Maintaining knowledge about temporal intervals

“Allen [1, 2] artificial intervalnatural relative abstraction interval property, no”

“For example, a cooperative response should warn a user that a plan will fail because some of its preconditions are not satisfied (Allen 1983b) or if there exists another plan that has the same effects but is in some sense a better plan (Pollack 1984; Joshi ef al.”

“Referring to the notion of “intervals algebra” as introduced by Allen [7] and the macro-algebra A 3 = {≺ , ∩ , ≻} as Golumbic and Shamir described in [8], we can think the direct succession relation as the “preceedings” ( X ≺ Y ) one and the parallelism relation as the “intersection” ( X ∩ Y ) one.”

“It is because Allen’s temporal interval algebra, [2], is not used as a basis for the directional relation definition in our approach: to determine which directional relation holds between two objects, center points of the objects’ MBRs are used [9].”

“The most popular TR framework used in TIE is Allen’s interval algebra (AIA) [Allen, 1983].”

“On the one hand, a CSTNU includes observation time-points to model discrete observations at run-time; on the other hand, a DTNU allows disjunctive constraints that can model non-convex durations, non-overlapping durations, and all of the other temporal relations from Allen’s interval algebra [2].”

“[10,13,14,24,25] as well as for intervals in R 1 [ 2 ,18], and a plethora of similar components exist for topological relations of”

“surgery, t) (representing the events which take place in the pattern), T = {before(e, f),during(t, f)} (representing the temporal relations among these events, the temporal relation representations are based on Allen’s First Order Interval Logic [3]).”

“Allen [1] has defined 13 basic binary relations between time intervals, six of which are inverses of the other six: before and after, overlaps and overlapped-by, starts and started-by, finishes and finished-by, during and contains, meets and met-by, and equals (see Fig.”

“Temporal calculi, such as the Interval Calculus [1] and the Semi-Interval Calculus [2], have been proposed.”

“has been seen previously in the artificial intelligence literature as Aamodt's implementation of Aliens' [ 15 ] temporal system in the long-established Creek semantic network-based case-based reasoning system (see [16]).”

“Allen (1983) and later Vilain, Kautz, and van Beek (1990) showed the algorithm to run in polynomial time w.r.t. the number of intervals in the database.”

“There are numerous simple relations (Allen 1983; Vilain and Kautz 1986) that can be defined between two intervals (equal, before, meets (i.e., immediately before), during, starts, ends, overlaps, and their inverses).”

“Originating from Allen’s work (1983) on temporal interval relations, QSR has been widely acknowledged as the AI approach to spatial knowledge representation and reasoning, with applications ranging from natural language understanding (Davis, 2013), robot navigation (Shi, Jian, & Krieg-Brückner, 2010; Falomir, 2012), g…”

“The temporal constraints rely on Allen (1983) relations but are far from customary musical vocabularies addressed in this paper.”

“For ordered temporal structures, we have considered here the so-called Allen Relations [1] which can hold between intervals, and from which corresponding relations between events can be derived (we consider the before and meets relations).”

“The first step is to determine temporal geometry, described as a set of twodimensional logical conditions proposed by Allen (1983).”

“Allen (1983) identified thirteen order relations between two temporal intervals embedded in IR 1 .”

“As a TN is defined by a set of time intervals, we can relate these time intervals based on Allen’s temporal algebra [ 13 ].”

“H¨oppner [10] mines temporal rules expressed with Allen’s [11] interval logic and a sliding window to restrict the pattern length.”

“Relations that are important for describing situations include 2D and 3D spatial relations, as well as temporal relations [32].”

“25 implemented Waltzer’s constraint engine and Allen’s transitivity tables of temporal database [27] in Allegro Common Lisp.”

“Structural aspects of time are defined by three subclasses, i.e. linear-, branching- and cyclic-TimeClass, each with numbers of temporal operations such as before, after, during, meets, etc. [1].”

“Because the interrupt point lies between time points t 4 and t5, the slide actor DEFSM changes from state SA ( 3 ) to SA (2) once the user interaction is complete—that is, after it executes transition DTA.”

“Allen (1983) showed that only 13 binary relations may be stated between two time intervals (meets, finishes, overlaps, etc.) Our model may be seen as a particular implementation of Allen's model, with important extensions as we will see below.”

“In order to be complete, a temporal graphical query language needs to be able to specify any primitive temporal relationship (Allen, 1983) as well as any combination of these primitives.”

“For example, it is the smallest set of base relations which allows topological distinctions rather than purely mereological; it is the spatial counterpart of Allen’s 11 temporal relations [1]; the cognitive adequacy of RCC8 base relations has been justified by empirical investigations [11].”

“For example, Allen [49] defined 13 types of temporal relations represented by two intervals, including before/after, during/contains, overlaps/overlapped-by, meets/met-by, starts/started-by, finishes/finished-by and equal.”

“We use Allen’s interval algebra [28] to define the temporal composability of energy services.”

“Generally, Allen’s interval algebra [53] is the most used model for topological temporal rela-”

“Since ATL is the logic of planning, an automated translation from ATL to BIP components enables to use rigorous design and implementation techniques and tools in a domain lacking them.”

“A TLM is a temporal logical module that supports, in general, the following temporal relationships: 13 Allen’s time-interval relationships [47], five relationships between the time point and the time interval, and three temporal relationships between the time points.”

“These relations are typically those de.ned by Allen [1].”

“HS allows one to express all possible ordering relations between any pair of intervals (the so-called Allen’s interval relations [2]), and it features one modal operator for each of them (obviously, no modal operator is needed for the equality relation), that is, 〈A〉 for meets, 〈B〉 for begins, 〈E〉…”

“A resolution of 30 minutes provides reasonable accuracy for many daily activities and allows TRAcME to compute robust features.”

