Abstract
In this paper we continue development of formal theory of a special class offuzzy logics, called EQ-logics. Unlike fuzzy logics being extensions of theMTL-logic in which the basic connective is implication, the basic connective inEQ-logics is equivalence. Therefore, a new algebra of truth values calledEQ-algebra was developed. This is a lower semilattice with top element endowed with two binaryoperations of fuzzy equality and multiplication. EQ-algebra generalizesresiduated lattices, namely, every residuated lattice is an EQ-algebra but notvice-versa.In this paper, we introduce additional connective $logdelta$ in EQ-logics(analogous to Baaz delta connective in MTL-algebra based fuzzy logics) anddemonstrate that the resulting logic has again reasonable properties includingcompleteness. Introducing $Delta$ in EQ-logic makes it possible to prove alsogeneralized deduction theorem which otherwise does not hold in EQ-logics weakerthan MTL-logic.
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