An Axiomatic Approach to Topology For Spatial Information Systems

The paper reports work on the topological formalism `RCC', a region-based `calculus of connection' developed at Leeds university over the past several years. Speci cally, it is shown that the nonempty regular closed sets of a class of topological spaces (connected T3-spaces) provide models for the RCC axiom-set. A brief assessment is made of RCC's potential as a formalism for applications in the area of spatial information systems (SIS). Two approaches to developing topological formalisms for SIS are compared, and a parallel is drawn with the two main parts of topology as understood by mathematicians.

[1]  Aristides A. G. Requicha,et al.  Mathematical Foundations of Constructive Solid Geometry: General Topology of Closed Regular Sets , 1978 .

[2]  Bowman L. Clarke,et al.  A calculus of individuals based on "connection" , 1981, Notre Dame J. Formal Log..

[3]  James R. Munkres,et al.  Elements of algebraic topology , 1984 .

[4]  Bowman L. Clarke,et al.  Individuals and points , 1985, Notre Dame J. Formal Log..

[5]  Timothy Williamson,et al.  Parts. A Study in Ontology , 1990 .

[6]  Anthony G. Cohn,et al.  A Spatial Logic based on Regions and Connection , 1992, KR.

[7]  Michael F. Worboys,et al.  A generic model for planar geographical objects , 1992, Int. J. Geogr. Inf. Sci..

[8]  A. Cohn COMPLETING SORT HIERARCHIES , 1992 .

[9]  Daniel R. Montello,et al.  Spatial Information Theory A Theoretical Basis for GIS , 1995, Lecture Notes in Computer Science.

[10]  Laure Vieu,et al.  A Logical Framework for Reasoning about Space , 1993, COSIT.

[11]  Michael F. Worboys,et al.  A Canonical Model for a Class of Areal Spatial Objects , 1993, SSD.

[12]  E. J.,et al.  Topological relations between regions with holes * , 1994 .

[13]  Nicholas Mark Gotts,et al.  How Far Can We 'C'? Defining a 'Doughnut' Using Connection Alone , 1994, KR.

[14]  Brandon Bennett,et al.  Spatial Reasoning with Propositional Logics , 1994, KR.

[15]  Laure Vieu,et al.  Toward a Geometry of Common Sense: A Semantics and a Complete Axiomatization of Mereotopology , 1995, IJCAI.

[16]  Max J. Egenhofer,et al.  On the Equivalence of Topological Relations , 1995, Int. J. Geogr. Inf. Sci..

[17]  Anthony G. Cohn,et al.  The ‘Egg-Yolk’ Representation of Regions with Indeterminate Boundaries , 2020 .

[18]  N. Gotts Topology from a Single Primitive Relation: Deening Topological Properties and Relations in Terms of Connection 1 , 1996 .

[19]  Nicholas Mark GottsDivision Formalizing Commonsense Topology : The INCH Calculus , 1996 .

[20]  A. Cohn,et al.  A connection based approach to common-sense topological description and reasoning , 1996 .

[21]  N. Gotts Using Thèrcc' Formalism to Describe the Topology of Spherical Regions 1 , 1996 .