## Spatio-temporal representation and reasoning based on RCC-8 (2000)

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Venue: | In Proceedings of the seventh Conference on Principles of Knowledge Representation and Reasoning, KR2000 |

Citations: | 58 - 10 self |

### BibTeX

@INPROCEEDINGS{Wolter00spatio-temporalrepresentation,

author = {Frank Wolter and Michael Zakharyaschev},

title = {Spatio-temporal representation and reasoning based on RCC-8},

booktitle = {In Proceedings of the seventh Conference on Principles of Knowledge Representation and Reasoning, KR2000},

year = {2000},

pages = {3--14},

publisher = {Morgan Kaufmann}

}

### OpenURL

### Abstract

this paper is to introduce a hierarchy of languages intended for qualitative spatio-temporal representation and reasoning, provide these languages with topological temporal semantics, construct effective reasoning algorithms, and estimate their computational complexity.

### Citations

2524 | Maintaining knowledge about temporal intervals
- Allen
- 1983
(Show Context)
Citation Context ...roduction Qualitative representation and reasoning---as a field within AI---has been quite successful in dealing with both time and space. There exists a wide spectrum of temporal languages (see e.g. =-=[1, 14, 32]-=-). There is a variety of spatial formalisms (e.g. [7, 9, 21, 26]). In both cases effective reasoning procedures have been developed and implemented (e.g. [20, 18, 25, 13, 2, 29]). The next apparent an... |

1620 |
A.: The Temporal Logic of Reactive and Concurrent Systems
- Manna, Pnueli
- 1992
(Show Context)
Citation Context ...that these two formalisms fit together perfectly well indeed.) PTL is one of the best known temporal logics which has found many applications in CS and AI (e.g. program verification and specification =-=[22, 23]-=-, distributed and multi-agent systems [11], or temporal databases [6]). It is decidable and PSPACE-complete (see e.g. [14]). Thus, the problem of constructing effective spatio-temporal formalisms can ... |

1594 |
Reasoning About Knowledge
- Fagin, Halpern, et al.
- 1995
(Show Context)
Citation Context ...ly well indeed.) PTL is one of the best known temporal logics which has found many applications in CS and AI (e.g. program verification and specification [22, 23], distributed and multi-agent systems =-=[11]-=-, or temporal databases [6]). It is decidable and PSPACE-complete (see e.g. [14]). Thus, the problem of constructing effective spatio-temporal formalisms can be viewed as designing decidable two-dimen... |

625 | A.: A Spatial Logic Based on Regions and Connection
- Randell, Cui, et al.
- 1992
(Show Context)
Citation Context ...ld within AI---has been quite successful in dealing with both time and space. There exists a wide spectrum of temporal languages (see e.g. [1, 14, 32]). There is a variety of spatial formalisms (e.g. =-=[7, 9, 21, 26]-=-). In both cases effective reasoning procedures have been developed and implemented (e.g. [20, 18, 25, 13, 2, 29]). The next apparent and natural step would be to combine these two kinds of reasoning.... |

409 |
Temporal Verification of Reactive Systems: Safety
- Manna, Pnueli
- 1995
(Show Context)
Citation Context ...that these two formalisms fit together perfectly well indeed.) PTL is one of the best known temporal logics which has found many applications in CS and AI (e.g. program verification and specification =-=[22, 23]-=-, distributed and multi-agent systems [11], or temporal databases [6]). It is decidable and PSPACE-complete (see e.g. [14]). Thus, the problem of constructing effective spatio-temporal formalisms can ... |

159 | Description logics with concrete domains: A survey
- Lutz
- 2003
(Show Context)
Citation Context ...um of temporal languages (see e.g. [1, 14, 32]). There is a variety of spatial formalisms (e.g. [7, 9, 21, 26]). In both cases effective reasoning procedures have been developed and implemented (e.g. =-=[20, 18, 25, 13, 2, 29]-=-). The next apparent and natural step would be to combine these two kinds of reasoning. The importance of such a step for both theory and applications is beyond any doubt. And of course there have bee... |

112 | Qualitative spatial representation and reasoning techniques
- Cohn
- 1997
(Show Context)
Citation Context ...s the booleans) only to RCC-8 formulas. (Actually even this language is enough to express, for instance, the assumption that change is continuous, or the notion of conceptual neighbourhoods; see e.g. =-=[10]-=-.) The most expressive one, ST + 2 , makes it possible to form unions, intersections, and complementations of spatial regions, and to apply temporal operators to both formulas and region terms (for in... |

110 |
Applications of the theory of Boolean rings to general topology
- Stone
- 1937
(Show Context)
Citation Context ...ble was shown by Bennett [2, 3] who encoded RCC-8 in propositional intuitionistic logic and modal system S4 using the well-known fact that both of them are complete with respect to topological spaces =-=[30, 31]-=-. An elementary proof of the correctness of the encoding is provided in [?]. To see the intuition behind this encoding, it suffices to observe 3 that C and the eight predicates of RCC8 can be represen... |

