Synopsis. In a cartesian closed category with an initial object and a dominance that classiies it, an intensional notion of approximation between maps |the path relation (c.f. link relation)| is deened. It is shown that if such a category admits strict/upper-closed factorisations then it preorder-enriches (as a cartesian closed category) with respect to the path relation. By imposing further ax...

The goal of this paper is to explain the usage and semantics of hierarchical defaults in logical specifications. We discuss the usefulness of defaults for different specification scenarios like specialization, aggregation, explanation, revision, etc. To understand defaults formally, we introduce a general framework parameterized on the underlying logical institution extended by an instantiation...

The Information Flow Framework (IFF) [1] is a descriptive category metatheory currently under development, which is being offered as the structural aspect of the Standard Upper Ontology (SUO). The architecture of the IFF is composed of metalevels, namespaces and meta-ontologies. The main application of the IFF is institutional: the notion of institutions and their morphisms are being axiomatize...

In this paper we study the topology of moduli spaces of tropical curves of genus g with n marked points. We view the moduli spaces as being embedded in a larger space, which we call the moduli space of metric graphs with n marked points. We describe the shrinking bridges strong deformation retraction, which leads to a substantial simplification of all these moduli spaces. In the rest of the pap...

By transferring the theory of hybrid systems to a categorical framework, it is possible to develop a homology theory for hybrid systems: hybrid homology. This is achieved by considering the underlying “space” of a hybrid system—its hybrid space or H-space. The homotopy colimit can be applied to this H-space to obtain a single topological space; the hybrid homology of an H-space is the homology ...

A process semantics for temporal logic specification is provided by relating a category of temporal theories and interpretations between theories where specification configuration and interconnection is achieved via colimits of diagrams, and a category of algebraic models of processes where parallel composition is explained in terms of limits of diagrams. This semantics is proved to be exact in...

The category of all monads over many-sorted sets (and over other " set-like " categories) is proved to have coequalizers and strong coin-tersections. And a general diagram has a colimit whenever all the monads involved preserve monomorphisms and have arbitrarily large joint pre-fixpoints. In contrast, coequalizers fail to exist e.g. for monads over the (presheaf) category of graphs. For more ge...

There is a 2-category J -Colim of small categories equipped with a choice of colimit for each diagram whose domain J lies in a given small class J of small categories, functors strictly preserving such colimits, and natural transformations. The evident forgetful 2-functor from J -Colim to the 2-category Cat of small categories is known to be monadic. We extend this result by considering not jus...

We present a framework for conceptual blending ? a concept invention method that is advocated in cognitive science as a fundamental, and uniquely human engine for creative thinking. Herein, we employ the search capabilities of ASP to find commonalities among input concepts as part of the blending process, and we show how our approach fits within a generalised conceptual blending workflow. Speci...

In this paper we study quotients of posets by group actions. In order to define the quotient correctly we enlarge the considered class of categories from posets to loopfree categories: categories without nontrivial automorphisms and inverses. We view group actions as certain functors and define the quotients as colimits of these functors. The advantage of this definition over studying the quoti...