Maintaining knowledge about temporal intervals

“Most notably, James Allen's interval algebra [1] has received much attention for its simplicity.”

“task A must follow directly after task B) could be expressed by the temporal relations defined by Allen [18].”

“Allen’s relations [2] provide an interesting framework for comparing these two presentations according to spatio-temporal criteria.”

“Multimedia Tools and Applications, 7, 5-7 (1998) .”

“Deciding consistency of TCSPs is known to be intractable.”

“, 3 weeks after end of chemotherapy), or a time-interval constraint where the time interval associated with the constrained event is compared with another time interval using Allen’s temporal-interval comparison operators [66].”

“The specific relations we are interested in are those of Allen’s interval algebra [3] and Ladkin’s extension of it over unions of convex time intervals [13] and also temporal distance (e.”

“Allen [ 1 ] proposed an algebraic framework named Interval Algebra (lA), for qualitative reasoning with time intervals where the binary relationship be­ tween a pair of intervals is represented by a subset of 13 atomic relations.”

“…[Grigni et al. 1995] No decision algorithm or .nite axiomatization is known, although the problem becomes both .nitely axiomatizable and polynomial-time decidable in any number of dimensions other than two [Allen 1983; Renz 1998], for some reasonable vocabularies of topological relations.”

“Previous research-Oers [12, 13, 15, 18] have added to this set temporal comparisons for pairs of timepoints (AT, BEFORE, AFTER) and for pairs of intervals (BEFORE, UNTIL, LEADS, STARTS, EQUALS, DURING, SPANS, FINISHES, FROM, and AFTER); the latter set is based on Allen's interval-based logic [19].”

“As in TIE, and instead of Allen-style intervals [1], CoTS uses a real-valued point-based temporal representation.”

“These methods have been borrowed from qualitative temporal reasoning à la Allen [1], and make use of a composition table.”

“These 13 relations correspond to the relations between time intervals introduced by Allen (1983), and applied to 1-”

“They feature two modalities which correspond to Allen’s meet and met by relations [ All83 ], intuitively capturing a right neighboring interval and a left neighboring interval.”

“This line of work builds on ideas from TimeBank (Puste-jovsky et al., 2003) and a number of different formal models for temporal reasoning, e.g. Allen (1983), Moens and Steedman (1988).”

“Allen proposes a qualitative temporal logic with a complete set of 13 distinct relations between two temporal intervals (Allen 1983).”

“In the terminology of Allen’s interval calculus [1,2], A and B are called co-temporal if πt(A) = πt(B) (we denote this by A =t B).”

“When dealing with time interval patterns, the formulation of patterns is much more intricate, because the number of possible binary relations rises from three relations for time points (before, equals, after) to Allen’s 13 interval relations [3].”

“There exists a wide spectrum of temporal logics (see, e.g., Allen, 1983; Clarke & Emerson, 1981; Manna & Pnueli, 1992; Gabbay, Hodkinson, & Reynolds, 1994; van Benthem, 1995).”

“For example, Nebel and Bürckert [30] consider this problem for the 13 interval relations of Allen [2] and van Beek [46] for the relations of point algebra.”

“For the definitions of these relations, as well as interval temporal relations see [22, 23].”

“We also assume that the temporal relationships described in [1] may be applied to intervals.”

“For TR between two intervals I and I ′ , there are 13 different relations in total given by Allen’s interval algebra (Allen (1983)).”

“Further research in this direction might be aimed at providing approximate consistency-checking algorithms for disjunctive temporal information that operate more e ciently and accurately than current approximate techniques based on constraint propagation [2, 39].”

“Allen has demonstrated that there exist a total of thirteen possible relationships between two intervals [5].”

“Zakour et al. [35] introduce a sliding window approach to extract frequent interval sequences from discrete temporal sequences.”

“In essence , an STP supports metric relations among points, time points anchored in absolute time, and primitive Allen interval relationships [34]; these structures are also efficient and can be solved by polynomial time algorithms [31] [35].”

“For example, the interval corresponding to the tenth day of January, 1990 is represented by [1990; 1; 10].”

“All of Allen’s interval constraints [21] can be captured using temporal constraints of the form described here, using time points representing the ends of the intervals.”

“As an example for an application, consider a database with, say, a cinema timetable, and you query the timetable “give me all performances ending before midnight”.”

“Although, overlapping intervals along the line of temporal work by Allen with regards to various entities of RBAC [2] have not been discussed, the semantics of overlapping intervals are elaborated for temporal hierarchies.”

“We apply a coarse version of the Interval Algebra (IA) by Allen (1983) to represent ordering information of landmarks and street segments along a specific route in the street network.”

“Allen shows 13 different types of inter-interval relationships (Allen 1983).”

“We have listed all possible temporal relationships [Allen 1983] between the truth periods of two formulas A and B.”

“J.F. Allen ( 1984) Towards a General Theo~ of Time and Action, Artificial Intelligence, 23, pp. 123-154.”

“Example predicates include Follows, Coincides, Parallels, and Mutates (Allen 1983; Freksa 1992; Hornsby and Egenhofer 1998).”

“• Allen’s interval algebra, and all its fragments [4, 23,27,31] • Problems in phylogenetic analysis [20,32] • Tree description constraints in computational linguistics [10,11,15] • Computational problems in the theory of relation algebras [16,24,30] • All CSPs in monotone monadic SNP without inequality [9, 17]”

“Detecting the semantic structure underlying a Web page is a technical challenge which is addressed by the application of the SGG. Buyukkokten et al. [2001] divided a Web page into several semantic textual units with the help of HTML tags.”

