A. G. Cohn, D. A. Randell, Z Cui, and B. Bennett. Qualitative spatial reasoning and representation. In P. Carrete and M. G. Singh, editors, Qualitative Reasoning and Decision Technologies, pages 513-522. CIMNE, Barcelona, June 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... to be utilized, reasoning can be carried out by checking every relation in the full set of sound relations in the domain to see whether it is a valid consequence of the composition considered (theorems to be proved) and eliminating the ones which are not consistent with the composition [RCC92, CRCB93] However, checking each relation in the composition table to prove or eliminate is not possible in general cases and is considered a challenge for theorem provers [RCC92] In this paper the transitivity property of the subset relations is used for the development of the general spatial ....

....matrix. z0 z1 z2 x0 1 1 1 x1 a 0 a x2 b 0 b The matrix represents the possible relations in figure 4 which correspond to relations R1 , R18 and R19 in table 2. The full composition table for reasoning over lines and regions is given in table 2. 3. 4 Reasoning with Complex Objects Cohn et al. [CRCB93] proposed definitions of spatial relationships between concave shaped objects (representing solid bodies) They distinguished between the relationships topologically inside (where one body is physically inside the interior of another) and geometrically inside (where one body lies inside the ....

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A.G. Cohn, D.A. Randell, Z. Cui, and B. Bennet. Qualitative Spatial Reasoning and Representation. In P. Carrete and M.G. Singh, editors, Qualitative Reasoning and Decision Technologies, 1993.

....with which this paper is concerned, is a fundamental aspect of spatial structure, but not the whole of it. The four doughnuts of figure 2 are topologically identical, but differ in their structure (the ways they can be divided into parts and how those parts inter relate) In recent papers (Cohn, Randell, Cui and Bennett 1993, Cohn et al. 1994) RCC s main concerns have moved toward computational issues, and the exploitation of an additional primitive concerning convexity introduced in (Randell and Cohn 1989) The purpose of this paper, by contrast, is to investigate the expressive power of the C predicate: how much ....

Cohn, A. G., Randell, D. A., Cui, Z. and Bennett, B.: 1993, Qualitative spatial reasoning and representation, in N. P. Carret'e and M. G. Singh (eds), Qualitative Reasoning and Decision Technologies, CIMNE, Barcelona, pp. 513--522.

....within AI. Similar work on time has a somewhat longer history, starting with Allen s work (Allen 1981, Allen and Hayes 1985, Allen and Hayes 1989) A much wider range of possible relations must be considered in the spatial case because of the multi dimensionality of space. In recent papers (Cohn, Randell, Cui and Bennett 1993, Cohn et al. 1994) RCC s main concerns have moved toward computational issues, and the exploitation of an additional primitive concerning convexity introduced in (Randell and Cohn 1989) The purpose of this paper, by contrast, is to investigate the expressive power of the C predicate: how much ....

Cohn, A. G., Randell, D. A., Cui, Z. and Bennett, B.: 1993, Qualitative spatial reasoning and representation, in N. P. Carret'e and M. G. Singh (eds), Qualitative Reasoning and Decision Technologies, CIMNE, Barcelona, pp. 513--522.

....provided by relations on a set , or between sets, using concepts from algebraic topology. Other important work which does not assume a Euclidean framework but attempts to describe directly spatial relationships such as contact and boundary includes the work of Clarke (1981, 1985) and later Cohn et al. 1993).on the Region Connection Calculus (RCC) Smith (1995) gives an account of mereotopology, which combines mereology (study of the part whole relationship) and topological notions. 3 Migrant flows 3.1 Population Migration In the UK, studies of migrant flows have received much recent attention, ....

COHN, A.G., RANDELL, D.A., CUI, Z. AND BENNETT, B., 1993. Qualitative Spatial Reasoning and Representation. In Carrete, P. and Singh, M.G. (eds.), Qualitative Reasoning and Decision Technologies, CIMNE, Barcelona.

....shows values of s, a, n 3 , and T for a number of theories for which composition tables have been constructed. RCC 8 is the basis of eight topological relations defined in Randell, Cui and Cohn (1992) RCC 23 is a basis of spatial relations involving containment whose definition is discussed in Cohn, Randell, Cui and Bennett (1993) (the complete composition table is given in Bennett (1994) IC 13 is Allen s (1983) temporal interval calculus; and LOS 14 is Galton s (1993) Line of Sight calculus. The final column gives T as a percentage of n 3 . Basis Set s a n 3 T RCC 8 4 2 512 104 20.3 RCC 23 7 8 21167 2116 17.4 ....

....arbitrary disjunction of possible relations. Moreover, in cases where disjunctive information and conceptual neighbourhood do coincide it may also be possible to exploit this in automatic reasoning. 5 Triangle Consistency I conclude with a brief outline of another open question (raised by Cui, Cohn and Randell (1993)) which is of great significance in determining the usefulness of composition based reasoning. Although composition tables provide for efficient implementation of certain inference steps, in general they cannot provide all the inferences we need for complete reasoning. What is not clear is under ....

Cohn, A. G., Randell, D. A., Cui, Z. and Bennett, B.: 1993, Qualitative spatial reasoning and representation, in N. P. Carret'e and M. G. Singh (eds), Qualitative Reasoning and Decision Technologies, CIMNE, Barcelona, pp. 513--522.

