Displaying similar documents to “Orthomodular lattices with state-separated noncompatible pairs”

Hypersubstitutions in orthomodular lattices

Ivan Chajda, Helmut Länger (2001)

Discussiones Mathematicae - General Algebra and Applications

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It is shown that in the variety of orthomodular lattices every hypersubstitution respecting all absorption laws either leaves the lattice operations unchanged or interchanges join and meet. Further, in a variety of lattices with an involutory antiautomorphism a semigroup generated by three involutory hypersubstitutions is described.

Orthocomplemented difference lattices with few generators

Milan Matoušek, Pavel Pták (2011)

Kybernetika

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The algebraic theory of quantum logics overlaps in places with certain areas of cybernetics, notably with the field of artificial intelligence (see, e. g., [19, 20]). Recently an effort has been exercised to advance with logics that possess a symmetric difference ([13, 14]) - with so called orthocomplemented difference lattices (ODLs). This paper further contributes to this effort. In [13] the author constructs an ODL that is not set-representable. This example is quite elaborate. A...

Orthomodular lattices with fully nontrivial commutators

Milan Matoušek (1992)

Commentationes Mathematicae Universitatis Carolinae

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An orthomodular lattice L is said to have fully nontrivial commutator if the commutator of any pair x , y ∈ L is different from zero. In this note we consider the class of all orthomodular lattices with fully nontrivial commutators. We show that this class forms a quasivariety, we describe it in terms of quasiidentities and situate important types of orthomodular lattices (free lattices, Hilbertian lattices, etc.) within this class. We also show that the quasivariety in question is not a variety...

Symmetric difference on orthomodular lattices and Z 2 -valued states

Milan Matoušek, Pavel Pták (2009)

Commentationes Mathematicae Universitatis Carolinae

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The investigation of orthocomplemented lattices with a symmetric difference initiated the following question: Which orthomodular lattice can be embedded in an orthomodular lattice that allows for a symmetric difference? In this paper we present a necessary condition for such an embedding to exist. The condition is expressed in terms of Z 2 -valued states and enables one, as a consequence, to clarify the situation in the important case of the lattice of projections in a Hilbert space. ...