Mereotopological Connection

The paper outlines a model-theoretic framework for investigating and comparing a variety of mereotopological theories. In the first part we consider different ways of characterizing a mereotopology with respect to (i) the intended interpretation of the connection primitive, and (ii) the composition of the admissible domains of quantification (e.g., whether or not they include boundary elements). The second part extends this study by considering two further dimensions along which different patterns of topological connection can be classified – the strength of the connection and its multiplicity.

[1]  Burnham Terrell,et al.  Philosophical Investigations on Space, Time and the Continuum , 1989 .

[2]  Christian Freksa,et al.  Temporal Reasoning Based on Semi-Intervals , 1992, Artif. Intell..

[3]  Eliseo Clementini,et al.  Topological Invariants for Lines , 1998, IEEE Trans. Knowl. Data Eng..

[4]  M. Aurnague,et al.  A three-level approach to the semantics of space , 1993 .

[5]  C. Kuratowski Sur l'opération Ā de l'Analysis Situs , 1922 .

[6]  Anthony G. Cohn,et al.  Modelling Topological and Metrical Properties in Physical Processes , 1989, KR.

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

[8]  Achille C. Varzi,et al.  Holes and Other Superficialities , 1994 .

[9]  Margaret M. Fleck The Topology of Boundaries , 2018, Artif. Intell..

[10]  Fabio Pianesi,et al.  Events, topology and temporal relations , 1996 .

[11]  Roderick M. Chisholm,et al.  BOUNDARIES AS DEPENDENT PARTICULARS , 1983 .

[12]  Scattered objects , 1997, Science.

[13]  Achille C. Varzi,et al.  The structure of spatial localization , 1996 .

[14]  Lars Kulik Qualitative Spatial Change , 2002, Künstliche Intell..

[15]  F. Brentano,et al.  Philosophische Untersuchungen zu Raum, Zeit und Kontinuum , 1976 .

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

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

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

[19]  Giangiacomo Gerla,et al.  Connection Structures , 1991, Notre Dame J. Formal Log..

[20]  Achille C. Varzi Parts, Wholes, and Part-Whole Relations: The Prospects of Mereotopology , 1996, Data Knowl. Eng..

[21]  Barry Smith,et al.  Mereotopology: A Theory of Parts and Boundaries , 1996, Data Knowl. Eng..

[22]  Achille C. Varzi Boundaries, Continuity, and Contact , 1997 .

[23]  A. Whitehead Process and reality : an essay in cosmology , 1978 .

[24]  M. J. Inwood,et al.  The Cambridge Companion to Husserl , 1996 .

[25]  Anthony G. Cohn,et al.  Connection Relations in Mereotopology , 1998, ECAI.

[26]  Nelson Goodman,et al.  The calculus of individuals and its uses , 1940, Journal of Symbolic Logic.

[27]  Achille C. Varzi Reasoning about space: The hole story , 2003 .

[28]  Antony Galton,et al.  Modes of Overlap , 1998, J. Vis. Lang. Comput..

[29]  Achille C. Varzi,et al.  Fiat and Bona Fide Boundaries , 2000 .

[30]  Nicola Guarino,et al.  A Pointless Theory of Space Based on Strong Connection and Congruence , 1996, KR.

[31]  Andrzej Grzegorczyk,et al.  Axiomatizability of geometry without points , 1960, Synthese.

[32]  Roberto Casati,et al.  Parts and Places: The Structures of Spatial Representation , 1999 .

[33]  Anthony G. Cohn,et al.  Qualitative Spatial Representation and Reasoning: An Overview , 2001, Fundam. Informaticae.

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

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

[36]  Fabio Pianesi,et al.  Refining Temporal Reference in Event Structures , 1996, Notre Dame J. Formal Log..

[37]  Dean W. Zimmerman,et al.  Indivisible Parts and Extended Objects: Some Philosophical Episodes from Topology's Prehistory , 1996 .

[38]  Bernard Bolzano Paradoxes of the infinite , 1950 .

[39]  Antony Galton Taking Dimension Seriously in Qualitative Spatial Reasoning , 1996, ECAI.

[40]  J. E. Tiles,et al.  Things that happen , 1981 .

[41]  Eliseo Clementini,et al.  A Small Set of Formal Topological Relationships Suitable for End-User Interaction , 1993, SSD.

[42]  Ivo Düntsch,et al.  A Proof System for Contact Relation Algebras , 2000, J. Philos. Log..

[43]  Hans W. Guesgen,et al.  Spatial and Temporal Reasoning , 2003, AI Commun..

[44]  Laure Vieu,et al.  Modes of Connection , 1999 .

[45]  M. Egenhofer,et al.  Point-Set Topological Spatial Relations , 2001 .

[46]  Giangiacomo Gerla,et al.  Connection Structures: Grzegorczyk's and Whitehead's Definitions of Point , 1996, Notre Dame J. Formal Log..

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

[48]  T. D. Laguna Point, Line, and Surface, as Sets of Solids , 1922 .

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

[50]  Anthony G. Cohn,et al.  Qualitative Spatio-Temporal Continuity , 2001, COSIT.

[51]  J. Thomson On being and saying : essays for Richard Cartwright , 1987 .

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

[53]  Ian Pratt-Hartmann,et al.  A Complete Axiom System for Polygonal Mereotopology of the Real Plane , 1998, J. Philos. Log..

[54]  Brandon Bennett,et al.  Carving Up Space: Steps Towards Construction of an Absolutely Complete Theory of Spatial Regions , 1996, JELIA.