Name
Abstract | ||
|---|---|---|
It is well known that MTL satisfies the finite embeddability property. Thus MTL is complete w.r.t. the class of all finite MTL-chains. In order to reach a deeper understanding of the structure of this class, we consider the extensions of MTL by adding the generalized contraction since each finite MTL-chain satisfies a form of this generalized contraction. Simultaneously, we also consider extensions of MTL by the generalized excluded middle laws introduced in [9] and the axiom of weak cancellation defined in [31]. The algebraic counterpart of these logics is studied characterizing the subdirectly irreducible, the semisimple, and the simple algebras. Finally, some important algebraic and logical properties of the considered logics are discussed: local finiteness, finite embeddability property, finite model property, decidability, and standard completeness. (c) 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1002/malq.200610044 | MATHEMATICAL LOGIC QUARTERLY |
Keywords | Field | DocType |
algebraic logic,fuzzy logics,generalized contraction,generalized excluded middle,left-continuous t-norms,MTL-algebras,non-classical logics,residuated lattices,standard completeness,substructural logics,varieties,weak cancellation | Discrete mathematics,Locally finite collection,Algebraic number,Finite model property,Algebra,Axiom,Fuzzy logic,Algebraic logic,Decidability,Completeness (statistics),Mathematics | Journal |
Volume | Issue | ISSN |
53 | 3 | 0942-5616 |
Citations | PageRank | References |
19 | 1.00 | 18 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Rostislav Horcík | 1 | 50 | 6.41 |
| Carles Noguera | 2 | 462 | 33.93 |
| Milan Petrik | 3 | 19 | 1.34 |