“By employing this particular concrete domain, we can express Allen’s 13 [1] interval relations in the language and enable the representation of temporal dependencies between events.”

“Allen (1983)was the 236 .”

“a beforeb,a overlapsb, etc.) ( Allen 1983 ) into higher-dimensional, spatial relationships.”

“, linear, branching and cyclic time, each with a number of temporal operations such as before, after, equal, meets, met, overlaps, overlapped, covers, during, starts, started, finishes, finished (Allen, 1983).”

“More interesting are the terms “ meets” and “met-by,” which are binary temporal relations between intervals, drawn from the work by (Allen, 1983).”

“Recently temporal logics have been discussed in connection with artificial intelligence ([Allen, 1983, Allen, 1984, McDermott, 1982])—a discussion that would have benefited greatly from a rigorous ontological characterization of approaches to describing intervals and events such as that of Van…”

“The interest in the temporal aspects of natural language is not new in the field of artificial intelligence (Allen, 1983).”

“Composition tables might be most familiar from work on the temporal interval calculus (Allen, 1983), but have also been used for spatial reasoning, for instance with the RCC (cf.”

“IEEE, New York, pp 86-91 Allen E, Edwards G, Bédard Y (1995) Qualitative causal modeling in temporal GIS.”

“4 Illustration of 13 base temporal relations de-fined in Allen’s interval algebra (Allen, 1983) 3.”

“Note that more advanced temporal relations exist, such as the ones presented in Allen’s interval algebra [30].”

“CASE E allows for modeling temporal relations between events based on the Allen’s time calculus [1] as well as sub-event relationships along the temporal dimension.”

“In this paper, rt refers to Allen relations [1] and rs refers to RCC8 relations [32] (see Figure 5 and 6).”

“The query given by the user will also be retrieved as a set of time intervals and the test whether a certain location satisfies a certain time restriction is done using Allen’s interval calculus [2], in particular, using the relations “contains” and “overlaps” between intervals.”

“The dissimilarity between (�� ti, �� ti) and (�� sj, �� sj) is defined as D(Rti, Rsj) which is derived from the idea of the interval neighborhood graph [ 15 ][21].”

“Allen’s temporal operators (Allen, 1983) can be used to describe relationships between situations (Figure 1).”

“Common-sense models of the natural world include those of time [Allen, 1983], space [Kautz, 1985], materials [Hayes, 1985], causality [Reiger and Grinberg, 1977], activity [Sathi et al., 1985], and qualitative physics [Kuipers, 1986].”

“Implicitly, time processing in EC is similar to Allen’s interval calculus [19], which is also based on event occurrences.”

“Allen’s [1] representation of standard time and relations.”

“More information about time intervals and relations between them can be found in [2].”

“There are common-sense models of time (Allen, 1983), space (Retz-Schmidt, 1988), causality (Reiger & Grinberg, 1977), and physics (Hayes, 1985; Kuipers, 1986).”

“These relationships can be used to express the complete set of Allen’s [4] temporal relations, those of which are immediately relevant during, overlaps, meets and their inverses, are summarised in Table 1.”

“In order to enable modelling and querying objects and events using the grammars, it should support a basic set of spatio-temporal relations like ones defined in [21] [22].”

“Furthermore, there are interesting analogies with ASBRU temporal ontology [14], which also models action intentions, and Allen’s temporal constraints [34], as well as delays and durations.”

“TVQL uses four double-sided sliders to allow users to express the relationship between interval endpoints, supporting Allen’s 13 relational primitives [2].”

“In his seminal work, Allen [1] proposed an algorithm to systematically search through all possible singleton networks resulting from instantiating binary constraints with atomic relations and then to enforce path consistency on these instantiated networks.”

“…the temporal expression in a formal structure representing three types: (cid:127) algebraic intervals with a hierachical relation as Allen’s [1] interval, such structure cleary appears in the expression “the first part of the XIX th Century”; (cid:127) metric as in the expression “for 80…”

“The computational properties of the interval calculus and algorithms for maintaining networks of temporal constraints are presented in [1,2,28].”

“DEFINITION 4.1 An almost-connected partial order on a set is a binary relation that satisfies the following conditions (for all , ), * ): (i) reflexive, i.e. ; (ii) antisymmetric, i.e. ) and) implies ); (iii) transitive, i.e. ) and) * implies *; (iv) almost-connected, i.e. ) implies ), * or * ).”

“To represent these cases with the visual interval representation described above, one has to resort to disjunctions of Allen’s relations; indeed, Case 1 can be modeled by the formula: (B starts A) ∨ (A starts B) ∨ (A equal B) which is visually represented in Figure 2, while Case 2 can be modeled by several formulas, e…”

“Unlike McDermott’s temporal logic which adopts states that are associated with time points, Allen develops his theory of time and action based on intervals as primitive rather than as derived structure from points (Allen 1983; Allen 1984).”

“We base definitions on the thirteen basic relations of Allen’s Interval Algebra. These relations appear in Table 1. New relations are defined as specific disjunctions of basic interval relations. Figure 1 shows these relations as overlays on the N ̈ ok l lattice. This partial order among the interval relations appears…”

“( − ,(I,3,4)) ( − ,(II,0,2)) Figure 5 Example Showing the Interval Set Operators Filter Operations: Allen has shown that there are 13 possible (distinct) relationships that can exist between two temporal intervals [1] { e.”

““Inverse” temporal relations have been omitted for the sake of brevity; the relations between time points, between time intervals, and between time points and time intervals we adopt are exactly those in Vilain and Kautz ( 1986), Allen (1983), and Vilain (1982) and are shown in Figure 4.”

“As regards qualitative information different algebrae of temporal relations have been proposed for dealing with time intervals [ 1 ], time points [15] or both of them [14].”