9 found
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  1. Effects, Observables, States, and Symmetries in Physics.David J. Foulis - 2007 - Foundations of Physics 37 (10):1421-1446.
    We show how effect algebras arise in physics and how they can be used to tie together the observables, states and symmetries employed in the study of physical systems. We introduce and study the unifying notion of an effect-observable-state-symmetry-system (EOSS-system) and give both classical and quantum-mechanical examples of EOSS-systems.
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  2.  9
    Coupled Physical Systems.David J. Foulis - 1989 - Foundations of Physics 19 (7):905-922.
    The purpose of this paper is to sketch an attack on the general problem of representing a composite physical system in terms of its constituent parts. For quantum-mechanical systems, this is traditionally accomplished by forming either direct sums or tensor products of the Hilbert spaces corresponding to the component systems. Here, a more general mathematical construction is given which includes the standard quantum-mechanical formalism as a special case.
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  3.  33
    Type-Decomposition of an Effect Algebra.David J. Foulis & Sylvia Pulmannová - 2010 - Foundations of Physics 40 (9-10):1543-1565.
    Effect algebras (EAs), play a significant role in quantum logic, are featured in the theory of partially ordered Abelian groups, and generalize orthoalgebras, MV-algebras, orthomodular posets, orthomodular lattices, modular ortholattices, and boolean algebras.We study centrally orthocomplete effect algebras (COEAs), i.e., EAs satisfying the condition that every family of elements that is dominated by an orthogonal family of central elements has a supremum. For COEAs, we introduce a general notion of decomposition into types; prove that a COEA factors uniquely as a (...)
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  4.  28
    The Universal Group of a Heyting Effect Algebra.David J. Foulis - 2006 - Studia Logica 84 (3):407 - 424.
    A Heyting effect algebra (HEA) is a lattice-ordered effect algebra that is at the same time a Heyting algebra and for which the Heyting center coincides with the effect-algebra center. Every HEA is both an MV-algebra and a Stone-Heyting algebra and is realized as the unit interval in its own universal group. We show that a necessary and sufficient condition that an effect algebra is an HEA is that its universal group has the central comparability and central Rickart properties.
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  5.  14
    The Universal Group of a Heyting Effect Algebra.David J. Foulis - 2006 - Studia Logica 84 (3):407-424.
    A Heyting effect algebra is a lattice-ordered effect algebra that is at the same time a Heyting algebra and for which the Heyting center coincides with the effect-algebra center. Every HEA is both an MV-algebra and a Stone-Heyting algebra and is realized as the unit interval in its own universal group. We show that a necessary and sufficient condition that an effect algebra is an HEA is that its universal group has the central comparability and central Rickart properties.
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  6.  9
    Observables, Calibration, and Effect Algebras.David J. Foulis & Stanley P. Gudder - 2001 - Foundations of Physics 31 (11):1515-1544.
    We introduce and study the D-model, which reflects the simplest situation in which one wants to calibrate an observable. We discuss the question of representing the statistics of the D-model in the context of an effect algebra.
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  7.  16
    Spin Factors as Generalized Hermitian Algebras.David J. Foulis & Sylvia Pulmannová - 2009 - Foundations of Physics 39 (3):237-255.
    We relate so-called spin factors and generalized Hermitian (GH-) algebras, both of which are partially ordered special Jordan algebras. Our main theorem states that positive-definite spin factors of dimension greater than one are mathematically equivalent to generalized Hermitian algebras of rank two.
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  8.  35
    Type-Decomposition of a Synaptic Algebra.David J. Foulis & Sylvia Pulmannová - 2013 - Foundations of Physics 43 (8):948-968.
    A synaptic algebra is a generalization of the self-adjoint part of a von Neumann algebra. In this article we extend to synaptic algebras the type-I/II/III decomposition of von Neumann algebras, AW∗-algebras, and JW-algebras.
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  9.  10
    Maximum Likelihood Estimation on Generalized Sample Spaces: An Alternative Resolution of Simpson's Paradox. [REVIEW]Matthias P. Kläy & David J. Foulis - 1990 - Foundations of Physics 20 (7):777-799.
    We propose an alternative resolution of Simpson's paradox in multiple classification experiments, using a different maximum likelihood estimator. In the center of our analysis is a formal representation of free choice and randomization that is based on the notion of incompatible measurements.We first introduce a representation of incompatible measurements as a collection of sets of outcomes. This leads to a natural generalization of Kolmogoroff's axioms of probability. We then discuss the existence and uniqueness of the maximum likelihood estimator for a (...)
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