eq-logics with delta connective

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.