Displaying similar documents to “Conditional states and joint distributions on MV-algebras”

Generalized versions of MV-algebraic central limit theorems

Piotr Nowak, Olgierd Hryniewicz (2015)

Kybernetika

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MV-algebras can be treated as non-commutative generalizations of boolean algebras. The probability theory of MV-algebras was developed as a generalization of the boolean algebraic probability theory. For both theories the notions of state and observable were introduced by abstracting the properties of the Kolmogorov's probability measure and the classical random variable. Similarly, as in the case of the classical Kolmogorov's probability, the notion of independence is considered. In...

A spectral theorem for σ MV-algebras

Sylvia Pulmannová (2005)

Kybernetika

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MV-algebras were introduced by Chang, 1958 as algebraic bases for multi-valued logic. MV stands for “multi-valued" and MV algebras have already occupied an important place in the realm of nonstandard (mathematical) logic applied in several fields including cybernetics. In the present paper, using the Loomis–Sikorski theorem for σ -MV-algebras, we prove that, with every element a in a σ -MV algebra M , a spectral measure (i. e. an observable) Λ a : ℬ ( [ 0 , 1 ] ) → ℬ ( M ) can be associated, where ℬ ( M ) denotes the Boolean...

Fuzzy quantum logics.

Maria Luisa Dalla Chiara, Roberto Giuntini (1996)

Mathware and Soft Computing

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Quantum logic is a particular example of a fuzzy quantum logic. QL is semantically characterized by the class of all quantum MV algebras. The standard quantum MV algebra is based on the set of all effects in a Hilbert space. From the physical point of view, effects represent physical properties that may be noisy and ambiguous.