Current Research in Operational Quantum Logic pp 81-114 | Cite as

# Test Spaces and Orthoalgebras

## Abstract

In a long series of papers published in the 1970s and early 1980s, D. J. Foulis and C. H. Randall developed a conceptually simple, but very compelling semantics for quantum logics and otherwise based on the notion of a *manual* or, in more recent usage, a *test space*. A test space is a collection A of non-empty sets, taken to represent the sets of outcomes associated with some collection of measurements, experiments or *tests*. Subject to a fairly mild constraint, one can construct from a test space A a “logic” II(A) having the structure of an orthoalgebra. All orthoalge-bras arise via this construction. This paper surveys gives an up-to-date survey of the theory of test spaces and orthoalgebras, including a discussion of recent work of the author on group actions on test spaces.

## Keywords

Hilbert Space Complete Lattice Effect Algebra Quantum Logic Central Support## Preview

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