The computational properties of qualitative spatial reasoning have been investigated to some degree. However, the question for the boundary between polynomial and NP-hard reasoning problems has not been addressed yet. In this paper we explore this boundary in the "Region Connection Calculus " RCC-8. We extend Bennett's encoding of RCC-8 in modal logic. Based on this encoding, we prove that reasoning is NP-complete in general and identify a maximal tractable subset of the relations in RCC-8 that contains all base relations. Further, we show that for this subset path-consistency is sufficient for deciding consistency.
|
1705
|
Maintaining knowledge about temporal intervals
– Allen
- 1983
|
|
877
|
Consistency in networks of relations
– Mackworth
- 1977
|
|
556
|
An Introduction to Modal Logic
– Hughes, Cresswell
- 1968
|
|
498
|
Modal Logic: An Introduction
– Chellas
- 1980
|
|
496
|
The complexity of theorem-proving procedures
– Cook
- 1971
|
|
368
|
A spatial logic based on regions and connection
– Randell, Cui, et al.
- 1992
|
|
354
|
Networks of constraints: Fundamental properties and applications to picture processing
– Montanari
- 1974
|
|
320
|
Constraint propagation algorithms for temporal reasoning: a revised report
– Vilain, Kautz, et al.
- 1989
|
|
260
|
The complexity of some polynomial network consistency algorithms for constraint satisfaction problems
– Mackworth, Freuder
- 1985
|
|
249
|
Proof methods for modal and intuitionistic logics
– Fitting
- 1983
|
|
247
|
The Complexity of Satisfiability Problems
– Schaefer
- 1978
|
|
243
|
Constraint Satisfaction
– Mackworth
- 1987
|
|
171
|
Reasoning about Binary Topological Relations
– Egenhofer
- 1991
|
|
160
|
Many-Valued Modal Logics
– Fitting
- 1991
|
|
148
|
Correspondence theory
– Benthem
- 1984
|
|
125
|
Computers and intractability—a guide to the theory of NP-completeness
– Garey, Johnson
- 1979
|
|
121
|
Reasoning about temporal relations: a maximal tractable subclasses of Allen’s Interval Algebra
– Nebel, Burckert
- 1994
|
|
88
|
Spatial reasoning with propositional logics
– Bennett
- 1994
|
|
77
|
Linear time algorithms for testing the satisfiability of propositional horn formulae
– Dowling, Gallier
- 1984
|
|
76
|
Complexity and algorithms for reasoning about time: a graphic-theoretic approach
– Golumbic, Shamir
- 1993
|
|
76
|
Qualitative spatial representation and reasoning techniques
– Cohn
- 1997
|
|
72
|
Modal logics for qualitative spatial reasoning
– Bennett
- 1996
|
|
68
|
On binary constraint problems
– Ladkin, Maddux
- 1994
|
|
65
|
Topological inference
– Grigni, Papadias, et al.
- 1995
|
|
51
|
D A Randell, ‘Qualitative simulation based on a logical formalism of space and time
– Cui, Cohn
- 1992
|
|
42
|
Computing transitivity tables: A challenge for automated theorem provers
– RANDELL, COHN, et al.
- 1992
|
|
40
|
Solving hard qualitative temporal reasoning problems: Evaluating the efficiency of using the ORD-Horn class
– Nebel
- 1997
|
|
37
|
Computational properties of qualitative spatial reasoning: First results
– Nebel
- 1995
|
|
35
|
A canonical model of the region connection calculus
– Renz
- 1998
|
|
32
|
Foundations of spatioterminological reasoning with description logics
– Haarslev, Lutz, et al.
- 1998
|
|
32
|
Unit refutations and horn sets
– Henschen, Wos
- 1974
|
|
31
|
Mathematical Induction
– Walther
- 1994
|
|
26
|
A complete classification of tractability in RCC-5
– JONSSON, DRAKENGREN
- 1997
|
|
25
|
Logical Representations for Automated Reasoning about Spatial Relationships
– Bennett
- 1997
|
|
21
|
Naive Topology: modeling the force pump
– Randell, Cohn, et al.
- 1992
|
|
20
|
Efficient methods for qualitative spatial reasoning
– Renz, Nebel
|
|
18
|
When does a composition table provide a complete and tractable proof procedure for a relational constraint language
– Bennett, Isli, et al.
- 1997
|
|
17
|
Combining topological and qualitative size constraints for spatial reasoning
– Gerevini, Renz
- 1998
|
|
16
|
Fast algebraic methods for interval constraint problems
– Ladkin, Reinefeld
- 1997
|
|
10
|
VITRA GUIDE: Multimodal route descriptions for computer assisted vehicle navigation
– Maa, Wazinski, et al.
- 1993
|
|
6
|
Combining multiple representations in a spatial reasoning system
– Bennett, Cohn, et al.
- 1997
|
|
4
|
Using spatial logic to describe visual programming languages
– Gooday, Cohn
- 1996
|
|
