Contact relation algebras

Contact relation algebras (CRAs), introduced in [25], arise from the study of “part—of” and “contact” relations rooted in mereology and have applications, for example, in qualitative spatial reasoning. We give an overview of the origins of CRAs and numerous examples.

[1]  Ian Pratt-Hartmann,et al.  Expressivity in Polygonal, Plane Mereotopology , 2000, J. Symb. Log..

[2]  R. Lyndon.  THE REPRESENTATION OF RELATIONAL ALGEBRAS , 1950 .

[3]  James F. Allen.  Towards a General Theory of Action and Time , 1984, Artif. Intell..

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

[5]  Ivo Düntsch,et al.  Relation restricted prediction analysis , 1999 .

[6]  Ivo Düntsch,et al.  A relation - algebraic approach to the region connection calculus , 2001, Theor. Comput. Sci..

[7]  Ivo Düntsch.  Rough Relation Algebras , 1994, Fundam. Informaticae.

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

[9]  Carola Eschenbach,et al.  Classical mereology and restricted domains , 1995, Int. J. Hum. Comput. Stud..

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

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

[12]  Bernhard Nebel,et al.  Efficient Algorithms for Qualitative Spatial Reasoning , 1998, ECAI.

[13]  J. Fodor,et al.  Parametrized preference structures and some geometrical interpretation , 1997 .

[14]  Eugene C. Luschei,et al.  The logical systems of Lesniewski , 1962 .

[15]  A. Tarski,et al.  A Formalization Of Set Theory Without Variables , 1987 .

[16]  Michael F. Worboys,et al.  Imprecision in Finite Resolution Spatial Data , 1998, GeoInformatica.

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

[18]  Anders Læsø Madsen,et al.  Proceedings of the 13th European Conference on Artificial Intelligence , 1998 .

[19]  Anthony G. Cohn,et al.  Computing Transivity Tables: A Challenge For Automated Theorem Provers , 1992, CADE.

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

[21]  Gunther Schmidt,et al.  A Necessary Relation Algebra for Mereotopology , 2001, Stud Logica.

[22]  Anthony G. Cohn,et al.  Qualitative Spatial Representation and Reasoning with the Region Connection Calculus , 1997, GeoInformatica.

[23]  Robin Hirsch,et al.  Expressive Power and Complexity in Algebraic Logic , 1997, J. Log. Comput..

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

[25]  Thomas Drakengren.  A Complete Classiication of Tractability in the Spatial Theory Rcc-5 , 1997 .

[26]  Hajnal Andréka,et al.  The lattice of varieties of representable relation algebras , 1994, Journal of Symbolic Logic.

[27]  Vaughan R. Pratt,et al.  Dynamic algebras as a well-behaved fragment of relation algebras , 1988, Algebraic Logic and Universal Algebra in Computer Science.

[28]  Godehard Link.  Algebraic semantics in language and philosophy , 1997 .

[29]  Alfred Tarski,et al.  Relational selves as self-affirmational resources , 2008 .

[30]  Brandon Bennett,et al.  Logical representations for automated reasoning about spatial relationships , 1997 .

[31]  Alfred Tarski,et al.  Distributive and Modular Laws in the Arithmetic of Relation Algebras , 1953 .

[32]  S. D. Comer,et al.  On connections between information systems, rough sets and algebraic logic , 1993 .

[33]  Ivo Düntsch,et al.  Tangent Circle Algebras , 2001, RelMiCS.

[34]  N. Gotts.  An Axiomatic Approach to Topology For Spatial Information Systems , 1996 .

[35]  Anthony G. Cohn,et al.  Qualitative Spatial Representation and Reasoning Techniques , 1997, KI.

[36]  Bernhard Nebel,et al.  Reasoning about temporal relations: a maximal tractable subclass of Allen's interval algebra , 1994, JACM.

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

[38]  B. Bennett,et al.  When does a Composition Table Provide a Complete and TractableProof Procedure for a Relational Constraint Language ? , 1997 .

[39]  Ivo Düntsch,et al.  Relations Algebras in Qualitative Spatial Reasoning , 1999, Fundam. Informaticae.

[40]  A. Tarski,et al.  Zur Grundlegung der Boole'schen Algebra. I , 1935 .

[41]  Ivo Düntsch.  Small integral relation algebras generated by a partial order , 1991 .

[42]  Andrzej Skowron,et al.  Rough mereology: A new paradigm for approximate reasoning , 1996, Int. J. Approx. Reason..

[43]  MAX J. EGENHOFER,et al.  Point Set Topological Relations , 1991, Int. J. Geogr. Inf. Sci..

[44]  Johan van Benthem,et al.  The Logic of Time , 1983 .

[45]  C. Pollard,et al.  Center for the Study of Language and Information , 2022 .

[46]  Bernhard Nebel,et al.  On the Complexity of Qualitative Spatial Reasoning: A Maximal Tractable Fragment of the Region Connection Calculus , 1999, Artif. Intell..

[47]  James F. Allen.  Maintaining knowledge about temporal intervals , 1983, CACM.

[48]  P. Simons.  Parts: A Study in Ontology , 1991 .

[49]  B. Jónsson.  Varieties of relation algebras , 1982 .

[50]  Carus Paul.  The Foundation of Mathematics. , 1920 .

[51]  Peter B. Ladkin,et al.  On binary constraint problems , 1994, JACM.

[52]  Jan Woleński.  Review of S. Leśniewski, Collected Works, Vols. I-II, ed. by S. J. Surma, J. T. Srzednicki, D. I. Barnett, and V. F. Rickey , 2000 .