Maintaining knowledge about temporal intervals

“Index Terms— Fuzzy ordering, fuzzy relation, interval algebra, question answering, temporal reasoning.”

“It also supports all temporal relations defined by Allen [2].”

“C0 is Days , the periodP is 7 days andX is composed by x1 = h[1; 1]; [3; 3]; [6; 6]i which identifies the single granule within the period, formed by the first, third, and sixth day, starting from 5/1/1998, and repeating every 7 days.”

“(1994) introduce fuzzy Allen relations as fuzzy sets of ordinary Allen relations agreeing with a neighborhood structure. Fuzzy sets which play a key role in modeling flexible constraints, have been used in several constraint-based approaches to temporal reasoning. Qian and Lu (1989) propose several propagation strateg…”

“For this reason, we use them in this paper.”

“They are used to filter the query results with spatial and temporal constraints (OGC Simple Feature Access topological relations and distance for the spatial part, and Allen’s interval relations [3] for the temporal part).”

“Allen’s [Allen, 1983] relations can be easily represented within Rit’s two-dimensional visualization of time intervals.”

“Like standard approaches using the TimeML standard, we draw inspiration from Allen’s (1983) seminal work on interval representations of time.”

“The field of Qualitative Spatial and Temporal Representation and Reasoning (QSTR) has evolved as a specialised discipline within Artificial Intelligence (Allen, 1983; Freksa, 1991; van Beek, 1992; Ladkin & Maddux, 1994; Cohn & Renz, 2007; Renz & Nebel, 2007).”

“The interval relations of Table 1 on the preceding page generate an integral RAI with 13 atoms on the set of all closed intervals of the real line, namely, the six relations in the table, their converses, and the identity; its composition table can be found in Allen (1983).”

“10Ladkin [19] uses a similar approach to map Allen’s interval calculus [20] to the language of rational numbers.”

“So, subplans is a set of plans, and a primitive plan's subplans is the empty set. order(p) is only defined for an and plan p and is a consistent set of temporal relations (Allen, 1983) over pairs of subplans.”

“Geographic Information Science, in particular, has been the field in which most QSTR models have been applied, for example, Allen’s Temporal Interval Relations calculus (Allen 1983), Region Connection Calculus (RCC) (Randell, Cui, and Cohn 1992), 9-Intersection model (Egenhofer 1995), etc.”

“In our work, the Allen algebra, illustrated in the Table 2, is used (Allen, 1983).”

“Allen’s temporal operators [4, 5] can be used to describe relationships between situations.”

“This leads to a kind of 2-D extension of Allen’s interval logic [ 2 ], with 13 exclusive ordering conditions on each axis.”

“As for the spatial relationship of 2-D B-string, there are in total 13 kinds of spatial relationships between two objects in one-dimensional space [13,22], as shown in Figure 4.”

“A question can be decomposed as general sub-question and a temporal sub-question with a SINGAN, and Allen introduced 13 temporal SIGNAL [46] (such as before, during, last, etc.”

“Most work in this area is based on the concept of temporal logic proposed by Allen [2], which introduces 13 unique operators that describe temporal relationships between intervals.”

“HS makes it possible to express all basic binary relations that may hold between any pair of intervals (the so-called Allen’s relations [1]) by means of four unary modalities, namely, ⟨B⟩, ⟨E⟩ and their transposes ⟨B̄⟩, ⟨Ē⟩, corresponding to Allen’s relations “begun by”, “ended by” and their inverses “begins”, “ends”,…”

“Time intervals can be related to each other in a knowledge base through temporal relations such as before, during, and overlaps Allen83].”

“Further, it is necessary to impose a constraint such that the minimum and the maximum values of the lifespan cardinality are equal to or greater than the minimum and maximum values of the snapshot cardinalities, respectively.”

“The earliest work on temporal reasoning involved the development of an interval algebra describing the possible relationships between intervals of time [1].”

“A specific flavor of temporal logic [1] was used to model temporal constraints.”

“Allen’s interval ( Allen, 1983 ), so their merge returns a new interval, which is the union of”

“These same concerns arise in computer science [11, 30] and engineering because of the need for synchronization among di erent computational units.”

“The reader can refer to [9] and [19] to obtain more information about real-time specification techniques.”

