We find a criterion for a morphism of coalgebras over a Barr-exact category to be effective descent and determine (effective) descent morphisms for coalgebras over toposes in some cases. Also, we study some exactness properties of endofunctors of arbitrary categories in connection with natural transformations between them as well as those of functors that these transformations induce between co...

We build an analogue for the Levi-Civita connection on Riemannian manifolds for sub-Riemannian manfiolds modeled on the Heisenberg group. We demonstrate some geometric properties of this connection to justify our choice and show that this connection is unique in having these properties.

Spatial reasoning with description logic has become an important research topic in the recent past. Several authors dealt with the problem of finding logical frameworks in which concept definitions can be made by using also spatial operators, particularly those of the Region Connection Calculus. Lutz and Miličić investigated the formal properties required to the concrete domain of the logical s...

LetM = (M,OM) be a smooth supermanifold with connection ∇ and Batchelor model OM ∼= ΓΛE∗ . From (M,∇) we construct a connection on the total space of the vector bundle E →M . This reduction of∇ is well-defined independently of the isomorphism OM ∼= ΓΛE∗ . It erases information, but however it turns out that the natural identification of supercurves inM (as maps from R1|1 toM) with curves in E r...

One of the essential functions of natural language is to talk about spatial relationships between objects. Linguistic constructs can express highly complex, relational structures of objects, spatial relations between them, and patterns of motion through spaces relative to some reference point. Learning how to map this information onto a formal representation from a text is a challenging problem...

We aim to combine the semantics of spatial natural language specified as a linguistically motivated ontology, the Generalized Upper Model, with spatial logics or ontologies that specify space according to certain conceptualisations, based on regions, shapes, orientations, distances, or object properties. Such combinations, however, introduce uncertainties of various kinds, caused by different l...

In qualitative spatial reasoning, there are three distinct properties for reasoning about spatial objects: connectivity, size, and direction. Reasoning over combinations of these properties can provide additional useful knowledge. To facilitate end-user spatial querying, it also is important to associate natural language with these relations. Some work has been done in this regard for lineregio...

The connection method (CM) provides a general framework for automated deduction. It differs from similar deductive frameworks, (such as resolution or tableaux), through its unique feature of establishing the truth of a statement by a thorough analysis of the syntactic structure of the statement, without cost-intensive search for some derivation in the traditional sense of logic. It may thus be ...