Quantum Set Theory
Citations
152 citations
Cites background from "Quantum Set Theory"
...For let P and Q be propositions, represented by the subsets SP and (24)If the distributive law is dropped we could move towards the quantum-set ideas of [71]; or, perhaps, the ideas of non-commutative geometry instigated by Alain Connes [14]....
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...For example, Baez’s advocation of n-categories [5, 6]; ‘categorial quantum theory’ [2, 73]; Takeuti’s theory(19) of ‘quantum sets’ [71]; and Crane’s work on categorial models of space-time [17]....
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129 citations
81 citations
Cites methods from "Quantum Set Theory"
...This allows us to use rich mathematical methods developed in Birkhoff-von Neumann quantum logic [17] and Takeuti’s quantum set theory [96]....
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52 citations
Cites background or methods from "Quantum Set Theory"
...Furthermore, Titani and Kozawa [74] provided a representation of unitary operators by complex numbers in V P (H)....
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...Thus, a potential way of establishing link between these quantum automata and our orthomodular lattice-valued automata is to use Takeuti, Titani and Kozawa’s representation of observables and unitary operators by real and complex numbers in the universe V P (H) of quantum set theory, where P (H) is the orthomodular lattice of closed linear subspaces of a Hilbert space H [71, 74]....
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...Kozawa [74] with a strong implication corresponding to the order in the lattice of truth values....
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49 citations
References
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