....of spatial properties and relations, and reasoning about those properties and relations. This approach, known as RCC ( Region Connection Calculus ) theory, has been under development for several years at the 1 University of Leeds (Randell, Cui and Cohn 1992, Cui, Cohn and Randell 1992b, Cohn, Randell, Cui and Bennett 1993, Cui, Cohn and Randell 1993, Bennett 1994, Gotts 1994, Cohn and Gooday 1994) 1 . The main rationale for this project is that qualitative descriptions of spatial properties and relationships, and qualitative spatial reasoning, are of fundamental importance in human thinking about the world: even ....

....and reasoning about those properties and relations. This approach, known as RCC ( Region Connection Calculus ) theory, has been under development for several years at the 1 University of Leeds (Randell, Cui and Cohn 1992, Cui, Cohn and Randell 1992b, Cohn, Randell, Cui and Bennett 1993, Cui, Cohn and Randell 1993, Bennett 1994, Gotts 1994, Cohn and Gooday 1994) 1 . The main rationale for this project is that qualitative descriptions of spatial properties and relationships, and qualitative spatial reasoning, are of fundamental importance in human thinking about the world: even where quantitative spatial ....

[Article contains additional citation context not shown here]

Cohn, A. G., Randell, D. A., Cui, Z. and Bennett, B.: 1993, Qualitative spatial reasoning and representation, in N. P. Carret'e and M. G. Singh (eds), Qualitative Reasoning and Decision Technologies, CIMNE, Barcelona, pp. 513--522.

....DC and CON regions x1 and x2 each of which has the same description in our language of shape. We must ensure that the partition between these two regions takes the form of a straight line, i.e. that CONV(conv(x) Gamma conv(x1) CONV(conv(x) Gamma conv(x2) 6 Changes in Shape In earlier papers (Cohn, Randell, Cui and Bennett 1993, Cohn et al. 1994) we presented the transition networks 6 for our sets of relations. These networks tell us that if a particular relation holds between a pair of regions at some particular time, then, assuming continuous motion and deformation 7 , what the next possible relationship that ....

Cohn, A. G., Randell, D. A., Cui, Z. and Bennett, B.: 1993, Qualitative spatial reasoning and representation, in N. P. Carret'e and M. G. Singh (eds), Qualitative Reasoning and Decision Technologies, CIMNE, Barcelona, pp. 513--522.

....the same position, the symbol ffl is used. The table was generated using meta level enforcement of the conv axioms in a Prolog implemented I 0 reasoning program. It was produced in 3h 31mins on a Sparc10 workstation. Such a table has hitherto never been computed by a proof oriented method. [3] contains a similar table constructed using a model building approach but it has subsequently been found that the table given there is too strict in that it rules out certain configurations, which are in fact possible for 3D spatial regions. My table has not been found to contain any false ....

Cohn, A., Randell, D., Cui, Z., and Bennett, B. Qualitative spatial reasoning and representation. In Qualitative Reasoning and Decision Technologies, P. Carrete and M. Singh, Eds. CIMNE, Barcelona, 1993.

.... Cohn 1996b, Haarslev 1995) This paper is devoted largely to presenting one particular formalism for QSR, the RCC 2 calculus which has been developed at the University of Leeds over the last few years in a series of papers 3 including (Randell, Cui and Cohn 1992, Cui, Cohn and Randell 1992, Cohn, Randell, Cui and Bennett 1993, Cui, Cohn and Randell 1993, Bennett 1994b, Gotts 1994b, Cohn and Gotts 1996a, Gotts, Gooday and Cohn 1996, Cohn 1995) and indeed is still the subject of ongoing research. This current paper is substantially based on material published in (Cohn, Bennett, Gooday and Gotts 1997) but has been ....

.... is devoted largely to presenting one particular formalism for QSR, the RCC 2 calculus which has been developed at the University of Leeds over the last few years in a series of papers 3 including (Randell, Cui and Cohn 1992, Cui, Cohn and Randell 1992, Cohn, Randell, Cui and Bennett 1993, Cui, Cohn and Randell 1993, Bennett 1994b, Gotts 1994b, Cohn and Gotts 1996a, Gotts, Gooday and Cohn 1996, Cohn 1995) and indeed is still the subject of ongoing research. This current paper is substantially based on material published in (Cohn, Bennett, Gooday and Gotts 1997) but has been modified so as to be of more ....

[Article contains additional citation context not shown here]

Cohn, A. G., Randell, D. A., Cui, Z. and Bennett, B.: 1993, Qualitative spatial reasoning and representation, in N. P. Carret'e and M. G. Singh (eds), Qualitative Reasoning and Decision Technologies, CIMNE, Barcelona, pp. 513--522.

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A. G. Cohn, D. A. Randell, Z Cui, and B. Bennett. Qualitative spatial reasoning and representation. In P. Carrete and M. G. Singh, editors, Qualitative Reasoning and Decision Technologies, pages 513-522. CIMNE, Barcelona, June 1993.

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Cohn A., Randell D., Cui Z., Bennett B. (1993), "Qualitative Spatial Reasoning and Representation," in: Qualitative Reasoning and Decision Technologies, Barcelona.

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A. G. Cohn, D. A. Randell, Z. Cui and B. Bennett, "Qualitative Spatial Reasoning and Representation," Proceedings of Qualitative Reasoning and Decision Technologies, eds., N. Piera Carrete and M. G. Singh, CIMNE, Barcelona, June 1993, pp. 513-522.

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Cohn, A.G., Randell, D.A., Cui, Z., Bennett, B., 1993. Qualitative spatial reasoning and representation. Proc of the IMACS Workshop on Qualitative Reasoning and Decision Technologies, QUARDET '93, 16-18 June, ed. by N. Piera Carrete and M.G. Singh. CIMNE, Barcelona, p.513-522.

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