On some Simplifications of the Axiomatization of Monoidal Logic
The class of t-norms has gained central importance in considerations on fuzzy sets as well as in fuzzy logic, mainly because they are natural candidates for non-idempotent conjunction and intersection operations.
For an inferential, and therefore syntactical treatment of such t-norm based conjunction connectives one needs an axiomatic basis, either for some particular t-norm, or preferably for whole classes of t-norms. Monoidal logic was a first attempt to find a logical calculus designed to handle the case of left continuous t-norms. Here its axiomatization shall be simplified and transformed in such a way that it becomes easy to compare monoidal logic syntactically with other, more recent systems for the treatment of t-norm based logics.
KeywordsResiduated Lattice Axiom System Fuzzy Subset Axiom Schema Truth Degree
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