F. Wolter and M. Zakharyaschev. Spatio-temporal representation and reasoning based on RCC-8. In Proceedings of the Seventh Conference on Principles of Knowledge Representation and Reasoning, KR2000.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....temporal calculus in Artificial Intelligence. On the spatial side we have, for instance, the Compass Calculus [10] the generalization of Allen s interval calculus to two dimensions [2] and the topological Region Connection Calculus RCC 8 [15] As pointed out by Wolter and Zakharyaschev [19], the next natural step would be to combine these two kinds of representation and reasoning. Most of the existing proposals for spatio temporal formalisms are more expressive than the above mentioned constraint calculi. Muller s [13] spatio temporal theory is basically a first order ....

....proposals for spatio temporal formalisms are more expressive than the above mentioned constraint calculi. Muller s [13] spatio temporal theory is basically a first order axiomatization of spatio temporal entities based on RCC [15] and for this reason it is undecidable. Wolter and Zakharyaschev [19] combined the constraint formalism RCC 8 with the propositional temporal logic PTL [11] This combination is very elegant because it can be expressed as a multi modal logic based on Bennett s [3] encoding of RCC 8 as a multi modal logic. However, the expressiveness of the resulting family of ....

[Article contains additional citation context not shown here]

F. Wolter and M. Zakharyaschev. Spatio-temporal representation and reasoning based on RCC-8. Proc. KR-2000.

....formalisms [6, 51] For incorporation of time into space, the most logical step would be to have a combination of these two streams of reasoning. In fact, there have been attempts to have spatio temporal hybrids [30, 7] A recent spatio temporal representation and reasoning based on RCC 8 is [58] . Motion can be seen as a form of spatial change and is used in such an interpretation here. In yet another approach to incorporate time into spatial reasoning, the RCC formalism [49] contained a function space(x; t) representing the space occupied by object x at a moment of time t. ....

F. Wolter and M. Zakharyaschev, `Spatio-temporal representation and reasoning based on RCC-8', in Principles of Knowledge Representation and Reasoning: Proc of the 7th Intl. Conf. (KR 2000.

....direction: we introduce some types of qualitative and quantitative size information, and we study their integration with topological information. Our work is based on RCC 8 [54] a well known constraint language for topological spatial reasoning that is based on the Region Connection Calculus [5,6,14,19,35,36,55,57,59,64]. In this framework, regions are independent with respect to rotation, translation, and several other transformations of the underlying space which makes them very simple and natural. This has also been observed in cognitive evaluations [39,58] The topological distinctions made by RCC 8 are ....

F. Wolter and M. Zakharyaschev:. Spatio-temporal representation and reasoning based on RCC-8. In Principles of Knowledge Representation and Reasoning Proceedings of the Seventh International Conference (KR'2000.

....time, one possibility is to take a snapshot viewpoint, and describe dynamic behaviour as a set of temporal states, where each state consists of a qualitative spatial representation and their temporal relationship described by a temporal logic. This approach has been extensively investigated by [24 26] and a number of useful complexity results are given. An alternative approach is to view the world as spatio temporal histories [27] and extend purely spatial qualitative representation languages to qualitative spatio temporal languages with relations which hold between such space time histories ....

Wolter, F., Zakharyaschev, M.: Spatio-temporal representation and reasoning based on RCC-8. In: Proceedings of the seventh Conference on Principles of Knowl- edge Representation and Reasoning, Morgan Kaufman (2000) 3 14

....1 W 2 has at most one free variable. Such formulae are called monodic, and the set of monodic L formulae is denoted by T 1 L. In spite of its relative narrowness the monodic fragment provides a way for quite realistic applications. For example, temporal extensions of the spatial formalism RCC 8 [Wol00] lie within the monodic fragment. Another example is the verification of properties of relational transducers for electronic commerce [AVFY00] which are expressed in the monodic language again. The decidability of T 1 L was proved in [HWZ00] while, in [WZ01] a finite Hilbertstyle axiomatization ....

M. Wolter, F. and. ZAkharyaschev. Spatio-temporal representation and reasoning based on rcc-8. In Proceedings of the 7th Conference on Principles of Knowledge Representation and Reasoning (KR'2000), pages 3--14, Montreal, Canada, 2000. Morgan Kaufmann.

