Orthomodular Lattices

By Elzbieta Madra, Adam Grabowski. Formalized Mathematics, 2008

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Orthomodular Lattices The main result of the article is the solution to the problem of short axiomatizations of orthomodular ortholattices. Based on EQP/Otter results [10], we gave a set of three equations which is equivalent to the classical, much longer equational basis of such a class. Also the basic example of the lattice which is not orthomodular, i.e. benzene (or B6) is defined in two settings - as a relational structure (poset) and as a lattice. As a preliminary work, we present the proofs of the dependence of other axiomatizations of ortholattices. The formalization of the properties of orthomodular lattices follows [4].

Subfields: Computational Theory and Mathematics, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/3fe7623a8c5b3ad26a8b6d845aa6763ba0e1c850