A. Gerevini, L. Schubert, and S. Schae#er, `Temporal reasoning in time graph i-ii', SIGART Bull 4, 3, 21--25, (1993).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....time intervals, and the famous interval algebra of Allen [ 1983 ] for expressing qualitative relations between time intervals. There are also combinations of these and extensions to handle metric time as well, such as Meiri s framework [ Meiri, 1991 ] and the works of Kautz and Ladkin [ 1991 ] Gerevini et al. 1993 ] Dechter et al. 1991 ] Jonsson and Backstrom [ 1996 ] and Drakengren and Jonsson [ 1997a ] However, it was early proved that the reasoning problem for these formalisms is very hard; e.g. reasoning in Allen s interval algebra is NP complete [ Vilain and Kautz, 1986 ] and NP hardness ....

Alfonso Gerevini, Lenhart Schubert, and Stephanie Schaeffer. Temporal reasoning in Timegraph I--II. SIGART Bulletin, 4(3):21--25, 1993.

....response to the computational hardness of the full Allen algebra, several polynomial subalgebras have been proposed in the literature [10, 11, 13, 1 24, 26] Some of these algebras have later been extended with mechanisms for handling quantitative information. For example the TimeGraph II system [12] extends the pointisable algebra [26] with a limited type of quantitative information. Of special interest is the ORD Horn algebra [24] which is the unique maximal tractable subclass of Allen s algebra containing all basic relations. Hence, it would be especially interesting to extend this algebra ....

....on the form Gammacr 1 (x Gamma y)r 2 d where r 1 ; r 2 2 f ; g. Definition 29 (Meiri [23] A CPA single interval formula is a formula on one of the following two forms: 1) c r 1 (x Gamma y) r 2 d; or (2) x r y where r 2 f ; 6= g and r 1 ; r 2 2 f ; g. Definition 30 (Gerevini et al. [12]) A TG II formula is a formula on one of the following forms: 1) c x d, 2) c x Gamma y d or (3) x r y where r 2 f ; 6= g. The tractable formalisms defined in Definitions 25 to 30 can trivially be expressed as Horn DLRs. Beside these six classes, other temporal classes that can be ....

A. Gerevini, L. Schubert, and S. Schaeffer. Temporal reasoning in Timegraph I--II. SIGART Bull. 4(3) (1993) 21--25.

....Definition 2 (Point algebra) The point algebra [Vil82] is the subclass of Horn DLRs consisting of the set of expressions xRy, where x and y are variables and R 2 f ; 6= g. Proposition 2. PAsat is solvable in linear time in the size of the instance. Proof. See Gerevini, et al. [GSS93]. The following problem will be studied in section 3, where we extend the subclasses of Allen s algebra to include metric duration information. Definition 3 (D Isat) For an interval I 2 V , we let d(I) denote the duration of I, i.e. I GammaI Gamma . An instance of the problem of ....

Alfonso Gerevini, Lenhart Schubert, and Stephanie Schaeffer. Temporal reasoning in Timegraph I--II. SIGART Bulletin, 4(3):21--25, 1993.

.... fragment of the interval algebra that can be reencoded in the point algebra, and the ORD Horn algebra [Nebel and Burckert, 1995] the fragment of the interval algebra which can be reencoded as Horn clauses of the 6 Indeed, this problem can be solved in linear time in the number of constraints) [Gerevini et al. 1993]. 7 Actually, the relation f g alone is not a sufficient cause for NP completeness. More interestingly, the seemingly harmless relation meets alone is sufficient to express all 13 basic relations, and together with either or it causes NP completeness the relation f mg generates the ....

....of the form (x Gamma y) 6= c or x 6= c, where r 2 f; 6=g. ffl Meiri [1991] considers sets of CPA single interval formulae, that is, formulae on either of the two forms (1) c r 1 (x Gamma y) r 2 d; or (2) x r y where r 2 f ; 6= g and r 1 ; r 2 2 f ; g. ffl The TimeGraph II system [Gerevini et al. 1993] allows formulae on either of the three forms (1) c x d, 2) c x Gamma y d or (3) x r y where r 2 f ; 6= g. A recent exception is the Horn DLR formalism by Jonsson and Backstrom [1996a, 1996b] which is the DLR formalism restricted to Horn DLRs, that is, DLRs where at most one ....

