Axiomatizácia fyzikálnych systémov a „kvantové logiky‟
Superpositions of states and a representation theorem
Uncertainty relations and state spaces
Compatibility and partial compatibility in quantum logics
Divisible effect algebras and interval effect algebras
It is shown that divisible effect algebras are in one-to-one correspondence with unit intervals in partially ordered rational vector spaces.
A note on the extensibility of states
Individual ergodic theorem on a logic
Extensions of partially ordered partial abelian monoids
The notion of a partially ordered partial abelian monoid is introduced and extensions of partially ordered abelian monoids by partially ordered abelian groups are studied. Conditions for the extensions to exist are found. The cases when both the above mentioned structures have the Riesz decomposition property, or are lattice ordered, are treated. Some applications to effect algebras and MV-algebras are shown.
Blocks in homogeneous effect algebras and MV-algebras
Book Reviews
Book Reviews
On representations of logics
Book Reviews
A remark on the comparison of Mackey and Segal models
Semiobservables on quantum logics
A spectral theorem for MV-algebras
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 -MV-algebras, we prove that, with every element in a -MV algebra , a spectral measure (i. e. an observable) can be associated, where denotes the Boolean -algebra...
Spectral resolutions for -complete lattice effect algebras
Quantum logics, vector-valued measures and representations
Uncertainty principle and joint distributions of observables
Relative conditional expectations on a logic
In this paper, the authors introduce the notion of conditional expectation of an observable on a logic with respect to a sublogic, in a state , relative to an element of the logic. This conditional expectation is an analogue of the expectation of an integrable function on a probability space.
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