.... for terminological logics in [BH91] Decidable fragments of LTL with Presburger constraints can be found in [CC00, DSPK01, ID01] Spatio temporal logics, as they are better known there, involve a hybrid of temporal logic and constraint systems, with varying degrees of interaction (see e.g. [WZ00, HWZ01, BC02]) For instance, one may be permitted to refer to the value of a variable x in the next time instant, leading to constraints of the form (x Xx) More generously, one may permit (x 3y) which asserts that the current value of x does not exceed the value of some future value of y (see also Sect. ....

....that the current value of x does not exceed the value of some future value of y (see also Sect. 2.4. 3 for developments about the freeze quanti er) While research in the area has focused mainly on logics involving constraint systems that have as domains intervals [All83, BC02] and regions [RCC92, Ben94, WZ00], with a variety of decidability and complexity results, there has been little progress with commonly used constraint systems of the form (D; with D as the integers Z, or the natural numbers N. Comon and Cortier [CC00] consider a constraint system with the reals as the underlying ....

[Article contains additional citation context not shown here]

F. Wolter and M. Zakharyaschev. Spatio-temporal representation and reasoning based on RCC-8. In KR'00, pages 3-14. Morgan Kaufmann, 2000.

....Introduction Taking products of modal logics is one of the most straightforward ways to combine two or more modal logics. Besides the aesthetic appeal of products of modal logics, they haved proved to be useful in reasoning about knowledge [2] and parallelism [10] and in spatiotemporal reasoning [17]. However, the nice computational behavior (low complexity, nite axiomatizability) of the component logics is not inherited by the product logic, in general. A natural question which arises is whether a product logic has the product nite model property (pfmp) i.e. whether every satis able ....

F. Wolter, and M. Zakharyaschev. Spatio-temporal representation and reasoning based on RCC-8. Proceedings of the 8th International Conference on Principles of Knowledge Representation and Reasoning (KR'00), Morgan Kaufman, 2000. 9

.... product frame F = F 0 Fn 1 , F is a frame for L i F i is a frame for L i ; for all i n: Products of modal logics have been studied in both pure modal logic (see Segerberg [16] Shehtman [17] Gabbay Shehtman [5] and in computer science applications (see Wolter Zakharyaschev [19] [20], Gabbay et al. . 3] and the references therein) Product logics are also relevant to nite variable fragments of modal and intermediate predicate logics, see Gabbay Shehtman [4] Axiomatization, decision and complexity problems of two dimensional products were thoroughly investigated in [5] Marx ....

F. Wolter and M. Zakharyaschev. Spatio-temporal representation and reasoning based on RCC-8. In Proceedings of the 7th Conference on Principles of Knowledge Representation and Reasoning (KR-

.... [14] the logic based languages for the handling of spatial information only deal with the qualitative representation and reasoning about space (see e.g. 17] And also the few attempts to manipulate time and space have led to languages for qualitative spatio temporal representation and reasoning [20]. On the other hand temporal [19, 6] and spatial [9, 15] database technologies are relatively mature, although, also in the database area, their combination is far from straightforward [3] In this context, the constraint database approach [10] appears to be very promising. Our spatio temporal ....

F. Wolter and M. Zakharyaschev. Spatio-temporal representation and reasoning based on RCC-8. In KR2000, pages 3-14. Morgan Kaufmann, 2000.

....to be found in traditional QR [180] and allows a stricter temporal order to be imposed on events occuring in a qualitative simulation. Motivated by the desire to exploit decidable modal logics for spatio temporal qualitative reasoning, a series of rather expressive such calculi have been proposed [182] in which it is possible easily to represent restrictions on continuous motion. An approach to automatically inferring continuity networks has been proposed by Muller [138, 139, 137] Taking up the idea of spatio temporal histories [111] he enriches a theory intended for spatial entities to ....

Wolter, F. and Zakharyaschev, M.: \Spatio-temporal representation and reasoning based on RCC-8", A. G. Cohn, F. Giunchiglia and B. Selman (eds.) Principles of Knowledge Representation and Reasoning: Proc. 7th Int. Conf. (KR 2000), 2000, pages 3-14.

.... useful to have an even more comprehensive theory enabling one to refer to entities of di erent dimensionality (as in e.g. 12] Another possible modi cation of the theory would be to take one of the dimensions as corresponding to the ow of time, in order to formulate a spatio temporal ontology [16, 24]. ....