108 | Temporal query languages: a survey
- Chomicki
- 1994
(Show Context)
Citation Context ...of the best known temporal logics which has found many applications in CS and AI (e.g. program verification and specification [22, 23], distributed and multi-agent systems [11], or temporal databases =-=[6]-=-). It is decidable and PSPACE-complete (see e.g. [14]). Thus, the problem of constructing effective spatio-temporal formalisms can be viewed as designing decidable two-dimensional modal logics one dim... |

108 |
A calculus of individuals based on ’Connection
- Clarke
- 1981
(Show Context)
Citation Context ...ld within AI---has been quite successful in dealing with both time and space. There exists a wide spectrum of temporal languages (see e.g. [1, 14, 32]). There is a variety of spatial formalisms (e.g. =-=[7, 9, 21, 26]-=-). In both cases effective reasoning procedures have been developed and implemented (e.g. [20, 18, 25, 13, 2, 29]). The next apparent and natural step would be to combine these two kinds of reasoning.... |

103 | Spatial reasoning with propositional logics
- Bennett
- 1994
(Show Context)
Citation Context ...um of temporal languages (see e.g. [1, 14, 32]). There is a variety of spatial formalisms (e.g. [7, 9, 21, 26]). In both cases effective reasoning procedures have been developed and implemented (e.g. =-=[20, 18, 25, 13, 2, 29]-=-). The next apparent and natural step would be to combine these two kinds of reasoning. The importance of such a step for both theory and applications is beyond any doubt. And of course there have bee... |

98 |
Using the universal modality: gains and questions
- Goranko, Passy
(Show Context)
Citation Context ...ility and complexity results formulated above are proved in Section 5 by means of embedding ST + 2 into a temporalized version of the propositional modal logic S4 extended with the universal modality =-=[16]-=- and then using the method of quasimodels developed in [33]. Denote by ML the propositional modal language whose connectives are the booleans, the necessity and possibility operators I and C of S4, th... |

87 | Modal logics for qualitative spatial reasoning
- Bennett
- 1995
(Show Context)
Citation Context ...nt RCC-8 of RCC containing eight jointly exhaustive and pairwise disjoint base relations between spatial regions. This fragment has attracted considerable attention of the spatial reasoning community =-=[2, 3, 19, 27, 28, 29]-=-. First, it is sufficiently expressive for various application purposes, say in GIS. And second, RCC-8 has nice computational properties: it turns out to be decidable [2], in fact NP-complete [29]. Ac... |

86 |
Higher-Order Logic
- Benthem, Doets
- 1983
(Show Context)
Citation Context ...roduction Qualitative representation and reasoning---as a field within AI---has been quite successful in dealing with both time and space. There exists a wide spectrum of temporal languages (see e.g. =-=[1, 14, 32]-=-). There is a variety of spatial formalisms (e.g. [7, 9, 21, 26]). In both cases effective reasoning procedures have been developed and implemented (e.g. [20, 18, 25, 13, 2, 29]). The next apparent an... |

74 |
Individuals and points. Notre Dame
- Clarke
- 1985
(Show Context)
Citation Context ...ds of reasoning. The importance of such a step for both theory and applications is beyond any doubt. And of course there have been attempts to construct spatio-temporal hybrids. For example, Clarke's =-=[7, 8]-=- intended interpretation of his region-based calculus was spatio-temporal. Region Connection Calculus RCC of [26] contained a function space(x; t) for representing the space occupied by object x at mo... |

62 | M.: Multi-dimensional description logics
- Wolter, Zakharyaschev
- 1999
(Show Context)
Citation Context ... Section 5 by means of embedding ST + 2 into a temporalized version of the propositional modal logic S4 extended with the universal modality [16] and then using the method of quasimodels developed in =-=[33]-=-. Denote by ML the propositional modal language whose connectives are the booleans, the necessity and possibility operators I and C of S4, the universal necessity and possibility operators 8 and 9, an... |

58 | A qualitative theory of motion based on spatio-temporal primitives
- MULLER
- 1998
(Show Context)
Citation Context ...n of his region-based calculus was spatio-temporal. Region Connection Calculus RCC of [26] contained a function space(x; t) for representing the space occupied by object x at moment of time t. Muller =-=[24]-=- developed a first-order theory for reasoning about motion of spatial entities. However, in contrast to the `one-dimensional' temporal and spatial cases, no effective procedures capable of reasoning a... |

55 |
Metamathematics of modal logic
- Goldblatt
- 1976
(Show Context)
Citation Context ...lowing lemma is actually based on the Stone--J'onsson--Tarski representation of topological boolean algebras, in particular, topological spaces, in the form of general frames (for definitions consult =-=[15]-=- or [5]). Lemma 18. (i) If a CI-formula ' is satisfied in a topological ML-model with FSA, then ' is satisfied in a Kripke ML-model with the FSA. (ii) If a CI fl -formula ' is satisfied in a topologic... |

51 |
Modeling topological spatial relations: Strategies for query processing
- Clementini, Sharma, et al.
- 1994
(Show Context)
Citation Context ...ld within AI---has been quite successful in dealing with both time and space. There exists a wide spectrum of temporal languages (see e.g. [1, 14, 32]). There is a variety of spatial formalisms (e.g. =-=[7, 9, 21, 26]-=-). In both cases effective reasoning procedures have been developed and implemented (e.g. [20, 18, 25, 13, 2, 29]). The next apparent and natural step would be to combine these two kinds of reasoning.... |

