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  1. Semantic analysis of orthologic.R. I. Goldblatt - 1974 - Journal of Philosophical Logic 3 (1/2):19 - 35.
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  • Logics based on partial Boolean σ-algebras (1).Janusz Czelakowski - 1974 - Studia Logica 33 (4):371 - 396.
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  • Partial and unsharp quantum logics.Maria Luisa Dalla Chiara & Roberto Giuntini - 1994 - Foundations of Physics 24 (8):1161-1177.
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  • Toward a formal language for unsharp properties.Roberto Giuntini & Heinz Greuling - 1989 - Foundations of Physics 19 (7):931-945.
    Some algebraic structures of the set of all effects are investigated and summarized in the notion of a(weak) orthoalgebra. It is shown that these structures can be embedded in a natural way in lattices, via the so-calledMacNeille completion. These structures serve as a model ofparaconsistent quantum logic, orthologic, andorthomodular quantum logic.
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  • Logics based on partial Boolean σ-algebras.Janusz Czelakowski - 1974 - Studia Logica 33 (4):371-396.
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  • Partial and unsharp quantum logics.M. L. Dalla Chiara & R. Giuntini - 1994 - Foundations of Physics 24 (8):1161-1177.
    The total and the sharp character of orthodox quantum logic has been put in question in different contexts. This paper presents the basic ideas for a unified approach to partial and unsharp forms of quantum logic. We prove a completeness theorem for some partial logics based on orthoalgebras and orthomodular posets. We introduce the notion of unsharp orthoalgebra and of generalized MV algebra. The class of all effects of any Hilbert space gives rise to particular examples of these structures. Finally, (...)
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  • Axiomatic unsharp quantum theory (From Mackey to Ludwig and Piron).Gianpiero Cattaneo & Federico Laudisa - 1994 - Foundations of Physics 24 (5):631-683.
    On the basis of Mackey's axiomatic approach to quantum physics or, equivalently, of a “state-event-probability” (SEVP) structure, using a quite standard “fuzzification” procedure, a set of unsharp events (or “effects”) is constructed and the corresponding “state-effect-probability” (SEFP) structure is introduced. The introduction of some suitable axioms gives rise to a partially ordered structure of quantum Brouwer-Zadeh (BZ) poset; i.e., a poset endowed with two nonusual orthocomplementation mappings, a fuzzy-like orthocomplementation, and an intuitionistic-like orthocomplementation, whose set of sharp elements is an (...)
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