Quasi-implication Algebras
نویسندگان
چکیده
A quasi-implication algebra is introduced as an algebraic counterpart of an implication reduct of propositional logic having noninvolutory negation (e.g. intuitionistic logic). We show that every pseudocomplemented semilattice induces a quasi-implication algebra (but not conversely). On the other hand, a more general algebra, a so-called pseudocomplemented q-semilattice is introduced and a mutual correspondence between this algebra and a quasi-implication algebra is shown.
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Quantum Implication Algebras
Quantum implication algebras without complementation are formulated with the same axioms for all five quantum implications. Previous formulations of orthoimplication, orthomodular implication , and quasi-implication algebras are analysed and put in perspective to each other and our results.
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