orthomodular

Definitions

adjective mathematics Describing a lattice that is both orthocomplemented and modular

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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 order-isomorphism, 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 sigma-orthomodular poset.

Puppet X: 1 2009