کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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389317 | 661129 | 2016 | 27 صفحه PDF | دانلود رایگان |
In a seminal paper Esteva and Godo introduced monoidal t-norm-based logic MTL and some of its prominent extensions such as NM and WNM. We notice that NM is axiomatisable from IMTL, and hence MTL, with one-variable axioms, by instantiating the WNM axiom over one variable. This observation leads us here to study the logic axiomatised by extending MTL by this one-variable axiom. We shall refer to its equivalent algebraic semantics as the variety of GHP-algebras, for those algebras will be shown to form the largest variety of MTL-algebras such that the falsum-free reducts of the positive cones of their chains are the most general totally ordered Gödel hoops. Among other results we obtain a general description of GHP standard algebras, and use the latter to characterise those extensions of WNM that can be obtained from GHP via the same set of extending axioms.
Journal: Fuzzy Sets and Systems - Volume 292, 1 June 2016, Pages 5–31