F. Wolter and M. Zakharyaschev. Spatio-temporal representation and reasoning based on RCC-8. In Proceedings of the seventh Conference on Principles of Knowledge Representation and Reasoning, pages 3-14, Breckenridge, USA, 2000. Morgan Kaufman.

....) a : C) fa=xg (aRb) R fa=x; b=yg ( A ) A and similarly for the other temporal operators. It is readily checked that a formula is satis able i its rst order translation is satis able. Our second example is a family of logics devised in [59, 62] for qualitative representation and reasoning about spatial regions moving in time. The logics are obtained by combining (propositional) temporal logics with the region connection calculus RCC 8. 7 Recall that RCC 8 contains eight binary relations between regions in topological spaces: DC ....

.... of any DPCT L formula belongs to QPCT L 1 QPCT L . So we have: Theorem 16. Satis ability of DPCT L formulas is decidable both in bundled and full trees. We now apply the results about rst order temporal logics to spatio temporal logics. Consider rst the linear case. Theorem 17 ([59]) Suppose satis ability of the one variable fragment of QT L in the class F of linear ows of time is decidable. Then satis ability of ST L formulas in F is decidable. Problem 7. Is the satis ability problem for arbitrary ST L formulas in models based on hN; i and other ows of time ....

F. Wolter and M. Zakharyaschev. Spatio-temporal representation and reasoning based on RCC-8. In Proceedings of the seventh Conference on Principles of Knowledge Representation and Reasoning, KR2000, Breckenridge, USA, pages 3{ 14, Montreal, Canada, 2000. Morgan Kaufmann.

....required in knowledge representation systems. Logics of distance spaces re ect only one aspect of possible application domains. We envisage these logics as components of more complex many dimensional representation formalisms involving, for instance, also logics of time and space (see e.g. [9]) However, to construct such formalisms with a non trivial interaction between dimensions, we need appropriate combination techniques preserving good computational properties of the components (see e.g. 7] 10 Acknowledgements The work of O. Kutz and F. Wolter was supported by DFG grant ....

F. Wolter and M. Zakharyaschev. Spatio-temporal representation and reasoning based on RCC-8. In Proceedings of the 7th Conference on Principles of Knowledge Representation and Reasoning (KR 2000.

....= T T ; T = T (A ) T = A T and similarly for the other temporal operators. It is readily checked that a DPCT L formula is satis able i its rst order translation T is satis able. 3. 2 Spatio temporal logics Our second example is a family of logics devised in [59, 62] for qualitative representation and reasoning about spatial regions moving in time. The logics are obtained by combining (propositional) temporal logics with the region connection calculus RCC 8. 7 Recall that RCC 8 contains eight binary relations between regions in topological spaces: DC ....

.... belongs to QPCT L 1 QPCT L 2 . So we have: Theorem 16. Satis ability of DPCT L formulas is decidable both in bundled and full trees. 7.2 Spatio temporal logics We now apply the results about rst order temporal logics to spatio temporal logics. Consider rst the linear case. Theorem 17 ([59]) Suppose satis ability of the one variable fragment of QT L in the class F of linear ows of time is decidable. Then satis ability of ST L formulas in F is decidable. Problem 7. Is the satis ability problem for arbitrary ST L formulas in models based on hN; i and other ows of time ....

F. Wolter and M. Zakharyaschev. Spatio-temporal representation and reasoning based on RCC-8. In Proceedings of the seventh Conference on Principles of Knowledge Representation and Reasoning, KR

....etc. Products of modal logics (i.e. sets of multi modal formulas that are valid in the Cartesian products of Kripke frames for those logics) have been studied in both pure modal logic (see e.g. 23, 24, 18, 7, 15, 19, 31] and applications in computer science and artificial intelligence (see e.g. [20, 3, 1, 21, 4, 27, 28, 29]) since the 1970s. It would not be an exaggeration to say that now multi dimensional logics in general and Cartesian products in particular are becoming the subject of one of the most important and interesting research fields in pure and applied modal logic. See e.g. applications of results and ....

F. Wolter and M. Zakharyaschev, Spatio-temporal representation and reasoning based on RCC-8. In Proceedings of the seventh Conference on Principles of Knowledge Representation and Reasoning, KR2000, pages 3--14. Morgan Kaufmann, 2000.

