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01-01-2014 | Foundations
An algebraic axiomatization of orthogonal posets
Published in: Soft Computing | Issue 1/2014
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Abstract
The so-called orthogonal posets form an important tool for some investigations in the logic of quantum mechanics because they can be recognized as so-called quantum structures. The motivation for studying quantum structures is included e.g. in the monograph by Dvurečenskij and Pulmannová or in the papers by Beltrametti and Maczyński. It is shown that every space of numerical events [see Chajda and Länger (Intern J Theor Phys 50:2403, 2011b), Dorninger and Länger (Intern J Theor Phys 52:1141–1147, 2013) and references therein] forms an orthogonal poset. Hence, orthogonal posets should be axiomatized by standard algebraic machinery. However, considering supremum as a binary operation, they form only partial algebras. The aim of the paper is to involve a different way which enables us to describe orthogonal posets as total algebras and get an algebraic axiomatization as an equational theory.