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With this chapter we provide a compact yet complete survey of two most remarkable “representation theorems”: every arguesian projective geometry is represented by an essentially unique vector space, and every arguesian Hilbert geometry is represented by an essentially unique generalized Hilbert space. C. Piron’s original representation theorem for… (More)

We show that the natural mathematical structure to describe a physical entity by means of its states and its properties within the Geneva-Brussels approach is that of a state property system. We prove that the category of state property systems (and morphisms), SP, is equivalent to the category of closure spaces (and continuous maps), Cls. We show the… (More)

Three of the traditional quantum axioms (orthocomplementation, orthomodularity and the covering law) show incompatibilities with two products introduced by Aerts for the description of joint entities. Inspired by Solèr’s theorem and Holland’s AUG axiom, we propose a property of ‘plane transitivity’, which also characterizes classical Hilbert spaces among… (More)

- Diederik Aerts, Eva Colebunders, A. Van der Voorde, B. Van Steirteghem
- Applied Categorical Structures
- 2002

State property systems were created on the basis of physical intuition in order to describe a mathematical model for physical systems. A state property system consists of a triple: a set of states, a complete lattice of properties and a specified function linking the other two components. The definition of morphisms between such objects was inspired by the… (More)

Three of the traditional quantum axioms (orthocomplementation, orthomodularity and the covering law) show incompatibilities with two products introduced by Aerts for the description of joint entities. Inspired by Solèr’s theorem and Holland’s AUG axiom, we propose a property of ‘plane transitivity’, which also characterizes classical Hilbert spaces among… (More)

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