“Allen (1983) identified 13 topological relations between two temporal intervals. The breakthrough on topological relations between spatial objects was made by the well-known 4-intersection and 9-intersection approaches proposed by Egenhofer and Franzosa (1991). A lot of research has been done based on this aspect (Ege…”

“We discuss the reasoning power of QTCC and apply the important reasoning technique of composition tables, originating from the domain of temporal reasoning [1].”

“All comparisons, including OVERLAPS , are expressed as formulas involving the Before relation (the relation on integers) and logical connectives [2].”

“Allen [8] defines 13 possible temporal relationships between any two given time intervals.”

“While the computationalproperties of qualitativetemporal reasoning [1] have been analyzed quite thoroughly [20, 19, 12], for qualitative spatial reasoning the situation appears to be completely di(cid:11)erent.”

“(2007) and Álvarez et al. (2010). Most of the approaches adopting this technique rely on an extended version of the Apriori algorithm (Mannila et al., 1997) to discover frequent sequences of events—the temporal distance between the events of a frequent sequence is computed using lower and higher frequency thresholds.…”

“An interval algebra network (IAN) [39] can be used to represent the temporal relationships among a set of events in an activity, where the nodes represent events and the directed links represent the temporal relationships among the events.”

“…reasoning has developed several sets of spatial relations (e.g., Cohn & Hazarika, 2001), and we chose the set of thirteen interval relations by Allen (1983) for the following reasons: The calculus is well investigated from a formal point of view (Ligozat, 1990) and has some interesting…”

“3 The interval algebra The most widely investigated relation algebra in the temporal context was given by Allen [1].”

“Allen’s approach is simple, transparent and easy to implement.”

“The additional information requires time points or intervals in action de(cid:12)nitions [Allen, 1983], or other such temporal representations.”

“Systems that interact with the world must therefore be adept at temporal reasoning [8]–[10].”

“To describe complex events, which often imply a temporal sequence of facts, we employ Allen’s temporal logic [41].”

“ing to the thirteen temporal relations of Allen’s interval algebra [32], the temporal aggregate functions, or the extension functions for constructing new temporal elements.”

“, topological in time) relationships (before, equal, meets, overlaps, during, starts, finishes) [11].”

“It is worth noting that the defined pattern language captures the set of all possible 13 relations on two temporal intervals as defined in [ 4 ].”

“– Allen’s 13 relations for time intervals [5] such as before, after, during, contains, overlaps.”

“Most non-fuzzy approaches are based on a set of basic relations, based on Allen’s interval relations [2], for instance Ref.”

“As has been discussed in [7,15], an important requirement of all temporal languages is to support Allen’s interval operators such as overlap, precede, contain, equal, meet, and intersect [ 1 ].”

“Temporal databases (Snodgrass 1992) and temporal reasoning (Allen 1983) have a long tradition in computer science, but the integration with spatial databases (http://www.dbnet.ece.ntua.gr/~choros/) and spatial reasoning (Egenhofer and Golledge 1998) is only in its infancy.”

“This will result in a safe crossing of the intersection as shown by The mechanics behind this reasoning process is rendered possible by the critical role of temporal semantics and Allen’s temporal intervals [55] as we demonstrated in [44].”

“These include standard firstorder logic, Allen’s interval calculus (Allen 1983), and various temporal logics (Clarke, Emerson, & Sistla 1983; Allen & Ferguson 1994; Bacchus & Kabanza 2000).”

“Having their seeds in Allen’s approach [ 5 ], in the last fifteen years a number of calculi have been proposed from which many still rely on the same reasoning mechanisms as Allen’s algorithm (see section 3.1).”

“As known from [30], all 13 Allen’s interval relations may be translated in terms of equivalent relations on the intervals’ endpoints.”

“Sacchi and coauthors 4 described a method for inferring relationships based on encoding the time series as a sequence of trends and discovering the relationships among them in terms of Allen ’ s intervals, 5 quantifying the evidence by con fi dence and support.”

“person, equipment, zones of interest), ”components” corresponding to the sub-events composing the event, ”forbidden components” corresponding to the events which should not occur during the main event, ”constraints” are conditions between the physical objects and/or the components (including symbolic, logical, spatial…”

“An atomic linear constraint over a set of variables X is an expression of the form a1x1+a2x2+· · ·+anxn b where a1, a2, . . . , an, b ∈ R, x1, x2, . . . , xn ∈ X, and is <,≤, >,≥, = or =.”

“As it has been shown in Section 3, FOSOL is a generalization to IA fuz of the classical problem of finding a solution of an IA-network: accordingly, classical backtracking algorithm with incremental path-consistency [1,40] can be generalized to a Branch & Bound algorithm, which searches through the possible singleton…”

“Interval temporal logics (ITLs) were introduced in the philosophy of time (see [Ben95] for a survey) but have proved useful in artificial intelligence and computer science [ All83 , HMM83, HS91, ZHR91].”

“These schemas use the five Allen relationships [1] to provide a means of combining multiple modalities into a composite modality.”

“chronization constraints are the ones based on Allen’s binary relations between intervals [ 2 ], or on the relationships between instants defined in [62].”

“They can correspond to Allen's relations between two intervals [35] if the execution of an intervention is viewed as an interval.”

“3) Time Dependency: In the time perspective, the relation can be classified into “α before β,” “α meets β,” “α equals β,” “α overlaps β,” “α during β,” “α starts β,” and “α finishes β.” These are seven relations among Allen’s [58] 13 relations, a well-known classification of time-dependent relations between two activi…”