Bennett, B., Isli, A., and Cohn, A. (1997). When does a composition table provide a complete and tractable proof procedure for a relational constraint language? In IJCAI 97, Proceedings of the Workshop of Spatial Reasoning. Lesnie.html.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....TPP(y,x) and NTPP(y,x) respectively. The topological spatial evolution along time of the dyadic relations between regions is also depicted in figure 1. The generalization of the RCC8 logic to n regions was done by a set of composition axioms which generates a structure called composition table [5]. These composition axioms expand consistently the known relations between x and y and between y and z to the consistent set of relations between x and z. The composition table for the RCC8 logic, showed in figure 2, is essential in ensuring that inferred states are complete and consistent, that ....

Bennett B., Isli A., Cohn A. (1996), When does a Composition Table Provide a Complete and Tractable Proof Procedure for a Relational Constraint Language?, Division of Artificial Intelligence, School of Computer Studies, University of Leeds, England.

.... of the binary relations part of and contact in the relational part of mereotopology, composition based reasoning with binary relations has been of interest to the QSR community, and the expressive power, consistency and complexity of relational reasoning has become an object of study [2 4, 33]. The first time that the relational calculus has been mentioned in (modern) spatial reasoning was in the interpretation of the 4 intersection matrix in [19] see also [37] It has been known for some time, that the expressiveness of reasoning with basic operations on binary relations is equal to ....

Bennett, B., Isli, A. & Cohn, A. (1997). When does a composition table provide a complete and tractable proof procedure for a relational constraint language? In IJCAI 97, Proceedings of the 15th International Joint Conference on Artificial Intelligence.

....system are that only the existence of the fusion of finite sets is postulated, and different notion of complement . Already in the early RCC presentation of Randell et al. 1992a) the importance of relational transitivity tables for qualitative reasoning about regions was recognized; recently, Bennett et al. 1997) have raised several questions regarding the expressiveness of relational reasoning, in particular with respect to the RCC. Relational reasoning as algebraic manipulation of relations has a long standing tradition, going back to A. De Morgan, C.S. Peirce, and E. Schrder (cf. Anellis and Houser, ....

....finite fragments, in particular, first order logic with three variables via relation algebras (cf. Tarski and Givant, 1987) In this paper we shall explore the relation algebraic aspects of the RCC relations, and suggest some modifications. We also hope to answer some of the questions raised in Bennett et al. 1997). The paper is structured as follows: We first introduce the necessary machinery of relation algebras; based on these, we will then discuss some aspects of Bennett et al. 1997) from a relation algebraic point of view. Section 4 introduces the RCC and lists some of its properties. We show that ....

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Bennett, B., Isli, A., and Cohn, A. (1997). When does a composition table provide a complete and tractable proof procedure for a relational constraint language? In IJCAI 97, Proceedings of the 15th International Joint Conference on Artificial Intelligence.

....of the corresponding column. Composition of two arbitrary RCC 8 relations can be obtained by computing the union of the composition of the base relations. Note that the composition table only corresponds to the given extensional definition of composition if the universal region is not permitted [6]. A spatial configuration can be described by a set Theta of spatial constraints. One important computational problem is deciding consistency of Theta, i.e. deciding whether it has a solution, which is an assignment of regions of some topological space to variables of Theta in a way that all ....

Brandon Bennett, Amar Isli, and Anthony G Cohn. When does a composition table provide a complete and tractable proof procedure for a relational constraint language? In Proceedings of the IJCAI-97 workshop on Spatial and Temporal Reasoning, Nagoya, Japan, 1997.

....PP PO,PP EC,PO,PP DR,PO,PP no.info DC EC PO TPP NTPP TPPi NTPPi EQ DC DC PPi DR,PO DR,PO PPi no.info NTPPi NTPPi NTPPi DR,PO,PPi Table 1. Composition table for the RCC 8 relations mechanism (i. e for which theories is it complete) This has been taken up in [54] and in [10] it has been suggested that the formalism of relational algebra is particularly suited to representing compositional reasoning and deserves further study and wider application. For cases when composition based reasoning is not sucient, then other more general constraint based reasoning may be ....

Bennett, B., Isli, A. and Cohn, A. G. : \When does a composition table provide a complete and tractable proof procedure for a relational constraint language?", Proc. IJCAI-97 Workshop on Spatial and Temporal Reasoning, Nagoya, Japan, 1997.

....reasoning. For example, reasoning with just three objects at a time will not necessarily determine all inconsistent situations in some calculi. An interesting question then arises: exactly when is composition table reasoning a sufficient inference mechanism (i.e. for which theories is it complete)[10] For cases when composition table based reasoning is not sufficient, then other more general constraint based reasoning may be sufficient[80, 76] more generally one may resort to theorem proving, or preferably, some kind of specialised theorem proving system[7, 113] for example. 11 This ....

B Bennett, A Isli, and A G Cohn. When does a composition table provide a complete and tractable proof procedure for a relational constraint language? In Proceedings of the IJCAI-97 workshop on Spatial and Temporal Reasoning, Nagoya, Japan, 1997. to appear.

....For example, reasoning with just three objects at a time will not necessarily determine all inconsistent situations in some calculi. An interesting question then arises: exactly when is composition table reasoning a sufficient inference mechanism (i.e. for which theories is it complete) Bennett et al. 1997 ] This question is taken up in [ Duentsch et al. 1998 ] For cases when composition table based reasoning is not sufficient, then other more general constraint based reasoning may be sufficient [ Hern andez, 1994; Guesgen and Hertzberg, 1992 ] more generally one may resort to theorem proving, ....

B Bennett, A Isli, and A G Cohn. When does a composition table provide a complete and tractable proof procedure for a relational constraint language? In Proceedings of the IJCAI-97 workshop on Spatial and Temporal Reasoning, Nagoya, Japan, 1997.

....in Rels. The method can be applied to larger networks of relation instances only insofar as it can be used to check consistency of every triangle within the network. However, for certain relation sets, consistency of each triple is sufficient to guarantee overall consistency of the whole network (Bennett, Isli and Cohn 1997). These observations motivate the introduction of a concept of compactness applicable to a relation set (relative to some theory) I say that a network of relations is total if every pair of nodes is constrained by some relation. I then stipulate that: A relation set Rels is k compact w.r.t. a ....

Bennett, B., Isli, A. and Cohn, A. G.: 1997, When does a composition table provide a complete and tractable proof procedure for a relational constraint language?, Proceedings of the IJCAI-97 workshop on Spatial and Temporal Reasoning, Nagoya, Japan.

....of the set of facts. However, Grigni et al. 1995) observe that if we constrain regions to be planar and bounded by Jordan curves, an RCC relation set may have no such model, even though it is consistent with the composition table. We have explored question of completeness of composition tables in (Bennett, Isli and Cohn 1997). 27.Our table coincides with that of (Egenhofer 1991) who built an eight relation calculus, which, although based on point set topology, has many similarities to RCC8. 28.Actually, in representing RCC relations in this way it is important to add for each region r an additional entailment ....

Bennett, B., Isli, A. and Cohn, A. G.: 1997, When does a composition table provide a complete and tractable proof procedure for a relational constraint language?, Proceedings of the IJCAI-97 workshop on Spatial and Temporal Reasoning, Nagoya, Japan. to appear.

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Bennett, B., Isli, A., and Cohn, A. (1997). When does a composition table provide a complete and tractable proof procedure for a relational constraint language? In IJCAI 97, Proceedings of the Workshop of Spatial Reasoning. Lesnie.html.

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