[Article contains additional citation context not shown here]

Alfonso Gerevini, Lenhart Schubert, and Stephanie Schaeffer. Temporal reasoning in Timegraph I--II. SIGART Bulletin, 4(3):21--25, 1993.

.... A 2 (r; b) 1 Find all strong components C in G 0 2 for every arc e in G whose relation does not contain j 3 if e connects two nodes in some C then 4 Reject 5 endif 6 endfor 7 Accept 2 In fact, this algorithm is very similar to that of van Beek [10] improved and used by Gerevini et al. [4], but here used on intervals instead of points. We now state a simple result which holds for directed graphs in general. Proposition 21 Let G be irreflexive 2 with an acyclic subgraph D. Then those arcs of G which are not in D can be reoriented so that the resulting graph is acyclic. Proof: ....

Alfonso Gerevini, Lenhart Schubert, and Stephanie Schaeffer. Temporal reasoning in timegraph I-II. SIGART Bulletin, 4(3):21--25, 1993.

.... reasoning with pure qualitative time in Allen s interval algebra [1] is NPcomplete [24] research has focused on identifying classes of problems where reasoning is tractable [7, 9, 12, 17, 20, 21, 22] Until recently, approaches have mostly been either metric or qualitative, with a few exceptions [12, 15, 8]. However, the approach of Jonsson and Backstrom [10] also developed independently by Koubarakis [14] manages to unify almost every approach to tractable reasoning about metric time, qualitative time and the integrated approaches in one framework, that of Horn disjunctive linear relations ....

....to distinguish between qualitative and metric information. Nevertheless, when it comes to identifying tractable subclasses, the distinction is still convenient. The Horn DLR approach subsumes almost all previously known approaches to tractable metric and qualitative temporal reasoning, e.g. [17, 13, 6, 15, 8]. It is worth mentioning that the maximal tractable algebras found by Drakengren and Jonsson [7] cannot be expressed as Horn DLR s. Although polynomial, the algorithm presented in Jonsson and Backstrom [10] is quite expensive (it relies on a linear programming algorithm) so when we do not need to ....

[Article contains additional citation context not shown here]

Alfonso Gerevini, Lenhart Schubert, and Stephanie Schaeffer. Temporal reasoning in Timegraph I-II. SIGART Bulletin, 4(3):21--25, 1993.

....primarily in [All84, VKvB89, vBC90, vB92, LM94, LR92, LR93, vBM96] NB95] have introduced the ORD Horn subclass of Interval Algebra and showed that it is a maximal tractable subclass. DJ96, JDB96, DJ97a, DJ97b] have also studied other tractable subclasses of the Interval Algebra. Finally, GS93, GSS93, GS95] have studied several algorithms for qualitative temporal constraints and have implemented them efficiently in their TimeGraph system. The class of quantitative temporal constraints has been studied originally by [DMP89] in the framework of simple temporal problems where constraints are ....

A. Gerevini, L. Schubert, and S. Schaeffer. Temporal Reasoning in Timegraph I-II. SIGART Bulletin, 4(3):21--25, 1993.

....time intervals, and the famous interval algebra of Allen [ 1983 ] for expressing qualitative relations between time intervals. There are also combinations of these and extensions to handle also metric time, such as Meiri s framework [ Meiri, 1991 ] and the works of Kautz and Ladkin [ 1991 ] Gerevini et al. 1993 ] Dechter et al. 1991 ] Jonsson and Backstrom [ 1996 ] and Drakengren and Jonsson [ 1997 ] However, it was early proved that the reasoning problem for these formalisms is very hard; e.g. reasoning in Allen s interval algebra is NP complete [ Vilain and Kautz, 1986 ] and NP hardness ....

Alfonso Gerevini, Lenhart Schubert, and Stephanie Schaeffer. Temporal reasoning in Timegraph I--II. SIGART Bulletin, 4(3):21--25, 1993.

.... discussed in by Ladkin and Maddux in [LM88a, LM88b, Lad87b, Lad87c, Lad87d, Lad87a, Lad86a, Lad86b] Finally, Len Schubert and his colleagues have implemented really practical algorithms for reasoning in PA networks as part of their natural language understanding system [MS88a, MS88b, MS90, GS93, GSS93] The work of [GA89] has also addressed similar implementation issues. Dechter, Meiri and Pearl studied quantitative or metric temporal constraints of the form a 1 T i Gamma T j b 1 Delta Delta Delta an T i Gamma T j b n where T i ; T j are real variables representing time points and ....

