On some questions concerning the axiomatisation of WNM-algebras and their subvarieties

详细信息    查看全文

• 作者：Stefano Aguzzoli ^{aguzzoli@di.unimi.it" class="auth_mail" title="E-mail the corresponding author} ; Matteo Bianchi ; ^{matteo.bianchi@unimi.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Many-valued logics ; MTL ; Weak Nilpotent Minimum ; Nilpotent Minimum ; t-Norms ; Axiomatisation of varieties
• 刊名：Fuzzy Sets and Systems
• 出版年：2016
• 出版时间：1 June 2016
• 年：2016
• 卷：292
• 期：Complete
• 页码：5-31
• 全文大小：4184 K

文摘

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.