A. Galton. Towards a qualitative theory of movement. In Spatial Information Theory, pages 377--396, 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....objects, we are particularly interested in an algebraic model of general spatio temporal data types including a comprehensive collection of spatio temporal operations [17] Nevertheless, behavioral time sequences could be used as one possible representation for our temporal objects. Galton [26, 27] stresses continuity as an important feature of movement. His goal is to devise a framework for formalizing common sense knowledge of the world, and he particularly focuses on how continuity fits into a qualitative setting. Based on different separation measures for regions he identifies different ....

....Occurs(e; i) is introduced which takes an event e and a time interval i and is true only if the event happened over the time interval i; there is no subinterval of i where the event happened. In both papers Allen s temporal logic is solely based on time intervals and not on time points. Galton [26] has extended Allen s approach to the treatment of temporally changing topological relationships. Topological relationships are based on the RCC model [10] which comes to similar results as Egenhofer s 9 intersection model. In contrast to Allen, Galton also takes time points into account, as we ....

A. Galton. Towards a Qualitative Theory of Movement. In 2nd Int. Conf. on Spatial Information Theory, LNCS 988, pages 377--396, 1995.

....objects, we are particularly interested in an algebraic model of general spatio temporal data types including a comprehensive collection of spatio temporal operations [16] Nevertheless, behavioral time sequences could be used as one possible representation for our temporal objects. Galton [25, 26] stresses continuity as an important feature of movement. His goal is to devise a framework for formalizing common sense knowledge of the world, and he particularly focuses on how continuity fits into a qualitative setting. Based on different separation measures for regions he identifies different ....

....A predicate Occurs(e; i) is introduced which takes an event e and a time interval i and only yields true if the event applies to the entire interval i but not to any proper subinterval of i. In both papers Allen s temporal logic is solely based on time intervals and not on time points. Galton [25] has extended Allen s approach to the treatment of temporally changing topological relationships. Topological relationships are based on the RCC model [10, 31] which comes to similar results as Egenhofer s 9 intersection model. In contrast to Allen, Galton also takes time points into account, as ....

A. Galton. Towards a Qualitative Theory of Movement. In 2nd Int. Conf. on Spatial Information Theory, LNCS 988, pages 377--396, 1995.

....of the bona fide boundary they are co located with. Consider, for example, the back boundary of Parking Spot 3 They have fiat boundary parts, for example, at intersections. 4 An interesting boundary case might be the moment the lights change in the sense of Galton s theory of domination, e.g. [Gal95, Gal00] . 6 T. Bittner The qualitative structure of built environments 1 in Figure 1. Since it is co located with a part of the bona fide boundary of the outer wall of the parking lot it becomes visible and inherits the property of being a barrier for other bona fide objects. We distinguish four ....

A. Galton. Towards a qualitative theory of movement. In A.U. Frank and W. Kuhn, editors, Spatial Information Theory - A Theoretical Basis for GIS, Semmering, Austria, 1995. Springer. T. Bittner / The qualitative structure of built environments 31

....qualitative description and manipulation of changes in space. Taxonomies of spatial changes (Claramunt and Thriault, 1995; Claramunt et al. 1998; Horsnby and Egenhofer, 1998) and transitive changes of spatial relationships have been identified (Randell et al. 1992; Egenhofer and Al Taha, 1992; Galton, 1995). Representing individual changes in space (i.e. endogeneous changes) is a first step toward the integration of time within GIS. A complementary theoretical issue is the development of formal models for studying spatio temporal patterns that involve the interaction of several regions in space and ....

....spatial relationships (Freksa, 1991) Similarly, the temporal space model can be discussed with regard to the possible transitions of its TSR relationships. A set of axioms can be derived from the combination of the possible combination of spatial relationships identified in (Randell et al. 1992; Galton, 1995), and from the study of the possible transitions of temporal intervals. The following diagram summarises the possible transitions of spatial relationships (adapted from Cohn et al. 1998) It can be read as, for example, if two regions touch for an interval of time, and both continue to exist ....

Galton, A., 1995, Towards a qualitative theory of movement. In Spatial Information Theory: A Theoretical Basis for GIS, edited by Frank, A. U. and Kuhn, W. (Berlin: Springer-Verlag), pp. 377-396.

....to derive these automatically would be very useful. An analysis of the structure of conceptual neighbourhoods is reported by Ligozat [92] goes some way towards this goal. A more foundational approach which exploits the continuity of the underlying semantic spaces has been investigated by [58] this analysis not only allows the construction of a conceptual neighbourhood for a class of relations from a semantics, but also infers which relations dominate other relations: a relation R 1 dominates R 2 if R 2 can hold over an interval followed preceded by R 1 instantaneously. e.g. in RCC8 ....

A Galton. Towards a qualitative theory of movement. In W Kuhn A Frank, editor, Spatial Information Theory: a theoretical basis for GIS, number 988 in Lecture Notes in Computer Science, pages 377--396, Berlin, 1995. Springer Verlag.

