CLASSICAL AND QUANTUM LOGICS: TEST SPACES, BOOLEAN ALGEBRAS, AND ORTHOALGEBRAS

Abstract

In this paper, the connections between classical propositional logic and Boolean algebras are explored. Then, an introduction to quantum logic explains that the distributive property does not hold, which gives rise to the need for a different structure for quantum logic. One of these systems, algebraic test spaces, is described, along with their connection to orthoalgebras, which are also analyzed.