Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License.
 adjective mathematics Describing a
lattice that is both orthocomplemented andmodular
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Examples

Let L be a complete, atomic, irreducible orthomodular lattice satisfying the atomic covering law.
Puppet X: 1 2009

Î will inherit from L the structure of a complete lattice, which will then automatically be orthomodular by Lemma 4.3.
Puppet X: 1 2009

In other words, in such cases we have only one logic, which is a complete orthomodular lattice.
Puppet X: 1 2009

Thus, orthomodular posets (the framework for Mackey's version of quantum logic) are equivalent to orthocoherent orthoalgebras.
Puppet X: 1 2009

This is not generally an orderisomorphism, but when it is, we obtain a complete orthomodular lattice, and thus come a step closer to the projection lattice of a Hilbert space.
Puppet X: 1 2009

Let us call a complete orthomodular lattice satisfying the hypotheses of Piron's theorem a Piron lattice.
Puppet X: 1 2009

Conversely, an orthocomplemented poset is orthomodular iff
Puppet X: 1 2009

V with L (V) orthomodular, is necessarily complete.
Puppet X: 1 2009

The lemma tells us that every orthocoherent orthoalgebra is, inter alia, an orthomodular poset.
Puppet X: 1 2009

Mackey presents a sequence of six axioms, framing a very conservative generalized probability theory, that underwrite the construction of a ˜logic™ of experimental propositions, or, in his terminology, ˜questions™, having the structure of a sigmaorthomodular poset.
Puppet X: 1 2009
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