....constraints. Mei91a] has also identified various classes of constraint networks with qualitative and quantitative constraints for which the above reasoning problems are tractable. The above flurry of research activity resulted in several implemented systems [DM87, Koo89, GA89, KL91, Bod93, GSS93, SAD93] YA93] gives a comparative performance analysis for most of these systems. Up to this point, we studied time and temporal inference in isolation. We will now turn our attention to formalisms and systems which combine a temporal dimension with a general framework for representing ....

[Article contains additional citation context not shown here]

A. Gerevini, L. Schubert, and S. Schaeffer. Temporal Reasoning in Timegraph I-II. SIGART Bulletin, 4(3):21--25, 1993.

....of time points related by the resticted interval algebra , achieving an experimental average linear cost for both updating and retrieval Timegraph [83] partitions a constraint networks into chains of point linked by and and handle both metric and qualitative information. Timegraph II [42, 41] extends its predecessor with = and 6= and automatic structuring though it does not yet handle metric information Dorn s sequence graphs [26] based on domain event sequences Concerning performance [119] in general, if one is facing large temporal datasets where information is added ....

A. Gerevini, L. Schubert, and S. Schaeffer. Temporal reasoning in timegraph I-II. SIGART bulletin, 4(3):T1--T4, 1993.

....R 1 ; R 2 2 f ; g. 2 Definition 2.20 (PA single interval formula) A PA single interval formula [Meiri, 1996] is a formula on one of the following forms: 1. cR 1 (x Gamma y)R 2 d, where R 1 ; R 2 2 f ; g 2. xRy where R 2 f ; 6= g 2 Definition 2. 21 (TG II formula) A TG II formula [Gerevini et al. 1993] is a formula on one of the following forms: 1. c x d, 2. c x Gamma y d 3. xRy where R 2 f ; 6= g 2 Except for these classes, other temporal classes that can be expressed as Horn DLRs have been identified by different authors. Examples include the approach by Barber [1993] the ....

Alfonso Gerevini, Lenhart Schubert, and Stephanie Schaeffer. Temporal reasoning in Timegraph I--II. SIGART Bulletin, 4(3):21--25, 1993.

....at the National Technical University of Athens and at Imperial College, London. At Imperial College financial support was received from project CHRONOS funded by EPSRC and DTI. constraints, an inequation can give rise to a disjunction of inequations. 2 In related temporal reasoning research [VK86, vB90, GS93, GSS93] have considered inequations of the form t 1 6= t 2 in the context of PA networks. Also, Mei91a] has studied inequations of the form t 6= r (r a real constant) in the context of point networks with almost single interval domains. In a more general context, researchers in constraint logic ....

A. Gerevini, L. Schubert, and S. Schaeffer. Temporal Reasoning in Timegraph I-II. SIGART Bulletin, 4(3):21--25, 1993.

....This system has been applied to operation planning for the space shuttle, and communication scheduling for plane flight management system. ffl A. Gerevini, L. Schubert and S. Schaeffer designed a temporal reasoning system ( Timegraph ) based on instants including metric information processing [12]. Representation relies on partitioned graphs. ffl F.A. Barber describes a metric time point and duration based temporal model [5] This approach is based on both time points and intervals which are integrated in a common framework. Temporal constraints are represented in a network structure ....

A. Gerevini, L. Schubert, and S. Schaeffer. Temporal reasoning in Timegraph I--II. Sigart Bulletin, 4(3):21-- 25, July 1993.

....Definition 5.5 (Strong component) A subgraph C of a graph G is said to be a strong component of G iff it is maximal such that for any nodes a, b in C, there is always a path in G from a to b. 2 In fact, this algorithm is very similar to that of van Beek [ 1992 ] improved and used by Gerevini et al. 1993 ] but here used on intervals instead of points. In Section 6, we will show how the algorithm runs on an example. We now state a simple result which holds for directed graphs in general. Proposition 5.7 Let G be loop free 4 with an acyclic subgraph D. Then those arcs of G which are not in D ....

