A Categorical Axiomatisation of Region-Based Geometry
Published 1 January 2001
Brandon Bennett
Citations41
SJR quartileQ3
SJR score0.29
SNIP0.62
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
Region Based Geometry is an axiomatic theory of qualitative configurations of spatial regions based on Tarski's Geometry of Solids, in which the parthood relation and the concept of sphere are taken as primitive.
Abstract
Region Based Geometry (RBG) is an axiomatic theory of qualitative configurations of spatial regions. It is based on Tarski's Geometry of Solids, in which the parthood relation and the concept of sphere are taken as primitive. Whereas in Tarski's theory the combination of mereological and geometrical axioms involves set theory, in RBG the interface is achieved by purely 1st-order axioms. This means that the elementary sublanguage of RBG is extremely expressive, supporting inferences involving both mereological and geometrical concepts. Categoricity of the RBG axioms is proved: all models are isomorphic to a standard interpretation in terms of Cartesian spaces over R.
Keywords
Computer Science
A Spatial Logic based on Regions and Connection.
1,927 Citations1992David Randell, Zhanfeng Cui +1 more
An interval logic for reasoning about space is described, which supports a simpler ontology, has fewer functions and relations, yet does not su(cid:11)er in terms of its useful expressiveness.
Parts : a Study in Ontology
983 Citations1987Peter Simons
Studies in logic and the foundations of mathematicsWhat is Elementary Geometry?
303 Citations1959Alfred Tarski
Lecture notes in computer scienceQualitative spatial representation and reasoning techniques
183 Citations1997Anthony G. Cohn
The state of the art in Qualitative Spatial Reasoning is surveyed, covering representation and reasoning issues as well as pointing to some application areas.
Toward a geometry of common sense: a semantics and a complete axiomatization of mereotopology
170 Citations1995Nicholas Asher, Laure Vieu
This work offers an alternative to Tarski, starting with mereotopological notions that have proved useful in the semantic analysis of spatial expressions and gives a complete axiomatization of this account of mereotipological reasoning.
Logic Journal of IGPLModal Logics for Qualitative Spatial Reasoning
131 Citations1996Brandon Bennett
It is shown how 0-order logics can be given a spatial interpretation: constants denote regions and logical operators correspond to operations on regions which are important for characterising spatial situations.
BIROn (Birkbeck, University of London)Spatio-temporal representation and reasoning based on RCC-8
131 Citations2000Frank Wolter, Michael Zakharyaschev
A pointless theory of space based on strong connection and congruence
125 Citations1996Stefano Borgo, Nicola Guarino +1 more
A logical theory of space where only tridimensional regions are assumed in the domain is presented, and three distinct primitives are used to describe their mereological, topological and morphological properties.
A Qualitative Theory of Motion Based on Spatio-Temporal Primitives.
111 Citations1998Philippe Müller
It is shown what kind of properties usually assumed as desirable parts of any space-time theory are recovered from the authors' model, thus giving a sound theoretical basis for a natural, qualitative representation of motion.
Maximal Tractable Fragments of the Region Connection Calculus: A Complete Analysis
102 Citations1999Jochen Renz
A general method for proving tractability of reasoning over disjunctions of jointly exhaustive and pairwise disjoint relations of Allen's temporal interval relations and their spatial counterpart, the R.CC8 relations by Randell, Cui, and Colin is presented.
Journal of Philosophical LogicA Complete Axiom System for Polygonal Mereotopology of the Real Plane
66 Citations1998Ian Pratt‐Hartmann, Dominik Schoop
A calculus for mereotopological reasoning in which two-dimensional spatial regions are treated as primitive entities in which polygonal open subsets of the real plane serve as elements of the domain is presented.
European Conference on Artificial IntelligenceSpatial reasoning in RCC-8 with Boolean region terms
54 Citations2000Frank Wolter, Michael Zakharyaschev
Squamous cell carcinoma of the skin was studied in 12 patients in vivo with the use of intralesional tritiated thymidine as a marker for cell proliferation kinetics and the application of cell kinetics to programming chemotherapy for skin cancer with phase-specific cytotoxins was discussed.
A foundation for region-based qualitative geometry
49 Citations2000Brandon Bennett, Anthony G. Cohn +2 more
A categorical axiom system, whose models can be interpreted classically in terms of Cartesian spaces over ℝ, and it is shown that within this system the concept of sphere and the congruence relation are interdefinable.
Artificial IntelligenceOn the complexity of qualitative spatial reasoning: A maximal tractable fragment of the Region Connection Calculus
44 Citations1999Jochen Renz, Bernhard Nebel
It is proved that reasoning is NP-complete in general and identified a maximal tractable subset of the relations in RCC-8 that contains all base relations and shows that for this subset path-consistency is sufficient for deciding consistency.
Artificial Intelligence in EngineeringA logical framework for commonsense predictions of solid object behaviour
36 Citations1988Ernest Davis
A first-order logic in which one can state simple physical problems and derive their solution deductively, without recourse to solving differential equations is presented, substantially more expressive and powerful than any previous AI representational system in this domain.
Describing Rigid Body Motions in a Qualitative Theory of Spatial Regions
32 Citations2000Brandon Bennett, Anthony G. Cohn +2 more
The expressive power of a recently developed qualitative region-based geometry is explored and applied to the problem of representing and reasoning about the motion of rigid bodies within a confining environment.
Undecidability of Plane Polygonal Mereotopology.
29 Citations1998Christoph Dornheim
It turns out that both the relations usually provided by mereotopolo-gies and more subtle topological relations are elementarily deenable in the model and Post's correspondence problem can be reduced to the decision problem of the model.
Spatial locations via morpho-mereology
16 Citations2000Matteo Cristani, Anthony G. Cohn +1 more
An axiomatisation for congruence, the chosen morphological primitive, the notion of mobile part, a subset of morphomereological relations suitable for representing spatial locations, and the computational complexity of this set are presented.