Equivalencies, Identities, Symmetric Differences, and Congruencies in Orthomodular Lattices |
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Authors: | Norman D. Megill Mladen Pavičić |
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Affiliation: | (1) Boston Information Group, Belmont, MA, 02478, U.S.A.;(2) Gradjevinski fakultet, University of Zagreb, Kaieva 26, HR-10001 Zagreb, Croatia |
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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. |
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Keywords: | quantum logic orthomodular lattice quantum identity equivalence relation congruence relation symmetric difference |
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