We present a highly expressive logical language for describing qualitative configurations of spatial regions, based on Tarski’s Geometry of Solids, in which the parthood relation and the concept of sphere are taken as primitive. We give a categorical axiom system, whose models can be interpreted classically in terms of Cartesian spaces overR.We show that within this system the concept of sphere...

An operational semantics is deened for the language of timed CSP, in terms of two relations: an evolution relation, which describes when a process becomes another simply by allowing time to pass; and a timed transition relation, which describes when a process may become another by performing an action at a particular time. It is shown how the timed behaviours used as the basis for the denotatio...

In the context of process algebras it is customary to define semantics in the form of a reaction relation supported by a structural congruence relation. Recently process algebras have grown more expressive in order to meet the modelling demands of fields as diverse as business modelling and systems biology. This leads to combining various features, such as general choice and parallelism that we...

In this thesis, a comprehensive formalization of Milner’s Calculus of Communicating Systems (also known as CCS) has been done in HOL theorem prover (HOL4), based on an old work in HOL88. This includes all classical properties of strong/weak bisimulation equivalences and observation congruence, a theory of congruence for CCS, various versions of “bisimulation up to” techniques, and several deep ...

Stochastic process algebras (SPA) provide primitive operators that serve as means to incorporate stochastic timing aspects into a process algebraic speciication. In this paper we add some comfortable operators to an SPA where the passing of time is separated from the occurrence of activities. We present a superset of Basic Lotos which integrates probabilistic branching and exponentially distrib...

It was shown recently that, in the case of Schwarschild black hole, one can obtain the correct thermodynamic relations by studying a model quantum system and using a particular duality transformation. We study this approach further for the case a general spherically symmetric horizon. We show that the idea works for a general case only if we define the entropy S as a congruence (“observer”) dep...

Exactly as in semigroups, Green’s relations play an important role in the theory of ordered semigroups—especially for decompositions of such semigroups. In this paper we deal with the -trivial ordered semigroups which are defined via the Green’s relation , and with the nil and Δ-ordered semigroups. We prove that every nil ordered semigroup is -trivial which means that there is no ordered semigr...