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Tensor products of \(D\)-posets and \(D\)-test spaces. (English) Zbl 0830.03031
A \(D\)-poset (or a difference poset) is a poset \(L\) with the greatest element 1 and a partial binary operation \(\ominus: L\times L\to L\) such that \(b\ominus a\) is defined iff \(a\leq b\) and, for \(a,b, c\in L\), we have (i) \(b\ominus a\leq b\); (ii) \((b\ominus (b\ominus a))=a\); (iii) if \(a\leq b\leq c\), then \(c\ominus b\leq c\ominus a\) and \((c\ominus a) \ominus (c\ominus b)= b\ominus a\). For any \(D\)-poset, there exists a \(D\)- test space [the authors, Rep. Math. Phys. 34, 151-170 (1994; Zbl 0820.03038)]. Using this representation, a tensor product and a state tensor product of \(D\)-posets is introduced and studied, and some examples are presented.

MSC:
03G12 Quantum logic
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
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