Displaying similar documents to “Characterizations of nonexpansive multipliers on partially ordered sets”

Quasi-implication algebras

Ivan Chajda, Kamil Dušek (2002)

Discussiones Mathematicae - General Algebra and Applications

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A quasi-implication algebra is introduced as an algebraic counterpart of an implication reduct of propositional logic having non-involutory 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.

Relatively pseudocomplemented posets

Ivan Chajda, Helmut Länger (2018)

Mathematica Bohemica

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We extend the notion of a relatively pseudocomplemented meet-semilattice to arbitrary posets. We show some properties of the binary operation of relative pseudocomplementation and provide some corresponding characterizations. We show that relatively pseudocomplemented posets satisfying a certain simple identity in two variables are join-semilattices. Finally, we show that every relatively pseudocomplemented poset is distributive and that the converse holds for posets satisfying the ascending...