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  • 1
    Electronic Resource
    Electronic Resource
    Tensor products of orthoalgebras (1993)
    Springer
    Order 10 (1993), S. 271-282 
    Details
    ISSN: 1572-9273
    Keywords: 81B10 ; 06C15 ; 03G12 ; 06E25 ; 08A55 ; Orthoalgebra ; tensor product ; test space ; orthocomplemented poset ; probability measure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We define a tensor product via a universal mapping property on the class oforthoalgebras, which are both partial algebras and orthocomplemented posets. We show how to construct such a tensor product forunital orthoalgebras, and use the Fano plane to show that tensor products do not always exist.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01110548
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  • 2
    Electronic Resource
    Electronic Resource
    States and the free orthogonality monoid (1972)
    Springer
    Theory of computing systems 6 (1972), S. 268-276 
    Details
    ISSN: 1433-0490
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract Let (X, #) be an orthogonality space such that the lattice C(X, #) of closed subsets of (X, #) is orthomodular and let (Γ, ⊥) denote the free orthogonality monoid over (X, #). Let C0(Γ, ⊥) be the subset of C(Γ, ⊥), consisting of all closures of bounded orthogonal sets. We show that C0(Γ, ⊥) is a suborthomodular lattice of C(Γ, ⊥) and we provide a necessary and sufficient condition for C0(Γ, ⊥) to carry a full set of dispersion free states.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01740718
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  • 3
    Electronic Resource
    Electronic Resource
    Specification of Finite Effect Algebras (2000)
    Springer
    International journal of theoretical physics 39 (2000), S. 665-676 
    Details
    ISSN: 1572-9575
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We study and relate five basic methods for specifying or describing a finite effectalgebra, indicate some computational algorithms for dealing with effect algebrasso specified, and mention in passing some open questions that await solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1003641905541
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  • 4
    Electronic Resource
    Electronic Resource
    MV and Heyting Effect Algebras (2000)
    Springer
    Foundations of physics 30 (2000), S. 1687-1706 
    Details
    ISSN: 1572-9516
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract 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 center valued pseudocomplementation, (iii) E admits a central cover mapping γ such that, for all p, q∈E, p∧q=0⇒γ(p)∧q=0.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1026454318245
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  • 5
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    Empirical Logic and Quantum Mechanics (1974)
    Dordrecht : Periodicals Archive Online (PAO)
    Synthese. 29:1/4 (1974:dec.) 81 
    Details
    ISSN: 0039-7857
    Topics: Natural Sciences in General , Philosophy
    Notes: PART I / LOGIC
    URL: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pao:&rft_dat=xri:pao:article:7609-1974-029-01-000007
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  • 6
    Electronic Resource
    Electronic Resource
    Multiplicative elements in Baer *-semigroups (1967)
    Springer
    Mathematische Annalen 175 (1967), S. 297-302 
    Details
    ISSN: 1432-1807
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02063214
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  • 7
    Electronic Resource
    Electronic Resource
    Transition to effect algebras (1995)
    Springer
    International journal of theoretical physics 34 (1995), S. 1369-1382 
    Details
    ISSN: 1572-9575
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract An account is given of the recent development of the theory of effect algebras, their connection with partially ordered abelian groups, and their use for the mathematical representation of fuzzy or unsharp events. We submit an annotated list of important open problems, appropriate research projects, and unresolved philosophical issues engendered by the developing theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00676249
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  • 8
    Electronic Resource
    Electronic Resource
    Sums and products of interval algebras (1994)
    Springer
    International journal of theoretical physics 33 (1994), S. 2119-2136 
    Details
    ISSN: 1572-9575
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Aninterval algebra is an interval from zero to some positive element in a partially ordered Abelian group, which, under the restriction of the group operation to the interval, is a partial algebra. In this paper we study interval algebras from a categorical point of view, and show that Cartesian products and horizontal sums are effective as categorical products and coproducts, respectively. We show that the category of interval algebras admits a tensor product, and introduce a new class of interval algebras, which are in fact orthoalgebras, calledχ-algebras.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00675796
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  • 9
    Electronic Resource
    Electronic Resource
    Filters and supports in orthoalgebras (1992)
    Springer
    International journal of theoretical physics 31 (1992), S. 789-807 
    Details
    ISSN: 1572-9575
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract An orthoalgebra, which is a natural generalization of an orthomodular lattice or poset, may be viewed as a “logic” or “proposition system” and, under a welldefined set of circumstances, its elements may be classified according to the Aristotelian modalities: necessary, impossible, possible, and contingent. The necessary propositions band together to form a local filter, that is, a set that intersects every Boolean subalgebra in a filter. In this paper, we give a coherent account of the basic theory of Orthoalgebras, define and study filters, local filters, and associated structures, and prove a version of the compactness theorem in classical algebraic logic.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00678545
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  • 10
    Electronic Resource
    Electronic Resource
    Quotients of interval effect algebras (1996)
    Springer
    International journal of theoretical physics 35 (1996), S. 2321-2338 
    Details
    ISSN: 1572-9575
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Nearly every orthostructure that has been proposed as a model for a logic of propositions affiliated with a physical system can be represented as an interval effect algebra; that is, as the partial algebra under addition of an interval from zero to an order unit in a partially ordered Abelian group. If the system is in a state that precludes certain elements of such an interval, an appropriate quotient interval algebra can be constructed by factoring out the order-convex subgroup generated by the precluded elements. In this paper we launch a study of the resulting quotient effect algebras.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02302450
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