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Stone duality generalizes to an equivalence between the categories Stone R of Stone spaces and closed relations and BA S of boolean algebras and subordination relations. Splitting equivalences in Stone R yields a category that is equivalent to the category KHaus R of compact Hausdorff spaces and closed relations. Similarly, splitting equivalences in BA S yields a category that is equivalent to the category De V S of de Vries algebras and compatible subordination relations. Applying the machinery of allegories then gives that KHaus R is equivalent to De V S , thus resolving a problem recently raised in the literature. The equivalence between KHaus R and De V S further restricts to an equivalence between the category KHaus of compact Hausdorff spaces and continuous functions and the wide subcategory De V F of De V S whose morphisms satisfy additional conditions. This yields an alternative to de Vries duality. One advantage of this approach is that composition of morphisms is usual relation composition. [ABSTRACT FROM AUTHOR]

Abstract A relation algebra is called measurable when its identity is the sum of measurable atoms, where an atom is called measurable if its square is the sum of functional elements. In this paper we show that atomic measurable relation algebras have rather strong structural properties: they are constructed from systems of groups, coordinated systems of isomorphisms between quotients of the groups, and systems of cosets that are used to “shift” the operation of relative multiplication. An atomic and complete measurable relation algebra is completely representable if and only if there is a stronger coordination between these isomorphisms induced by a scaffold (the shifting cosets are not needed in this case). We also prove that a measurable relation algebra in which the associated groups are all finite is atomic. [ABSTRACT FROM AUTHOR]

Abstract: That matrices of relations also obey the rules of relation algebra is well known. When the powerset ordering is considered, partialities may be conceived as lattice-continuous mappings — corresponding to existential images which are often studied independently. A partiality is suited to describe progress of yet partial information or availability. This has already been presented in Schmidt (2006) . Matrices of partialities will considerably improve the possibility to study non-strictness, streams, partial evaluation, and net properties in a compact relation-algebraic form. They seem, however, to lead inevitably to some borderline cases as the Boolean lattice 0 and row-less matrices. It will be shown how these can be fruitfully applied concerning constructions with temporarily non-connected relation algebras. [Copyright &y& Elsevier]

Abstract: We study the Boolean algebras of regular languages, context-sensitive languages and decidable languages, respectively, over any alphabet. It is well known that , with proper inclusions. After observing that these Boolean algebras are all isomorphic, we study some immunity properties: for instance we prove that for every coinfinite decidable language there exists a decidable language such that , is infinite, and there is no context-sensitive language , with unless is finite; similarly, for every coinfinite regular language there exists a context-sensitive language such that , is infinite, and there is no regular language such that , unless is finite. [Copyright &y& Elsevier]

Abstract: In this paper, we are concerned with a special timetabling problem. It was posed to us by the administration of our university and stems from the adoption of the British-American system of university education in Germany. This change led to the concrete task of constructing a timetable that enables the undergraduate education of secondary school teachers within three years in the “normal case” and within four years in the case of exceptional combinations of subjects. We develop two relation-algebraic models of the timetabling problem and in each case algorithms for computing solutions. The latter easily can be implemented in the Kiel RelView tool showing that RelView can be used for timetabling. [ABSTRACT FROM AUTHOR]

Abstract: The language of our Boolean logic with relations is a Boolean language to which relation symbols have been added. Such a language turns out to be a useful tool for describing relational structures and algebraic structures. This paper introduces the concepts of Kripke semantics and Boolean semantics for our language. It addresses the traditional issues of decidability/complexity and axiomatization/completeness but it also defines the new concepts of weak canonicity and strong canonicity. [ABSTRACT FROM AUTHOR]