The rotation of the product t-norm provides the tool to show that Łukasiewicz logic cannot be axiomatised as an extension of MTL by means of any set of axioms with at most one variable. As a corollary, also BL cannot be axiomatised from MTL by means of single-variable axioms.
A note on minimal axiomatisations of some extensions of MTL / S. Aguzzoli, A.R. Ferraioli, B. Gerla. - In: FUZZY SETS AND SYSTEMS. - ISSN 0165-0114. - 242(2014 May), pp. 148-153. [10.1016/j.fss.2013.09.012]
A note on minimal axiomatisations of some extensions of MTL
S. Aguzzoli;
2014
Abstract
The rotation of the product t-norm provides the tool to show that Łukasiewicz logic cannot be axiomatised as an extension of MTL by means of any set of axioms with at most one variable. As a corollary, also BL cannot be axiomatised from MTL by means of single-variable axioms.
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