Equivalences, Identities, Symmetric Differences, and Congruences in Orthomodular Lattices

Abstract

It is shown that operations of equivalence cannot serve for building algebras which would induce orthomodular lattices as the operations of implication can. Several properties of equivalence operations have been investigated. Distributivity of equivalence terms and several other 3 variable expressions involving equivalence terms have been proved to hold in any orthomodular lattice. Symmetric differences have been shown to reduce to complements of equivalence terms. Some congruence relations related to equivalence operations and symmetric differences have been considered.