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A Model Theoretic Semantics for Quantum Logic

Published online by Cambridge University Press:  28 February 2022

E.-W. Stachow
E.-W. Stachow*
Affiliation:
Institut für Theoretische Physik Universität zu Köln, Köln, W.-Germany
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Extract

The purpose of this contribution is to consider a model theoretic semantics of quantum logic. The quantum logic to which we refer here comprises the system of sequential quantum logic (Stachow 1980b). This system establishes the implication relation with respect to logically connected propositions and also with respect to the more general class of sequentially connected propositions of the language of quantum physics.

A dialogic semantics for logically connected sentences is developed in Stachow (1976, p. 203), where it is shown that a logical system, usually called the system of quantum logic, is complete and sound with respect to the dialogic semantics. The dialogic semantics is extended to sequentially connected sentences in Stachow (1980b) and to modal sentences in Mittelstaedt (1979, p. 479).

In comparison with other approaches to a language for science, the dialogic approach is developed from a pragmatic and methodological point of view (Stachow 1980a).

Type
Part IX. The Cat Paradox and Quantum Logic
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1980 , Issue 1: Volume One: Contributed Papers 1980 , 1980 , pp. 272 - 280
Copyright
Copyright © 1980 by the Philosophy of Science Association

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References

Mittelstaedt, P. (1979). “The Modal Logic of Quantum Logic.” Journal of Philosophical Logic 8: 479–504.CrossRefGoogle Scholar
Stachow, E.-W. (1976). “Completeness of Quantum Logic:” Journal of Philosophical Logic 5: 237–280. (As reprinted in C.A. Hooker (ed.). (1979). Physical Theory as Logico-Operational Structure. Dordrecht: D. Reidel. Pages 203–243.)CrossRefGoogle Scholar
Stachow, E.-W. (1980a). “On a Game-Theoretical Approach to a Scientific Language.” In PSA 1978, Vol. 2. Edited by Asquith, P.D. & Hacking, Ian. East Lansing: Philosophy of Science Association. Forthcoming.Google Scholar
Stachow, E.-W. (1980b). “On the Logical Foundation of Quantum Mechanics.” International Journal of Theoretical Physics. Forthcoming.CrossRefGoogle Scholar
van Fraassen, B.C. (1971). Formal Semantics and Logic. New York: Macmillan Company.Google Scholar