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Displaying similar documents to “Book Reviews”

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.

States on basic algebras

Ivan Chajda, Helmut Länger (2017)

Mathematica Bohemica

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States on commutative basic algebras were considered in the literature as generalizations of states on MV-algebras. It was a natural question if states exist also on basic algebras which are not commutative. We answer this question in the positive and give several examples of such basic algebras and their states. We prove elementary properties of states on basic algebras. Moreover, we introduce the concept of a state-morphism and characterize it among states. For basic algebras which...

Axiomatizing quantum MV-algebras.

Roberto Giuntini (1997)

Mathware and Soft Computing

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We introduce the notion of p-ideal of a QMV-algebra and we prove that the class of all p-ideals of a QMV-algebra M is in one-to-one correspondence with the class of all congruence relations of M.

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...