N.M. Gotts. Using the RCC formalism to describe the topology of spherical regions. Technical Report 96.24, School of Computer Studies, University of Leeds, 1996.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... Gamma Gamma Gamma 6 Time Space Space t t 0 n n Figure 1: Spatial regions moving in time. Our intended models of space are a variant of mereotopological models: the primitive entities regions are interpreted as regular closed sets of topological spaces [ Grzegorczyk, 1960; Gotts, 1996b ] so that any two regions can stand Who else 2 in precisely one of the eight relations depicted in Fig. 2 [ Egenhofer and Franzosa, 1991; Randell et al. 1992 ] As concerns time, we consider three fundamental paradigms: linear point based time (discrete, dense, etc. branching point based ....

N.M. Gotts. Using the RCC formalism to describe the topology of spherical regions. Technical Report 96.24, School of Computer Studies, University of Leeds, 1996.

.... of this issue can be found in [41, 35, 103, 143] Another ontological question is what is the nature of the embedding space, i.e. the universal spatial entity Conventionally, one might take this to be R n for some n, but one can imagine applications where discrete (e.g. 66] nite (e.g. [102]) or non convex (e.g. non connected) universes might be useful. There is a tension between the continuous space models favoured by high level approaches to handling spatial information and discrete, digital representations used at the lower level. An attempt to bridge this gap by developing a ....

Gotts, N. M.: \Using the RCC formalism to describe the topology of spherical regions", Technical Report No. - 96.24, School of Computer Studies, University of Leeds, 1996.

....= C Ia(X) where C is the closure operator on U dual to I. The intended meaning of C(X; Y ) regions X and Y share at least one point is formalized then as follows: T j= a C(X; Y ) iff a(X) a(Y ) 6= From the computational point of view RCC is too expressive: as was observed by Gotts [17], the full first order theory of RCC is undecidable. Fortunately, there are various decidable (and even tractable) fragments of RCC. One of the most important is known as RCC 8. RCC 8. If we are interested only in relationships between spatial regions without taking into account their topological ....

N.M. Gotts. Using the RCC formalism to describe the topology of spherical regions. Technical Report 96.24, School of Computer Studies, University of Leeds, 1996.

.... of this issue can be found in [27, 73, 26] Another ontological question is what is the nature of the embedding space, i.e. the universal spatial entity Conventionally, one might take this to be R n for some n, but one can imagine applications where discrete (e.g. 43] finite (e.g. [72], or non convex (e.g. non connected) universes might be useful. Once one has decided on these ontological questions, there are further issues: in particular, what primitive computations will be allowed In a logical theory, this amounts to deciding what primitive non logical symbols one will ....

N M Gotts. Using the RCC formalism to describe the topology of spherical regions. Technical report, Report 96.24, School of Computer Studies, University of Leeds, 1996.

....= C Ia(X) where C is the closure operator on U dual to I. The intended meaning of C(X; Y ) regions X and Y share at least one point is formalized then as follows: T j= a C(X; Y ) iff a(X) a(Y ) 6= From the computational point of view RCC is too expressive: as was observed by Gotts [17], the full first order theory of RCC is undecidable. Fortunately, there are various decidable (and even tractable) fragments of RCC. One of the most important is known as RCC 8. RCC 8. If we are interested only in relationships between spatial regions without taking into account their topological ....

N.M. Gotts. Using the RCC formalism to describe the topology of spherical regions. Technical Report 96.24, School of Computer Studies, University of Leeds, 1996.

....in it (so an open set is equal to its interior) The closure of a set is the smallest closed set containing it (so a closed set is equal to its closure) A regular closed set is one which is equal to the closure of its interior. A regular open set is one equal to the interior of its closure (Gotts 1996a, pg. 4) Regular open sets are topologically well formed in that sense that they do not contain isolated points or infinitely thin spikes . The boundary of a set is the set theoretic difference of its closure and its interior. In the remainder of this paper we use NERC (NERO) to refer to ....

....topologically well formed in that sense that they do not contain isolated points or infinitely thin spikes . The boundary of a set is the set theoretic difference of its closure and its interior. In the remainder of this paper we use NERC (NERO) to refer to non empty regular closed (open) sets (Gotts 1996a) cl(x) i(x) b(x) to refer to the closure, the interior and the boundary of a set x, and we use , and to refer to the set theoretic operations union, intersection, difference and complement. Topological spaces can be characterized in several ways. One of the most important properties is ....

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Gotts, N. M. (1996). Using the 'RCC' Formalism to Describe the Topology of Spherical Regions. Leeds, University of Leeds.

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Gotts, N. M.: 1996d, Using the RCC formalism to describe the topology of spherical regions, Technical report, Report 96.24, School of Computer Studies, University of Leeds.

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