Displaying similar documents to “Orthomodular Posets Can Be Organized as Conditionally Residuated Structures”

Pseudocomplemented and Stone Posets

Ivan Chajda (2012)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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We show that every pseudocomplemented poset can be equivalently expressed as a certain algebra where the operation of pseudocomplementation can be characterized by means of remaining two operations which are binary and nullary. Similar characterization is presented for Stone posets.

Orthomodular lattices with state-separated noncompatible pairs

R. Mayet, Pavel Pták (2000)

Czechoslovak Mathematical Journal

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In the logico-algebraic foundation of quantum mechanics one often deals with the orthomodular lattices (OML) which enjoy state-separating properties of noncompatible pairs (see e.g. , and ). These properties usually guarantee reasonable “richness” of the state space—an assumption needed in developing the theory of quantum logics. In this note we consider these classes of OMLs from the universal algebra standpoint, showing, as the main result, that these classes form quasivarieties....