dorsal/arxiv
View SchemaEquivalences, Identities, Symmetric Differences, and Congruences in Orthomodular Lattices
| Authors | Norman D. Megill, Mladen Pavicic |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0310063 |
| URL | https://arxiv.org/abs/quant-ph/0310063 |
| DOI | 10.1023/B:IJTP.0000006006.18494.1c |
| Journal | International Journal of Theoretical Physics, Vol. 42, No. 12, 2797-2805 (2003). |
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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"abstract": "It is shown that operations of equivalence cannot serve for building algebras\nwhich would induce orthomodular lattices as the operations of implication can.\nSeveral properties of equivalence operations have been investigated.\nDistributivity of equivalence terms and several other 3 variable expressions\ninvolving equivalence terms have been proved to hold in any orthomodular\nlattice. Symmetric differences have been shown to reduce to complements of\nequivalence terms. Some congruence relations related to equivalence operations\nand symmetric differences have been considered.",
"arxiv_id": "quant-ph/0310063",
"authors": [
"Norman D. Megill",
"Mladen Pavicic"
],
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"doi": "10.1023/B:IJTP.0000006006.18494.1c",
"journal_ref": "International Journal of Theoretical Physics, Vol. 42, No. 12,\n 2797-2805 (2003).",
"title": "Equivalences, Identities, Symmetric Differences, and Congruences in Orthomodular Lattices",
"url": "https://arxiv.org/abs/quant-ph/0310063"
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