On the standard and rational completeness of some axiomatic extensions of the monoidal t-norm logic

被引：86

作者：

Esteva F. ^{[1
]}

Gispert J. ^{[1
,3
]}

Godo L. ^{[1
]}

Montagna F. ^{[2
]}

机构：

[1] Institut d'Investigació en Intel Ligencia Artificial - CSIC, Campus Univ. Autònoma de Barcelona s/n

[2] Dipartamento de Matematica, Università degli Studi di Siena, 53100 Siena

[3] Facultat de Matemàtiques, Universitat de Barcelona

来源：

Studia Logica | 2002年 / 71卷 / 2期

关键词：

Finite strong completeness; Fuzzy logic; Rational embedding property; Real embedding property; Standard completeness;

D O I：

10.1023/A:1016548805869

中图分类号：

学科分类号：

摘要：

The monoidal t-norm based logic MTL is obtained from Hájek 's Basic Fuzzy logic BL by dropping the divisibility condition for the strong (or monoidal) conjunction. Recently, Jenei and Montgana have shown MTL to be standard complete, i.e. complete with respect to the class of residuated lattices in the real unit interval [0,1] defined by left-continuous t-norms and their residua. Its corresponding algebraic semantics is given by pre-linear residuated lattices. In this paper we address the issue of standard and rational completeness (rational completeness meaning completeness with respect to a class of algebras in the rational unit interval [0,1]) of some important axiomatic extensions of MTL corresponding to well-known parallel extensions of BL. Moreover, we investigate varieties of MTL algebras whose linearly ordered countable algebras embed into algebras whose lattice reduct is the real and/or the rational interval [0,1]. These embedding properties are used to investigate finite strong standard and/or rational completeness of the corresponding logics. © 2002 Kluwer Academic Publishers.

引用

页码：199 / 226

页数：27

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