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Open Maps and Observational Equivalences for Timed Partial Order Models

Virbitskaite I.B., Gribovskaya N.S.

Fundamenta Informaticae

2004

Vol. 60, nr 1-4

383--399

The intention of the paper is to show the applicability of the general categorical framework of open maps to the setting of timed extensions of partial order models, in order to transfer general concepts of equivalences to the models. In particular, we define categories of timed event structures, whose morphisms are to be thought of as simulations, and accompanying (sub)categories of observations, to which the corresponding notions of open maps are developed. We then use the open maps framework to obtain abstract bisimilarities which are established to coincide with timed extensions of well-known partial order based equivalences.

A categorical axiomatisation of Region-Based Geometry

Bennett B.

Fundamenta Informaticae

2001

Vol. 46, nr 1,2

145-158

Region Based Geometry (RBG) is an axiomatic theory of qualitative configurations of spatial regions. It is based on Tarski's Geometry of Solids, in which the parthood relation and the concept of sphere are taken as primitive. Whereas in Tarski's theory the combination of mereological and geometrical axioms involves set theory, in RBG the interface is achieved by purely 1st-order axioms. This means that the elementary sublanguage of RBG is extremely expressive, supporting inferences involving both mereological and geometrical concepts. Categoricity of the RBG axioms is proved: all models are isomorphic to a standard interpretation in terms of Cartesian spaces over \mathbbR.