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.

کلیدواژه ها:

EQ-algebra ، EQ-logic ، Equational logic ، Delta connective ، Generalized deduction theorem