49 | Qualitative spatial reasoning with topological information
- Renz
- 2002
(Show Context)
Citation Context ...nt RCC-8 of RCC containing eight jointly exhaustive and pairwise disjoint base relations between spatial regions. This fragment has attracted considerable attention of the spatial reasoning community =-=[2, 3, 19, 27, 28, 29]-=-. First, it is sufficiently expressive for various application purposes, say in GIS. And second, RCC-8 has nice computational properties: it turns out to be decidable [2], in fact NP-complete [29]. Ac... |

47 | A canonical model of the region connection calculus
- Renz
(Show Context)
Citation Context ...nt RCC-8 of RCC containing eight jointly exhaustive and pairwise disjoint base relations between spatial regions. This fragment has attracted considerable attention of the spatial reasoning community =-=[2, 3, 19, 27, 28, 29]-=-. First, it is sufficiently expressive for various application purposes, say in GIS. And second, RCC-8 has nice computational properties: it turns out to be decidable [2], in fact NP-complete [29]. Ac... |

46 | A decision algorithm for full propositional temporal logic
- Kesten, Manna, et al.
- 1993
(Show Context)
Citation Context ...um of temporal languages (see e.g. [1, 14, 32]). There is a variety of spatial formalisms (e.g. [7, 9, 21, 26]). In both cases effective reasoning procedures have been developed and implemented (e.g. =-=[20, 18, 25, 13, 2, 29]-=-). The next apparent and natural step would be to combine these two kinds of reasoning. The importance of such a step for both theory and applications is beyond any doubt. And of course there have bee... |

30 | A complete classification of tractability in RCC-5
- Jonsson, Drakengren
- 1997
(Show Context)
Citation Context |

26 |
Aussagenkalkül und die Topologie, Fund
- Tarski, Der
- 1938
(Show Context)
Citation Context ...ble was shown by Bennett [2, 3] who encoded RCC-8 in propositional intuitionistic logic and modal system S4 using the well-known fact that both of them are complete with respect to topological spaces =-=[30, 31]-=-. An elementary proof of the correctness of the encoding is provided in [?]. To see the intuition behind this encoding, it suffices to observe 3 that C and the eight predicates of RCC8 can be represen... |

23 |
Logics containing K4, Part II
- Fine
- 1985
(Show Context)
Citation Context ... (v; km ) j= K / and so (v; n) j= K 3 + /. The case of 2 + / is treated similarly. Note that we use FSA only when ' contains a CI-term with 3 + or 2 + . The existence of R-maximal points follows from =-=[12]-=- (see Theorem 10.36 in [5]). 2 A quasi-order hV; Si is said to be of depths1 if V can be represented as the disjoint union of two sets, V 1 and V 0 , in such a way that S is the reflexive closure of a... |

14 |
Modal Logic, Oxford Logic Guides 35
- Chagrov, Zakharyaschev
- 1997
(Show Context)
Citation Context ...ourse, every Kripke model (based on hW; Ri) is equivalent to some topological model (with\Omega 2 W ; I ff as the underlying topological space, where IX is the maximal R-closed subset of X); see e.g. =-=[5]-=-. But the converse does not hold. Proposition 12. The formula 3 + Cp $ C3 + p is valid in every Kripke MLmodel but not in every topological ML-model. Proof The former claim is clear. To see that there... |

14 |
On the incompleteness of modal logics of space: advancing complete modal logics of place
- Lemon, Pratt
- 1998
(Show Context)
Citation Context |

13 | Using the RCC formalism to describe the topology of spherical regions
- Gotts
- 1996
(Show Context)
Citation Context ...`regions X and Y share at least one point'---is formalized then as follows: T j= a C(X; Y ) iff a(X) " a(Y ) 6= ;: From the computational point of view RCC is too expressive: as was observed by G=-=otts [17]-=-, the full first-order theory of RCC is undecidable. Fortunately, there are various decidable (and even tractable) fragments of RCC. One of the most important is known as RCC-8. RCC-8. If we are inter... |

13 |
On the complexity of qualitative spatial reasoning
- Renz, Nebel
- 1999
(Show Context)
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9 |
A survey of Concurrent MetateM—The language and its applications, in
- Fisher
- 1994
(Show Context)
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6 |
A decision procedure for combinations of propositional temporal logic and other specialized theories
- Plaisted
- 1986
(Show Context)
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5 | Multi-dimensional multi-modal logics as a framework for spatio-temporal reasoning
- Bennett, Cohn
- 1999
(Show Context)
Citation Context ...topological space and another one the flow of time hN; !i. 1 The idea of using such kind of multidimensional modal logics for spatio-temporal reasoning has recently been advocated by Bennett and Cohn =-=[4]-=-. The computational behaviour of a combined spatio-temporal logic depends (i) on the choice of spatial and temporal operators, and (ii) on the degree of the permitted interaction between them. These t... |