| B. Bennett. Determining consistency of topological relations. Constraints, 3(2&3):213-225, June 1998. |
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B. Bennett. Determining consistency of topological relations. Constraints, 3(2&3):213-225, June 1998.
.... for representing and reasoning about qualitative spatial information is now an active research area, both within AI, and within the field of geographical information systems [14] Much of the e#ort has been devoted to developing e#cient representations for reasoning about topological information [2, 25, 24, 20], although other aspects such as orientation [22, 19] distance [18] and qualitative morphology [12] have also been investigated. Qualitative representations have a natural facility to handle indefinite and imprecise information by abstracting away from metrical details. However, specific ....
B. Bennett. Determining consistency of topological relations. Constraints, 3(2&3):213--225, June 1998.
.... containing several di erent modal operators have been studied [ Thomason, 1984; Marx et al. 1996; Bennett, 1996; Gabbay, 1996; 1998 ] Another recent trend is to regard modal logics not purely as propositional logics but more generally as formalisms for reasoning about algebraic constraints [ Bennett, 1998 ] The idea of a multi dimensional modal logic was introduced by [ Segerberg, 1973 ] who presented an axiomatisation for a 2 dimensional extension of S5. Further details and development of multi dimensional modal logics can be found in [ Venema, 1992 ] and [ Gabbay, 1998 ] The operators of ....
B. Bennett. Determining consistency of topological relations. Constraints, 3(2&3):213-225, June 1998.
....conjunctions of the modal formulae on the right. The predicates NE and regular correspond to the conditions of non emptiness and regularity which are normally placed on regions. 1 Yet another variant of the approach is to represent topological relations as equational constraints, as described in [Bennett, 1998]. A thorough account of all these di erent encoding techniques can be found in [Bennett, 1997] In the modal encoding and are the S5 operators, and the S4 box and diamond operator (because they behave respectively as interior and closure operators) are written as i and c. The theorem ....
B. Bennett. Determining consistency of topological relations. Constraints, 3(2&3):213-225, June 1998.
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B. Bennett, Determining consistency of topological relations, Constraints 3 (2&3) (1998) 213--225.
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Bennett, B. (1998). Determining consistency of topological relations. Constraints, 3, 213--225.
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