Alfonso Gerevini, Lenhart Schubert, and Stephanie Schaeffer. Temporal reasoning in Timegraph I--II. SIGART Bulletin, 4(3):21--25, 1993.

.... and Jonsson, 1996; Golumbic and Shamir, 1993; Kautz and Ladkin, 1991; Nebel and Burckert, 1995; van Beek and Cohen, 1990; van Beek, 1989; van Beek, 1992) Until recently, approaches have mostly been either metric or qualitative, with a few exceptions (Kautz and Ladkin, 1991; Meiri, 1991; Gerevini et al. 1993). However, the approach of Jonsson and Backstrom (1996) also developed independently by Koubarakis, 1996) manages to unify almost every approach to tractable reasoning about metric time, qualitative time and the integrated approaches in one framework, that of Horn disjunctive linear relations ....

....when it comes to identifying tractable subclasses, the distinction is still convenient. The Horn DLR approach subsumes almost all previously known approaches to tractable metric and qualitative temporal reasoning, e.g. Nebel and Burckert, 1995; Koubarakis, 1992; Dechter et al. 1991; Meiri, 1991; Gerevini et al. 1993). It is worth mentioning that the maximal tractable algebras found by Drakengren and Jonsson (1996) cannot be expressed as Horn DLRs. Although polynomial, the algorithm presented in Jonsson and Backstrom (1996) is quite expensive (it relies on a linear programming algorithm) so when we have no ....

[Article contains additional citation context not shown here]

Gerevini, A., Schubert, L., and Schaeffer, S. (1993). Temporal reasoning in Timegraph I--II. SIGART Bulletin, 4(3):21--25.

.... Paper I It is known in the literature that testing satisfiability of a set of point variables over real numbers related with the relations , and 6= that is, using the point algebra [ Vilain, 1982 ] can be done in polynomial time [ Ladkin and Maddux, 1994; van Beek and Cohen, 1990; Gerevini et al. 1993 ] and that there are several tractable special cases of checking satisfiability using Allen s interval algebra [ van Beek, 1989; van Beek, 1990; Golumbic and Shamir, 1993; Nebel and Burckert, 1995 ] 5 (the general case is NP complete [ Vilain and Kautz, 1986 ] However, not much is known ....

.... which was indeed the first one to be pursued: Vilain and Kautz [ 1986 ] found that when the point 11 algebra [ Vilain, 1982 ] is used (that is, relating time point variables with the relations , and 6= satisfiability can be solved in polynomial time (the algorithm was improved by Gerevini et al. 1993 ] to a linear time one) and expressing interval relations in terms of these yields a fragment of Allen s algebra for which computing satisfiability is polynomial; the pointisable subalgebra. However, it was not clear whether this subalgebra could be extended further, until Nebel and Burckert [ ....

Alfonso Gerevini, Lenhart Schubert, and Stephanie Schaeffer. Temporal reasoning in Timegraph I--II. SIGART Bulletin, 4(3):21--25, 1993.

....are represented separately. Disjunctions of inequations have been introduced in [Kou92] following the observation that in the process of eliminating variables from a set of temporal constraints, an inequation can give rise to a disjunction of inequations. 1 In related temporal reasoning research [VK86,vB90a,GS93,GSS93] have considered inequations of the form t 1 6= t 2 in the context of point algebra (PA) networks. Also, Mei91a] has studied inequations of the form t 6= r (r a real constant) in the context of point networks with almost single interval domains. In a more general context, researchers in ....

A. Gerevini, L. Schubert, and S. Schaeffer. Temporal Reasoning in Timegraph I-II. SIGART Bulletin, 4(3):21--25, 1993.

....representation (d graph) allows for applying rather classical techniques for addition (the addition of a further constraint and re building of the d graph is O(n 2 ) in the very worst case [20] and provides a constant time retrieval. Representations based on not completely connected graphs [17, 14, 10] provide lower addition cost though they pay some performance penalty at retrieval time. See the recent paper [24] for experimental results on the suitability of the various representations according to the characteristics of the application. In general, the many alternatives for the temporal ....

