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Many-dimensional observables on Łukasiewicz tribe: constructions, conditioning and conditional independence

Tomáš Kroupa (2005)

Kybernetika

Probability on collections of fuzzy sets can be developed as a generalization of the classical probability on σ -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 σ -algebra of sets and satisfying some additional properties; formally, the role of an observable is in a sense analogous...

Many-sorted coalgebraic modal logic : a model-theoretic study

Bart Jacobs (2001)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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...

Many-Sorted Coalgebraic Modal Logic: a Model-theoretic Study

Bart Jacobs (2010)

RAIRO - Theoretical Informatics and Applications

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...

Marczewski-Burstin Representations of Boolean Algebras Isomorphic to a Power Set

Artur Bartoszewicz (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

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.

Mathematical aspects of the theory of measures of fuzziness.

Doretta Vivona (1996)

Mathware and Soft Computing

After recalling the axiomatic concept of fuzziness measure, we define some fuzziness measures through Sugeno's and Choquet's integral. In particular, for the so-called homogeneous fuzziness measures we prove two representation theorems by means of the above integrals.

Matrix identities involving multiplication and transposition

Karl Auinger, Igor Dolinka, Michael V. Volkov (2012)

Journal of the European Mathematical Society

We study matrix identities involving multiplication and unary operations such as transposition or Moore–Penrose inversion. We prove that in many cases such identities admit no finite basis.

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