Abstract
It is shown that the identity rule — arule of inference which has the form of modus ponens butwith the operation of identity substituted for theoperation of implication — turns any ortholatticeinto either an orthomodular lattice (a model of a quantumtheory) or a distributive lattice (a model of aclassical theory). It is also shown that — asopposed to the implication algebras — one cannotconstruct an identity algebra although the identity rule contains theoperation of identity as the only operation.
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Pavicic, M. Identity Rule for Classical and Quantum Theories. International Journal of Theoretical Physics 37, 2099–2103 (1998). https://doi.org/10.1023/A:1026637918703
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DOI: https://doi.org/10.1023/A:1026637918703