Non-commutative first-order EQ-logics

摘要

EQ-algebras are meet semilattices endowed with two additional binary operations: fuzzy equality and multiplication. These algebras serve as a basic algebraic structure of truth values for many-valued logics based on (fuzzy) equality instead of implication. Therefore, they generalize residuated lattices in the sense that each residuated lattice is an EQ-algebra but not vice-versa.