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PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, 1974
One can and often does use the word ‘logic’ in a variety of metaphorical ways, speaking of “the logic of the situation”, “the logic of events”, “the logic of history”, and so on. No harm is done, so long as one realizes that these usages are metaphorical, and should not be given any deeper significance – at least without extensive discussion of the ...
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One can and often does use the word ‘logic’ in a variety of metaphorical ways, speaking of “the logic of the situation”, “the logic of events”, “the logic of history”, and so on. No harm is done, so long as one realizes that these usages are metaphorical, and should not be given any deeper significance – at least without extensive discussion of the ...
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Foundations of Physics, 1984
The status and justification of quantum logic are reviewed. On the basis of several independent arguments it is concluded that it cannot be a logic in the philosophical sense of a general theory concerning the structure of valid inferences. Taken as a calculus for combining quantum-mechanical propositions, it leaves a number of significant aspects of ...
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The status and justification of quantum logic are reviewed. On the basis of several independent arguments it is concluded that it cannot be a logic in the philosophical sense of a general theory concerning the structure of valid inferences. Taken as a calculus for combining quantum-mechanical propositions, it leaves a number of significant aspects of ...
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The Logic of Quantum Mechanics
The Annals of Mathematics, 1936\glqq Experimentelle Aussagen\grqq{} über den Zustand eines quantenmechanischen Systems haben die Form: \(n\) gegebene gleichzeitig meßbare Größen haben Werte, die mit Sicherheit einer gegebenen Menge \(S\) von Wertsystemen angehören. Im Hilbertschen Raum der Zustandsfunktionen \(\psi\) entspricht jeder experimentellen Aussage ein abgeschlossener ...
Garrett Birkhoff, John von Neumann
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PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, 1974
It has been shown by Birkhoff and v. Neumann (1936) and by Jauch and Piron (1963,1964,1968) that the subspaces of Hilbert space constitute an orthocomplemented quasi-modular lattice Lq, if one considers between two subspaces (elements) a, b the relation a⊆b and the operations a∩b, a∪b, a⊥.
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It has been shown by Birkhoff and v. Neumann (1936) and by Jauch and Piron (1963,1964,1968) that the subspaces of Hilbert space constitute an orthocomplemented quasi-modular lattice Lq, if one considers between two subspaces (elements) a, b the relation a⊆b and the operations a∩b, a∪b, a⊥.
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Quantum logic and linear logic
International Journal of Theoretical Physics, 1994By tradition, the subject of quantum logic is the lattices of closed subspaces of Hilbert spaces or, more abstractly, orthomodular lattices. \textit{D. J. Foulis} showed in Can. J. Math. 17, 40-51 (1965; Zbl 0146.029) that an orthomodular lattice can be coordinatized by a Baer \(*\)- semigroup. On the other hand, \textit{C. J. Mulvey} [Rend. Circ. Math.
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The modal logic of quantum logic
Journal of Philosophical Logic, 1979Modal logic is concerned with the concepts of necessity and possibility and a certain class of object propositions. In this paper we develop the basic concepts of a modal logic which is related to propositions about quantum physical objects. Since the object logic of quantum mechanical propositions is given by the calculi of quantum logic, the ...
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The Conditional in Quantum Logic
Synthese, 1974Besides the physicomathematical controversy concerning the ‘phenomenological justification’ and the specific formal structure of the calculus known as quantum logic (QL), there is a philosophical controversy concerning whether this ‘calculus of experimental propositions’ is properly speaking a logic rather than simply an algebraic structure only ...
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