A general method for constructing left-continuous t-norms

doi:10.1016/S0165-0114(02)00275-0

2003-06-01

PRE

Sándor Jenei

Franco Montagna

DOI：10.1016/S0165-0114(02)00275-0

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摘要

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A new method for constructing (left-continuous) t-norms is introduced and analyzed in this paper. We shall construct via embedding a left-continuous t-norm from any countable residuated totally and densely ordered commutative integral monoid. Moreover, we can construct a left-continuous t-norm from any countable, totally ordered, commutative integral monoid which is not necessarily densely ordered and residuated. A special case, the embedding of such monoids on lexicographic product spaces is investigated in detail, and several examples are demonstrated. The results shed some light to Chang's MV-algebra, to a recently proposed 'extraordinary' t-norm, and to the standard semantics of the recently introduced logic H-MTL of HJjek. (C) 2002 Elsevier Science B.V. All rights reserved.

Keyword:

residuated lattice

conjunction for non-classical logics

T-norm