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Entailment and Quantum Logic

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Current Issues in Quantum Logic

Abstract

Let L be an orthomodular lattice (OML). It is well-known that there is no operation → definable in terms of lattice operations such that → satisfies most of the desirable conditions for a non-modal implication.5 Some authors have come to the conclusion that perhaps the implication in quantum logic must be treated as the relation ≤ in L.4

This paper has been written under a contract of the first two authors and the Republic Fund for Scientific Work of Serbia.

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References

  1. A.R. Anderson and N.D. Belnap Jr., “Entailment: the Logic of Relevance and Necessity, Vol. I”, Princeton University Press (1975).

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  2. G.N. Georgacarakos, Orthomodularity and Relevance, J. Philos. Logic 8 (1979), pp. 415–432.

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  3. G. Gratzer, “Universal Algebra”, Van Nostrand (1968).

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  4. R.J. Greechie and S.P. Gudder, Quantum logics, “Research in the Foundations and Philosophy of Quantum Theory”, C.A. Hooker ed. Reidei, Dordrecht (1974).

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  5. G.M. Hardegree, The conditional in abstract and concrete quantum logic, in “Logico-Algebraic Approach to Quantum Mechanics, Vol. II”, C.A. Hooker ed.. Reidei, Dordrecht (1979), pp. 49–108.

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© 1981 Plenum Press, New York

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Kron, A., Maric, Z., Vujosevic, S. (1981). Entailment and Quantum Logic. In: Beltrametti, E.G., van Fraassen, B.C. (eds) Current Issues in Quantum Logic. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3228-2_14

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  • DOI: https://doi.org/10.1007/978-1-4613-3228-2_14

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-3230-5

  • Online ISBN: 978-1-4613-3228-2

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