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Displaying 1541 –
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3896
We show that each sequentially continuous (with respect to the pointwise convergence) normed measure on a bold algebra of fuzzy sets (Archimedean -algebra) can be uniquely extended to a sequentially continuous measure on the generated Łukasiewicz tribe and, in a natural way, the extension is maximal. We prove that for normed measures on Łukasiewicz tribes monotone (sequential) continuity implies sequential continuity, hence the assumption of sequential continuity is not restrictive. This yields...
In analogy with effect algebras, we introduce the test spaces and -test spaces. A test corresponds to a hypothesis on the propositional system, or, equivalently, to a partition of unity. We show that there is a close correspondence between -algebras and -test spaces.
If element of a lattice effect algebra is central, then the interval is a lattice effect algebra with the new top element and with inherited partial binary operation . It is a known fact that if the set of central elements of is an atomic Boolean algebra and the supremum of all atoms of in equals to the top element of , then is isomorphic to a subdirect product of irreducible effect algebras ([18]). This means that if there exists a MacNeille completion of which is its extension...
Probability on collections of fuzzy sets can be developed as a generalization of the classical probability on -algebras of sets. A Łukasiewicz tribe is a collection of fuzzy sets which is closed under the standard fuzzy complementation and under the pointwise application of the Łukasiewicz t-norm to countably many fuzzy sets. An observable is a fuzzy set-valued mapping defined on a -algebra of sets and satisfying some additional properties; formally, the role of an observable is in a sense analogous...
This paper gives a semantical underpinning for a many-sorted modal logic associated with certain dynamical systems, like transition systems, automata or classes in object-oriented languages. These systems will be described as coalgebras of so-called polynomial functors, built up from constants and identities, using products, coproducts and powersets. The semantical account involves Boolean algebras with operators indexed by polynomial functors, called MBAOs, for Many-sorted Boolean Algebras with...
This paper gives a semantical underpinning for a many-sorted modal
logic associated with certain dynamical systems, like transition
systems, automata or classes in object-oriented languages. These
systems will be described as coalgebras of so-called polynomial
functors, built up from constants and identities, using products,
coproducts and powersets. The semantical account involves Boolean
algebras with operators indexed by polynomial functors, called MBAOs,
for Many-sorted Boolean Algebras with...
The paper contains some sufficient conditions for Marczewski-Burstin representability of an algebra 𝓐 of sets which is isomorphic to 𝓟(X) for some X. We characterize those algebras of sets which are inner MB-representable and isomorphic to a power set. We consider connections between inner MB-representability and hull property of an algebra isomorphic to 𝓟 (X) and completeness of an associated quotient algebra. An example of an infinite universally MB-representable algebra is given.
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