EQ-algebra; EQ-logic; equational logic; delta connective

In this paper, extension of EQ-logic by the delta connective is introduced. The former is a new kind of logic based on EQ-algebra of truth values, i.e. the algebra in which fuzzy equality is the fundamental operation and implication is derived from it. First, we extend the EQ-algebra by the delta operation and then introduce axioms and inference rules of EQ-logic endowed by delta connective. We also prove the deduction theorem formulated using fuzzy equalities.