Reports on Mathematical Logic

No. 43

Wojciech DZIK

Unification in some Substructural Logics of BL-algebras and Hoops

A b s t r a c t. It is shown that substructural logics of $k$-potent BL-algebras and $k$-potent hoops have unitary unification (in fact, transparent unifiers) while Basic Fuzzy Logic, BL (the logic of BL-algebras), and $\infty$-valued {\L}ukasiewicz logic (the logic of MV-algebras) do not have unitary unification. It follows that every $k$-potent substructural logic containing BL is structurally complete in the restricted sense, but Basic Logic itself is not.

Institute of Mathematics, Silesian University, Katowice, Poland
In Theorem 1(i). The -> in the given formula should be =>.

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