13 found
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  1.  59
    Effect Algebras and Unsharp Quantum Logics.D. J. Foulis & M. K. Bennett - 1994 - Foundations of Physics 24 (10):1331-1352.
    The effects in a quantum-mechanical system form a partial algebra and a partially ordered set which is the prototypical example of the effect algebras discussed in this paper. The relationships among effect algebras and such structures as orthoalgebras and orthomodular posets are investigated, as are morphisms and group- valued measures (or charges) on effect algebras. It is proved that there is a universal group for every effect algebra, as well as a universal vector space over an arbitrary field.
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  2.  76
    Phi-Symmetric Effect Algebras.M. K. Bennett & D. J. Foulis - 1995 - Foundations of Physics 25 (12):1699-1722.
    The notion of a Sasaki projectionon an orthomodular lattice is generalized to a mapping Φ: E × E → E, where E is an effect algebra. If E is lattice ordered and Φ is symmetric, then E is called a Φ-symmetric effect algebra.This paper launches a study of such effect algebras. In particular, it is shown that every interval effect algebra with a lattice-ordered ambient group is Φ-symmetric, and its group is the one constructed by Ravindran in his proof that (...)
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  3.  28
    A Note on Misunderstandings of Piron's Axioms for Quantum Mechanics.D. J. Foulis & C. H. Randall - 1984 - Foundations of Physics 14 (1):65-81.
    Piron's axioms for a realistically interpreted quantum mechanics are analyzed in detail within the context of a formal mathematical structure expressed in the conventional set-theoretic idiom of mathematics. As a result, some of the serious misconceptions that have encouraged recent criticisms of Piron's axioms are exposed.
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  4.  85
    Empirical Logic and Quantum Mechanics.D. J. Foulis & C. H. Randall - 1974 - Synthese 29 (1-4):81 - 111.
  5.  46
    Properties and Operational Propositions in Quantum Mechanics.C. H. Randall & D. J. Foulis - 1983 - Foundations of Physics 13 (8):843-857.
    In orthodox quantum mechanics, it has virtually become the custom to identify properties of a physical system with operationally testable propositions about the system. The causes and consequences of this practice are explored mathematically in this paper. Among other things, it is found that such an identification imposes severe constraints on the admissible states of the physical system.
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  6.  18
    MV and Heyting Effect Algebras.D. J. Foulis - 2000 - Foundations of Physics 30 (10):1687-1706.
    We review the fact that an MV-algebra is the same thing as a lattice-ordered effect algebra in which disjoint elements are orthogonal. An HMV-algebra is an MV-effect algebra that is also a Heyting algebra and in which the Heyting center and the effect-algebra center coincide. We show that every effect algebra with the generalized comparability property is an HMV-algebra. We prove that, for an MV-effect algebra E, the following conditions are mutually equivalent: (i) E is HMV, (ii) E has a (...)
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  7.  45
    Superposition in Quantum and Classical Mechanics.M. K. Bennett & D. J. Foulis - 1990 - Foundations of Physics 20 (6):733-744.
    Using the mathematical notion of an entity to represent states in quantum and classical mechanics, we show that, in a strict sense, proper superpositions are possible in classical mechanics.
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  8.  30
    Logical Connectives on Lattice Effect Algebras.D. J. Foulis & S. Pulmannová - 2012 - Studia Logica 100 (6):1291-1315.
    An effect algebra is a partial algebraic structure, originally formulated as an algebraic base for unsharp quantum measurements. In this article we present an approach to the study of lattice effect algebras (LEAs) that emphasizes their structure as algebraic models for the semantics of (possibly) non-standard symbolic logics. This is accomplished by focusing on the interplay among conjunction, implication, and negation connectives on LEAs, where the conjunction and implication connectives are related by a residuation law. Special cases of LEAs are (...)
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  9.  53
    Charles Hamilton Randall: 1928–1987. [REVIEW]D. J. Foulis & M. K. Bennett - 1990 - Foundations of Physics 20 (5):473-476.
  10.  31
    Stochastic Quantum Mechanics Viewed From the Language of Manuals.F. E. Schroeck & D. J. Foulis - 1990 - Foundations of Physics 20 (7):823-858.
    The language of manuals may be used to discuss inference in measurement in a general experimental context. Specializing to the context of the frame manual for Hilbert space, this inference leads to state dominance of the inferred state from partial measurements; this in turn, by Sakai's theorem, determines observables which are described by positive operator-valued measures. Symmetries are then introduced, showing that systems of covariance, rather than systems of imprimitivity, are natural objects to study in quantum mechanics. Experiments measuring different (...)
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  11.  19
    Manuals, Morphisms and Quantum Mechanics.D. J. Foulis & C. H. Randall - 1978 - In A. R. Marlow (ed.), Mathematical Foundations of Quantum Theory. Academic Press. pp. 105--126.
  12. The Difference Poset of Monotone Functions.D. J. Foulis & M. K. Bennet - 1994 - Foundations of Physics 24:1325-1346.
     
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  13. Efect AlgelJ 璐 and Unsharpquantuur L Cs.D. J. Foulis & M. K. Bennet - 1994 - Foundations of Physics 24:1331-1352.