A. Gerevini, L. Schubert, and S. Schaeffer. Temporal reasoning in timegraph I-II. SIGART bulletin, 4(3):T1--T4, 1993.

....time intervals, and the famous interval algebra of Allen [ 1983 ] for expressing qualitative relations between time intervals. There are also combinations of these and extensions to handle metric time as well, such as Meiri s framework [ Meiri, 1991 ] and the works of Kautz and Ladkin [ 1991 ] Gerevini et al. 1993 ] Dechter et al. 1991 ] Jonsson and Backstrom [ 1996 ] and Drakengren and Jonsson [ 1997 ] However, it was early proved that the reasoning problem for these formalisms is very hard; e.g. reasoning in Allen s interval algebra is NP complete [ Vilain and Kautz, 1986 ] and NP hardness ....

Alfonso Gerevini, Lenhart Schubert, and Stephanie Schaeffer. Temporal reasoning in Timegraph I--II. SIGART Bulletin, 4(3):21--25, 1993.

.... for domains in which a large data base of relations needs to be managed [1] Recently, other approaches based on graph algorithms have been proposed whose main characteristic is that of providing better performance in practice compared to the more traditional constraint based approaches [9, 12, 14, 15, 17, 18, 19, 28]. The present paper follows a similar direction. Our goal is to efficiently manage large data sets of qualitative temporal relations including at least the pointizable relations and disjointness relations, without sacrificing completeness. Thus we begin with the Point Algebra (PA) 41] and add ....

A. Gerevini, L. Schubert, and S. Schaeffer. Temporal reasoning in TimeGraph I-II. SIGART Bulletin, 4(3):21--25, July 1993.

.... relation. Dotted arrows indicate paths, solid lines 6= edges. In all the graphs there is an implicit relation between v and w. 2 Representing temporal relations through TL graphs In this section we first introduce the necessary terminology and theoretical background (partly taken from (Gerevini and Schubert 1993a) Definition 1 A temporally labeled graph (TL graph) is a graph with at least one vertex and a set of labeled edges, where each edge (v; l; w) connects a pair of distinct vertices v; w. The edges are either directed and labeled or , or undirected and labeled 6= Figure 2 shows an example of ....

....n from v 0 to v n , n 1, is a cycle ( cycle) if v 0 = v n . A TL graph is acyclic if it does not contain any cycle. 1 For instance if l = then R( is the relation, i.e. the set of pairs ht 1 ; t 2 i such that t 1 t 2 and t 1 ; t 2 2 T . Analogously for and for 6= In (Gerevini and Schubert 1993a) we proved the following theorems about determining consistency of a TL graph 2 : Theorem 1 A TL graph is consistent iff it does not contain any cycle, or any cycle that has two vertices connected by an edge with label 6= Theorem 2 A TL graph can be recognized as being inconsistent, or ....

[Article contains additional citation context not shown here]

Gerevini, A., and L. K. Schubert 1993b. Temporal reasoning in Timegraph I-II. SIGART Bulletin, 4(3), July 1993.

.... another interval J , or that I is before J ) However, the ability to refer to end points of intervals is useful in plan reasoning, as noted above; furthermore, point based representations provide a good basis for building efficient, scalable systems for basic temporal database management (see [7, 10, 14, 11, 12, 15]) Thus we have chosen to address the issue of disjointness from a point based perspective, and that involves the introduction of 3 point or 4 point relations. We analyze 56 3 point and 4 point relations and we prove that the problems of determining the consistency and of finding a solution of a ....

....from an interval with ordered endpoints. Current work concerns the design and the implementation of algorithms for handling disjunctions of PA relations which, in practice, work efficiently [11] This work is being done in the context of a temporal reasoning system called TimeGraph II (TG II) [12, 14], which is an extension of an older system (TGI) developed by Schubert, Papalaskaris, Taugher and Miller [20, 26, 27] in the context of natural language understanding, and which is aimed at generalizing the approach to a wider class of applications. ....

A. Gerevini, L. Schubert, and S. Schaeffer. Temporal reasoning in TimeGraph I-II. SIGART Bulletin, 4(3):21--25, July 1993.

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A. Gerevini, L. Schubert, and S. Schae#er, `Temporal reasoning in time graph i-ii', SIGART Bull 4, 3, 21--25, (1993).

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Gerevini A., Schubert L., Schaeffer S.: Temporal Reasoning in Time Graph I-II, SIGART Bull 4 (3) (1993) 21-25

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A. Gerevini, L. Schubert, and S. Schae#er, `Temporal reasoning in time graph i-ii', SIGART Bull 4, 3, 21--25, (1993).

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