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1

Tracing Relations Probabilistically

100%

Doberkat E.-E.

Fundamenta Informaticae

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2005

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tom Vol. 66, nr 3

259--275

EN

We investigate similarities between non-deterministic and probabilistic ways of describing a system in terms of computation trees. We show that the construction of traces for both kinds of relations follows the same principles of construction. Representations of measurable trees in terms of probabilistic relations are given. This shows that stochastic relations may serve as refinements of their non-deterministic counterparts. A convexity argument formalizes the observation that non-deterministic system descriptions are underspecified when compared to probabilistic ones. The mathematical tools come essentially from the theory of measurable selections.

2

Tracing Relations Probabilistically

100%

Doberkat E.-E.

Fundamenta Informaticae

|

2005

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tom Vol. 65, nr 3

193--209

EN

We investigate similarities between non-deterministic and probabilistic ways of describing a system in terms of computation trees. We show that the construction of traces for both kinds of relations follows the same principles of construction. Representations of measurable trees in terms of probabilistic relations are given. This shows that stochastic relations may serve as refinements of their non-deterministic counterparts. A convexity argument formalizes the observation that non-deterministic system descriptions are underspecified when compared to probabilistic ones. The mathematical tools come essentially from the theory of measurable selections.

3

Representation Theorems for Lattice-ordered Modal Algebras and their Axiomatic Extensions

88%

Radzikowska A. M.

Fundamenta Informaticae

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2016

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tom Vol. 144, nr 2

183--203

EN

In this paper we present relational representation theorems for lattice-based modal algebras and their axiomatic extensions taking into account well-known schemas of modal logics. The underlying algebraic structures are bounded, not necessarily distributive lattices. Our approach is based on the Urquhart’s result for non-distributive lattices and Allwein and Dunn developments for algebras of liner logics.

4

Contact Algebras and Region-based Theory of Space: A Proximity Approach - I

63%

Dimov G. , Vakarelov D.

Fundamenta Informaticae

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2006

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tom Vol. 74, nr 2,3

209-249

EN

This work is in the field of region-based (or Whitehedian) theory of space, which is an important subfield of Qualitative Spatial Reasoning (QSR). The paper can be considered also as an application of abstract algebra and topology to some problems arising and motivated in Theoretical Computer Science and QSR Different axiomatizations for region-based (or Whiteheadian) theory of space are given. The most general one is introduced under the name ``Contact Algebra". Adding some extra first- or second-order axioms to those of contact algebras, some new or already known algebraic notions are obtained. Representation theorems and completion theorems for all such algebras are proved. Extension theories of the classes of all semiregular T0-spaces and all N-regular (a notion introduced here) T1-spaces are developed.

5

Lambda abstraction algebras : coordinatizing models of lambda calculus

63%

Pigozzi D. , Salibra A.

Fundamenta Informaticae

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1998

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tom Vol. 33, nr 2

149-200

EN

Lambda abstraction algebras are designed to algebraize the untyped lambda calculus in the same way cylindric and polyadic algebras algebraize the first-order logic; they are intended as an alternative to combinatory algebras in this regard. Like combinatory algebras they can be defined by true identities and thus from a variety in the sense if universal algebra. One feature of lambda abstraction algebras that sts them apart from combinatory algebras is the way variables in the lambda calculus are abtracted; this provides each lambda abstraction algebra with an implicit coordinate system. Another peculiar feature in the algebraic reformulation of (b)-conversion as the definition of abstract substitution. Functional lambda abstraction algebras arise as the 'coordinatizations' of environment models or lambda models, the natural combinatory models of the lambda calculus. As in the case of cylindric and polyadic algebras, questions of the functional representation of various subclasses of lambda abstraction algebras are an important part of the theory. The main result of the paper is a stronger version of the functional representation theorem for locally finite lambda abstraction algebras, the algebraic analogue of the completeness theorem of lambda calculus. This result is used to study the connection between the combinatory models of the lambda calculus and lambda abstraction algebras. Two significant results of this kind are the existence of a strong categorical equivalence between lambda algebras and locally finite lambda abstraction algebras, and between lambda models and rich, locally finite lambda abstraction algebras.