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Extensions of partially ordered partial abelian monoids

Sylvia Pulmannová — 2006

Czechoslovak Mathematical Journal

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.

A spectral theorem for σ MV-algebras

Sylvia Pulmannová — 2005


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 : ( [ 0 , 1 ] ) ( M ) can be associated, where ( M ) denotes the Boolean σ -algebra...

Relative conditional expectations on a logic

Oľga NánásiováSylvia Pulmannová — 1985

Aplikace matematiky

In this paper, the authors introduce the notion of conditional expectation of an observable x on a logic with respect to a sublogic, in a state m , relative to an element a of the logic. This conditional expectation is an analogue of the expectation of an integrable function on a probability space.

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