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Abstract: In this paper I investigate how one might arrive at a set of existential axioms that would specify a complete 1st-order theory of spatial regions. In such a theory all formulae would be true or false (given that constants are taken as existentially quantified with widest scope). The RCC spatial logic based on the relation of connectedness, C, will be taken as the starting point. This theory is not complete, since it does not guarantee the realisation of all possible configurations of regions.... (Update)
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.... (Clarke 1981) Among these, particular relevance for AI purposes has the so called RCC theory (Randell and Cohn 1992, Gotts 1994, Bennett 1995, Gotts et al. 1996) which has been recently joined by other proposals originating in the area of philosophy and linguistics...
...that the external connection may be tangency or overlapping, for example) while in the RCC 8 model this distinction is possible. Bennett (1994, 1995), used propositional logic to represent RCC reasoning problems. He observed that, given a propositional logic, and interpreting...
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BibTeX entry: (Update)
Bennett, B. (1995a). Carving Up Space: existential axioms for a formal theory of spatial regions. IJCAI-95 workshop on Spatial and Temporal Reasoning. http://citeseer.ist.psu.edu/bennett95carving.html More
@misc{ bennett-carving,
author = "B. Bennett",
title = "Carving Up Space: existential axioms for a formal theory of spatial regions",
text = "Bennett, B. (1995a). Carving Up Space: existential axioms for a formal
theory of spatial regions. IJCAI-95 workshop on Spatial and Temporal Reasoning.",
url = "citeseer.ist.psu.edu/bennett95carving.html" }
Citations (may not include all citations):225 A spatial logic based on regions and connection - Randell, Cui et al. - 1992
76 Parts: A Study In Ontology (context) - Simons - 1987
73 connection (context) - Clarke - 1981
64 Individuals and points (context) - Clarke - 1985
48 An interval-based representation of temporal knowledge (context) - Allen - 1981
41 Process and Reality (context) - Whitehead - 1929
39 A more expressive formulation of many sorted logic (context) - Cohn - 1987
32 What is elementary geometry (context) - Tarski - 1959
31 How far can we `C (context) - Gotts - 1994
30 Foundations of the geometry of solids (context) - Tarski - 1956
28 The calculus of individuals and its uses (context) - Leonard, Goodman - 1940
25 The Logic of Time Representation - Ladkin - 1987
12 Connection structures (context) - Biacino, Gerla - 1991
4 Some observations and puzzles about composing spatial and te.. - Bennett - 1994
1 Towards a decision procedure for the RCC theory of spatial r.. - Bennett - 1995
Documents on the same site (http://www.scs.leeds.ac.uk/staff/brandon.html):
Towards a Decision Procedure for the RCC Theory of Spatial.. - Bennett (1995) (Correct)
Spatial Reasoning with Propositional Logics - Bennett (1994) (Correct)
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