.... 2000] 1 based on classical quantitative models of kinematics (see e.g. Rajagopalan and Kuipers, 1994; Hays, 1989 ] surprisingly little has been done to design qualitative spatio temporal representation formalisms [ Vieu, 1991; Galton, 1997; Muller, 1998; Hornsby and Egenhofer, 2000; Wolter and Zakharyaschev, 2000b ] let al..one implementations. More refs Or fewer Although a deep ontological analysis of qualitative spatio temporal entities seems still missing [ Vieu, 1997 ] yet there is a quite simple naive approach to constructing such formalisms. Just take your favorite temporal logic T and your ....

....flow of time F is easily, but exponentially, reducible to satisfiability of PT L formulas in F. As we saw in Section 2.2.3, BRCC 8 is reducible to S5, which, in turn, can be exponentially reduced to PT L. Moreover, for hN; i a PSPACE satisfiability checking algorithm was constructed in [ Wolter and Zakharyaschev, 2000b ] To sum up, using Theorem 15, we obtain: Theorem 25. Let C be one of the classes defined in Section 3.3. Then the satisfiability problem for ST 0 formulas in tt models based on flows of time in C is decidable in EXPSPACE. For hN; i it is PSPACE complete. It is an open problem ....

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F. Wolter and M. Zakharyaschev. Spatiotemporal representation and reasoning based on RCC-8. In Proceedings of the seventh Conference on Principles of Knowledge Representation and Reasoning, KR2000, Breckenridge, USA, pages 3--14, Montreal, Canada, 2000. Morgan Kaufmann.

....as well. Consequently, over the last years we have observed a growing interest in so called temporalizations of logical formalisms. We mention [14, 15] for a general approach, 13, 34] for extensions of epistemic logics by means of temporal operators to model, among others, multi agent systems, [33] which supplies a logic of space with temporal operators in order to describe the evolution of regions in time, 1, 12] for work on temporal databases, and [20, 23, 24, 28] which investigate temporal logic based on (fragments of) first order logic. Particularly many researchers are concerned with ....

....domain models. In a follow up paper we are going to extend our tableau method so as to give a solution to this problem. More generally, we believe that our method of combining tableaux can be fruitfully applied also for obtaining algorithms for various spatio temporal logics in the sense of [33] and, even more generally, for monodic fragments of first order logics in the sense of [20] 30 The work is mainly conceptual, of course, since it still requires some work to obtain an efficient implementable tableau from the one presented here. This is left for the future. It should be clear, ....

F. Wolter and M. Zakharyaschev. Spatio-temporal representation and reasoning based on rcc-8. In Proceedings of the sixth Conference on Principles of Knowledge Representation and Reasoning, Montreal, Canada, 2000. Morgan Kaufman.

....of distances, and that are at the same time as computationally tractable as possible. The next step will be to integrate the developed languages with formalisms intended for qualitative spatial reasoning (e.g. RCC 8) temporal reasoning, and maybe even combined spatio temporal reasoning (e.g. [19]) The requirement of computational effectiveness imposes rather severe limitations on possible languages of metric spaces. For instance, we can hardly use the full power of the common mathematical formalism which allows arithmetic operations and quantification over distances as in the usual ....

F. Wolter and M. Zakharyaschev. Spatio-temporal representation and reasoning based on RCC-8. In Proceedings of the seventh Conference on Principles of Knowledge Representation and Reasoning, KR2000, Breckenridge, USA, pages 3-- 14, Montreal, Canada, 2000. Morgan Kaufman.

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F. Wolter and M. Zakharyaschev. Spatio-temporal representation and reasoning based on RCC-8. In Proceedings of the Seventh Conference on Principles of Knowledge Representation and Reasoning, KR2000.

No context found.

F. Wolter and M. Zakharyaschev. Spatio-temporal representation and reasoning based on RCC-8. In KR'00, pages 3-14. Morgan Kaufmann, 2000.

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F. Wolter and M. Zakharyaschev. Spatio-temporal representation and reasoning based on RCC-8. In Proceedings of the seventh Conference on Principles of Knowledge Representation and Reasoning, pages 3--14, Breckenridge, USA, 2000. Morgan Kaufman.

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F. Wolter and M. Zakharyaschev. Spatio-temporal representation and reasoning based on RCC-8. In Proceedings of the seventh Conference on Principles of Knowledge Representation and Reasoning, KR

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