Generalized possibilistic theories: the multipartite experiments problem

• Published in: Quantum Studies : Mathematics and Foundations Vol. 10; no. 4; pp. 443 - 482
• Main Author: Buffenoir, Eric
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.11.2023; Springer Nature B.V; Springer
• Subjects: General Mathematics; History and Philosophical Foundations of Physics; Mathematical analysis; Mathematical and Computational Physics; Mathematical Physics; Mathematics; Mathematics and Statistics; Physics; Quantum Physics; Quantum theory; Regular Paper; Tensors; Theoretical; Orders; 18B35; Quantum logic (quantum-theoretic aspects)/ Categorical semantics of formal languages / Preorders; Domains and lattices (viewed as categories); 81P10; Logical foundations of quantum mechanics; 18C50; domains and lattices (viewed as categories); orders
• ISSN: 2196-5609; 2196-5617
• DOI: 10.1007/s40509-023-00306-3

In a recent paper, the author introduced an operational description of physical theories where probabilities are replaced by counterfactual statements belonging to a three-valued (i.e., possibilistic) semantic domain. The complete axiomatic of these generalized possibilistic theories is generalized and clarified in the present paper. The problem of bipartite experiments is then addressed as the main skill of this paper. An axiomatic for the tensor product of our spaces of states is given and different solutions are explicitly constructed. This description of tensor products of Inf semi-lattices is partly independent from the usual mathematical description of this problem. The nature of the tensor product of ortho-complemented Inf semi-lattices is then also explored. This subject is indeed fundamental for the development of a reconstruction program for quantum theory within our framework. Our analysis constitutes a first step toward this achievement.