.... of these is modelled straightforwardly with a set of incompatibility statements; this follows from theorem 3 of (Kuipers 1994) which states that 8 Although the RCC simulator described above in (Cui, Cohn, Randell 1992a; 1992b) does not distinguish these two different kinds of temporal state, (Galton 1995) has extended the RCC conceptual neighbourhood to take account of these distinctions which could be exploited if desired. each QSIM constraint C is associated with a setfP 1 : P ngof provisions that are easily evaluated given a tuple of qualitative values for the variables appearing in C, ....

Galton, A. 1995. Towards a qualitative theory of movement. In A Frank, W. K., ed., Spatial Information Theory: a theoretical basis for GIS, number 988 in Lecture Notes in Computer Science, 377--396.

....not identical to the true conceptual neighbourhood or continuity graph some links are missing. 8 The construction of an envisioner [86] rather than a simulator would also be possible of course. 9 There are the odd exceptions [6] underlying semantic spaces has been investigated by Galton [39] but the process is still far from automatic. 5.2 Complexity and Completeness Metatheoretic results such as completeness and complexity results are still quite sparse in the QSR literature. The intuitionistic formulation of RCC8 has been shown to provide a polynomial procedure to test the ....

A Galton. Towards a qualitative theory of movement. In W Kuhn A Frank, editor, Spatial Information Theory: a theoretical basis for GIS, number 988 in Lecture Notes in Computer Science, pages 377--396, Berlin, 1995. Springer Verlag.

....a sequence of spatial and spatio temporal predicates a development. Since we are dealing with predicates, it is not surprising that logic based approaches are related to our work. Allen (Allen, 1984) defines a predicate Holds(p,i) which asserts that a property p is true during a time interval i. Galton (Galton, 1995) has extended Allen s approach to the treatment of temporally changing two dimensional topological relationships. Topological predicates are taken from the RCC model (Cui et al. 1993) which comes to similar results as Egenhofer s 9 intersection model which is briefly discussed below. In contrast ....

Galton, A. (1995) Towards a Qualitative Theory of Movement, Int. Conf. on Spatial Information Theory, LNCS 988, 377-396.

....(like before, equal, meets, overlaps, during) between intervals, Allen in [2] defines a predicate Holds(p,i) which asserts that a property p is true during a time interval i. If p is one of the aforementioned thirteen predicates, the p s validity during an interval can be expressed. Galton [20] has extended Allen s approach to the treatment of temporally changing two dimensional topological relationships. Topological predicates are taken from the RCC model [8] which comes to similar results as Egenhofer s 9 intersection model which is briefly discussed below. In contrast to these ....

Galton, A.: Towards a Qualitative Theory of Movement, Int. Conf. on Spatial Information Theory, LNCS 988, 1995, 377-396.

....need for an integrated representation of geographical and historical data which corresponds as closely as possible to the way the real world changes. Although various conceptual models combining space and time have been proposed (Langran 1992, Cheylan 1993, Peuquet 1994, Frank 1994, Worboys 1994, Galton 1995), research on temporal GISs (TGIS) is still in an early stage of development. The development of TGISs requires a formal foundation comparable to the work realised for spatial models. A comprehensive framework and mathematical models of spatiotemporal relationships are needed for the development ....

.... 2 and e i x(e ) y(e i ) Two states of two distinct spatial entities e i and e share the same location in space (i.e. P(e i ) P(e j ) if and only if [x(e i ) x(e j ) y(e i ) y(e j ) Galton defines the position of an entity as the total region of space it occupies at a given time (Galton 1995). We go further and represent the total region of space occupied by a geographic entity as the union of its interior and boundary plus the location of its centre of gravity. The distinction can thus be made between contraction, expansion and deformation from translation and rotation evolution ....

GALTON, A., 1995, Towards a qualitative theory of movement. In Spatial Information Theory: A Theoretical Basis for GIS, edited by A. U. Frank and W. Kuhn (Berlin: Springer-Verlag), pp. 377-396.

....(see Hernandez 1994 for a review of these models) deal with static characteristics of space such as topological relations, orientation relations and more recently distance relations (Frank et al. 1996) Recent works start to address dynamic issues of qualitative spatial reasoning. For example, Galton (1996) proposes a qualitative theory of movement based on a logical framework integrating four theories of time, space, objects and position. Although pure logical frameworks are quite useful from a theoretical point of view, it is difficult to use them for implementation purposes, mainly for ....

Galton A. (1996), Towards a qualitative theory of movement, In (Frank et al. 1996), 377-396.

....by Le sniewski) to describe the formal theory of part, whole and related concepts. 6. Ladkin (1986) has investigated temporal non convex interval logics. The spatial logic we present below will also allow non convex spatial entities. 7. This problem has already been noted in a temporal context (Galton 1990). 8. Alternatively, non empty regular closed sets of connected T 3 spaces have been proved to be models for the RCC axiom set (Gotts 1996a) 9. The argument sorts for space are Region and Period, respectively, while the result sort is Spatial t NULL. Period is a sort denoting temporal intervals. ....

Galton, A.: 1995a, Towards a qualitative theory of movement, in A. Frank and W. Kuhn (eds), Spatial Information Theory --- Proceedings of the international conference COSIT'95, number 998 in LNCS, Sorubger, Austria, pp. 377--396.

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A. Galton. Towards a qualitative theory of movement. In Spatial Information Theory, pages 377--396, 1995.

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