Abstract
In recent investigations of Spatial Reasoning, SpatialKnowledge Representation, and Geographic Information Systems, asignificant effort has been spent by many scholars of the areaabout the problem of representing properties of spatial objects bymeans of logical theories.
An analogous effort has been the problem of analyzingthe qualitative relations which can be established between twospace regions. These investigations have led to a generalframework of the field known by the term ``mereo-topology''.
Though both the above mentioned approaches have proved to besuccessful in the investigation of formal and practically relevantaspects of spatial objects, no attempt has been carried out in the direction of integrating the approaches and looking at the relationshipbetween a general logical theory of space and mereo-topology from an analytical point of view, in particular for exploiting thecombinatorial behaviour of such an integrated model.
This paper intends to fill the gap and analyze the behaviour ofspatial formulae of a logical theory of space as objects which canbe classified based on the behaviour they exhibit with respect tothe parts and supertparts of the regions where they are true. Wename these categories of behaviourinheritance modalities.
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References
Allen, J.F. (1984).Towards a General Theory of Action and Time, Artificial Intelligence 232): 123–154.
Belussi, A. and Cristani, M. (1999).Defining Truth Inheritance of Spatial Predicates trough Region Chains.In Conference on Spatial Information Theory.
Bennett, B. (1994).Spatial Reasoning with Propositional Logic.In J. Doyle and E. Sandewall and P. Torasso (eds.), Proceedings of the 4th International Conference on Principles of Knowledge Representation and Reasoning (KR-94) (pp. 165–176).San Francisco, CA, USA: Morgan Kaufmann.
Bennett, B. (1995).Carving Up Space: Existential Axioms for a Formal Theory of Spatial Regions.In Proceedings of the IJCAI 95 Workshop on Spatial and Temporal Reasoning.Montreal.
Bennett, B. (1996) Modal Logics for Qualitative Spatial Reasoning, Journal of the Interest Group in Pure and Applied Logic (IGPL) 4(1): 23–45.
Bennett, B. (1997).Logical Representations for Automated reasoning about Spatial Relationships.PhD thesis, School of Computer Studies, University of Leeds, Leeds, UK.
Bennett, B., Cohn, A.G., Torrini, P. and Hazarika, S. (2000a).Describing Rigid Body Motions in a Qualitative Theory of Spatial Regions.In Proceedings of the 17th National Conference on AI (AAAI-2000) (pp. 503–509).Austin, Texas.
Bennett, B., Cohn, A.G., Torrini, P. and Hazarika, S.M. (2000b).A Foundation for Region-Based Qualitative Geometry.In W. Horn (ed.), Proceedings of ECAI-2000 (pp. 204–208).
Borgo, S., Guarino, N. and Masolo, C. (1996).A Pointless Theory of Space Based On Strong Connection and Congruence.In L. Carlucci Aiello and J. Doyle (eds.), Proceedings of the 6th International Conference on Principles of Knowledge Representation and Reasoning (KR-96) (pp. 220–229).San Francisco, CA, USA: Morgan Kaufmann.
Cohn, A.G. (1987).A More Expressive Formulation of Many Sorted Logic, Journal of Automated Reasoning 3: 113–200.
Cohn, A.G. (1993).Modal and Non-modal Qualitative Spatial Logics.In H.W. Guesgen, F.D. Anger and J. van Benthem (eds.), Proceedings of the Workshop on Spatial and Temporal Reasoning, IJCAI-93, IJCAI.
Echenbach, C. (2001).Composition Tables as Axiomatic Systems.In Proceedings of the second International Conference on Formal Ontology in Information Systems.
Egenhofer, M.J. (1991).Reasoning about Binary Topological Relations.In O. Gunther and H. J. Schek (eds.), '91, number 525 in Lecture Notes in Computer Science (pp. 143–160).New York, NY, USA: Springer-Verlag.
