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Quantum and Classical Implication Algebras with Primitive Implications

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Abstract

Join in an orthomodular lattice is obtained inthe same form for all five quantum implications. Theform holds for the classical implication in adistributive lattice as well. Even more, the definition added to an ortholattice makes it orthomodularfor quantum implications and distributive for theclassical one. Based on this result a quantumimplication algebra with a single primitive — andin this sense unique — implication is formulated. Acorresponding classical implication algebra is alsoformulated. The algebras are shown to be special casesof a universal implication algebra.

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Authors
  1. Mladen Pavicic
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  2. Norman D. Megill
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Pavicic, M., Megill, N.D. Quantum and Classical Implication Algebras with Primitive Implications. International Journal of Theoretical Physics 37, 2091–2098 (1998). https://doi.org/10.1023/A:1026685801864

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  • DOI: https://doi.org/10.1023/A:1026685801864

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