MMN-771
Variety of orthomodular posets
Abstract
Orthomodular posets play an important role in the so-called logical structure of a physical system as formerly pointed out by numerous authors. In particular, they play an essential role in the logic of quantum mechanics. To avoid usual problems with partial algebras, we define the so-called orthomodular directoid as an everywhere defined algebra and we show that every orthomodular poset can be converted into an orthomodular directoid and vice versa. Since orthomodular directoids are defined equationally, they form a variety having nice congruence properties.
Vol. 15 (2014), No. 2, pp. 361-371