Related papers: Transforming Geospatial Ontologies by Homomorphism…
Ontologies are widely used for representing domain knowledge and meta data, playing an increasingly important role in Information Systems, the Semantic Web, Bioinformatics and many other domains. However, logical reasoning that ontologies…
By introducing various topologies on the homotopy groups of a topological space, some researchers make these well known notions in algebraic topology more useful and powerful. In this paper, first we recall and review some known topologies…
The homotopy type of the complement of a complex coordinate subspace arrangement is studied by fathoming out the connection between its topological and combinatorial structures. A family of arrangements for which the complement is homotopy…
The study of topological information of spatial objects has for a long time been a focus of research in disciplines like computational geometry, spatial reasoning, cognitive science, and robotics. While the majority of these researches…
Ontology operations, e.g., aligning and merging, were studied and implemented extensively in different settings, such as, categorical operations, relation algebras, typed graph grammars, with different concerns. However, aligning and…
Ontologies are the prime way of organizing data in the Semantic Web. Often, it is necessary to combine several, independently developed ontologies to obtain a knowledge graph fully representing a domain of interest. The complementarity of…
We investigate a special kind of contraction of symmetric spaces (respectively, of Lie triple systems), called homotopy. In this first part of a series of two papers we construct such contractions for classical symmetric spaces in an…
Geometric morphisms between realizability toposes are studied in terms of morphisms between partial combinatory algebras (pcas). The morphisms inducing geometric morphisms (the {\em computationally dense\/} ones) are seen to be the ones…
We introduce quasi-homomorphisms of cluster algebras, a flexible notion of a map between cluster algebras of the same type (but with different coefficients). The definition is given in terms of seed orbits, the smallest equivalence classes…
Ontologies usually suffer from the semantic heterogeneity when simultaneously used in information sharing, merging, integrating and querying processes. Therefore, the similarity identification between ontologies being used becomes a…
Homotopy is an important feature of associative and Jordan algebraic structures: such structures always come in families whose members need not be isomorphic among other, but still share many important properties. One may regard homotopy as…
We introduce semiframes (an algebraic structure) and investigate their duality with semitopologies (a topological one). Both semitopologies and semiframes are relatively recent developments, arising from a novel application of topological…
In previous works by the authors, a bifunctor was associated to any operadic twisting morphism, taking a coalgebra over a cooperad and an algebra over an operad, and giving back the space of (graded) linear maps between them endowed with a…
Rectangular layouts, subdivisions of an outer rectangle into smaller rectangles, have many applications in visualizing spatial information, for instance in rectangular cartograms in which the rectangles represent geographic or political…
Ontology embeddings map classes, relations, and individuals in ontologies into $\mathbb{R}^n$, and within $\mathbb{R}^n$ similarity between entities can be computed or new axioms inferred. For ontologies in the Description Logic…
In this paper, we study the machine learning elements which we are interested in together as a machine learning system, consisting of a collection of machine learning elements and a collection of relations between the elements. The…
The set theory relations \in, \backslash, \Delta, \cap, and \cup have corollaries in subspace relations. Geometric Algebra is introduced as the ideal framework to explore these subspace operations. The relations \in, \backslash, and \Delta…
Symmetries and isomorphisms play similar conceptual roles when we consider how models represent physical situations, but they are formally distinct, as two models related by symmetries are not typically isomorphic. I offer a rigorous…
Given a topological group G, its orbit category Orb_G has the transitive G-spaces G/H as objects and the G-equivariant maps between them as morphisms. A well known theorem of Elmendorf then states that the category of G-spaces and the…
Ontologies form the basic interest in various computer science disciplines such as semantic web, information retrieval, database design, etc. They aim at providing a formal, explicit and shared conceptualization and understanding of common…