logic,variety,weak nilpotent minimum logic,WNM-algebra | Algebraic sentence,Discrete mathematics,Combinatorics,Non-classical logic,Axiom,Algebraic logic,Predicate functor logic,Intermediate logic,Completeness (order theory),Mathematics,Nilpotent | Journal |
Volume | Issue | ISSN |
54 | 4 | 0942-5616 |
Citations | PageRank | References |
17 | 0.87 | 13 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Carles Noguera | 1 | 462 | 33.93 |
| Francesc Esteva | 2 | 1885 | 200.14 |
| Joan Gispert | 3 | 260 | 17.82 |