Egenhofer, M.J. and Franzosa, R. (1991).Point-Set Topological Spatial Relations.International Journal of Geographical Information Systems 5(2): 161–174.
Egenhofer, M.J. and Herring, J. (1990).A Mathematical Framework for the Definition of Topological Relationships.In Fourth International Symposium on Spatial Data Handling (pp. 803–813).Zurich, Switzerland.
Eschenbach, C. (August 1999).A Predication Calculus for Qualitative Spatial Representations.In C. Freksa and D. M. Mark (eds.), Proceedings of the International Conference on Spatial Information Theory, number 1661 in Lecture Notes in Computer Science (pp. 157–172).Stade, Germany: Springer Verlag.
Grigni, M. and Chen, Z. and Papadimitriou, C. (1996).Planar Map Graphs.In Proceedings of the Thirteenth Annual ACM Symposium on the Theory of Computing, May 23-26, 1998, Dallas, Texas, USA (pp. 514–523).ACM.
Grigni, M., Papadias, D. and Papadimitriou, C. (August 1995).Topological Inference.In C. Mellis (ed.), Proceeding of the 14th International Joint Conference on Artificial Intelligence (IJCAI-95) (pp. 901–906).Montréal, PQ, Canada: Morgan Kaufmann.
Guarino, N. (1995).Formal Ontology, Conceptual Analysis and Knowledge Representation, International Journal of Human and Computer Studies 43(5/6): 625–640.
Lemon, O.J. (1996).Semantical Foundations of Spatial Logics.In L. Carlucci Aiello and J. Doyle (eds.), Proceedings of the 6th International Conference on Principles of Knowledge Representation and Reasoning (KR-96) (pp. 212–219).San Francisco, CA, USA: Morgan Kaufmann.
Paredaens, J. and Kuijpers, B. (1998).Data Models and Query Languages for Spatial Databases.Data and Knowledge Engineering 25: 29–53.
Paredaens, J., Kuijpers, B. and Van den Bussche, L. (1995).Losseles Representation of Topological Spatial Data.In M.J. Egenhofer and J.R. Herring (eds.), Advances in Spatial Databases, 4th International Symposium, SSD'95, Portland, Maine, USA, August 6- 9, 1995, Proceedings, volume 951 of Lecture Notes in Computer Science (pp. 1–13).Springer.
Randell, D.A. and Cohn, A.G. (May 1989).Modelling Topological and Metrical Properties of Physical Processes.In R.J. Brachman and H.J. Levesque and R. Reiter (eds.), Proceedings of the 1st International Conference on Knowledge Representation and Reasoning (KR-89) (pp. 55–66).Toronto, ON, Canada: Morgan Kaufmann.
Randell, D.A. and Cui, Z. and Cohn, A.G. (October 1992).A Spatial Logic Based on Regions and Connection.In B. Swartout and B. Nebel (eds.), Proceedings of the 3rd International Conference on Principles of Knowledge Representation and Reasoning (KR-92) (pp. 165–176).Cambridge, MA, USA: Morgan Kaufmann.
Shoham, Yoav (1988).Reasoning About Change: Time and Causation From the Standpoint of Artificial Intelligence.Cambridge, Massachusetts: The MIT Press.
Simons, P. (1987).Parts: A Study in Ontology.Oxford, UK: Clarendon Press.
Varzi, A. (1996).Parts, Wholes and Part-Whole Relations: The Prospects of Mereotopology.Data and Knowledge Engineering 20(3).Special Issue on Modelling Parts and Wholes.
Vianu, V., Papadimitriou, C.H. and Suciu, D. (1996).Topological Queries in Spatial Databases.In Proceedings of the Fifteenth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, June 3-5, 1996, Montreal, Canada (pp. 81–92).ACM Press.
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Belussi, A., Cristani, M. Mereological inheritance. Spatial Cognition and Computation 2, 467–494 (2000). https://doi.org/10.1023/A:1015536208092
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DOI: https://doi.org/10.1023/A:1015536208092