“Allen’s temporal relationships [24] are used to express parallelism and mutual exclusion between components”

“As discussed in [1, 2], there are 13 possible temporal relations between two actions, that is, before, meets, overlaps, starts, during, finishes, equals, and their inverse relations.”

“Here we re-use TempEval-3 task ABC, where systems are required to perform end-to-end TimeML annotation from plain text, including the complete set of temporal relations (Allen, 1983).”

“The complete TimeML specification assumes the temporal interval relations as defined by Allen (Allen, 1983) in Figure 1.”

“Schlieder ( 1995 ) developed a calculus that resulted in a set of 14 spatial relations among ordered linear segments, based on an extension of Allen's ( 1983 ) interval relations to two‐dimensional space and the order information of triples of points, where points are the vertices of the segments.”

“• Qualitative constraints: Allen’s interval algebra [2] and Vilain and Kautz’s point algebra [34] are two fundamental representatives.”

“Currently only temporal constraints are explicitly represented, by using qualitative relations based on Allen’s interval algebra [1] and simple quantitative information.”

“In this paper, we adopt Allen's [2] interval algebra framework for representing hierarchical and possibly inde nite and incomplete temporal information about the relations between events or intervals of time.”

“Considering two upper-bound constraints U1 and U2 where U1 is between ai1 and aj1 , and U2 is between ai2 and aj2 , based on Allen’s temporal interval logic [Allen 1983; Chinn and Madey 2000], we can conclude that there are two groups of basic relationships between U1 and U2.”

“For example, Allen used an interval representation [4], Dutta added fuzzy membership values to interval calculus [5], and Dubois used generic fuzzy numbers [6].”

“According to this approach, work is currently underway to develop a methodology and a computational model of geosemantic proximity that will end up with geosemantic proximity predicates that are homomorphic with current spatial and temporal topological predicates ( Allen 1983, Egenhofer 1993, Clementini and Di Felice…”

“Allen’s interval temporal logic [25] may also be extended to describe the temporal relationships among multimedia data [26].”

“The problem of automatically preserving the consistency of a set of temporal assertions has been considered by Allen [ 1 ] and by Barbie and Maiocchi [7].”

“If Allen’s temporal relations between intervals [3] are used, this set is defined as op ∈ {<, =, >, d, di, o, oi, m, mi, s, si, f, fi}.”

“In a "bars' structure, if one bar becomes longer, the other one has to become shorter: they have to satisfy the meet constraint (using Allen's (1983) terminology).”

“Finally we should mention that when the feature to discretize is either time or space (the term aggregation is also used), dedicated approaches have been developed [8, 575].”

“These filters are used to filter the results with spatial and temporal constraints (OGC Simple Feature Access topological relations and distance for the spatial part, and Allen’s interval calculus [6] for the temporal part).”

“Temporal calculi have been proposed, such as the Interval Calculus (Allen, 1983) and the Semi-Interval Calculus (Freksa, 1992a).”

“A number of path consistency algorithms have been proposed (Allen, 1983; Macworth and Freuder, 1985).”

“It is inspired by Allen's and Chang's work in [1] and [2].”

“Due to this independence, the database system can physically organize the data for best performance without worrying about influencing the client's view of the data [1].”

“1 Temporal Models A common representation for the temporal component of time-dependent data is based on temporal intervals [12, 23, 24] in what is called temporal-interval-based (TIB) modeling.”

“, time intervals [11, 4]).”

“A specific flavor of temporal logic (Allen, 1983) was used to model temporal constraints. The following are some of the limitations of their technique: (1) it cannot be easily generalized to generate test cases to stress test other kinds of resources, such as network traffic, as this would require important changes in…”

“Note that in this work, α can only take values from the set of 13 Allen's base relations (Allen, 1983) i.e.”

“…positions in a sequence— precedes , sameOrientationAs , and oppositeOrientationAs — are expanded with additional restrictions that cover the full range of sequential relationships (Allen, 1983): strictlyPrecedes , meets , overlaps , contains , strictlyContains , equals , finishes , and starts .”

“Compositions of basic (non-disjunctive) relations are defined at [1].”

“In [15], Halpern and Shoham introduce a modal logic for reasoning about interval structures, called HS, with modal operators corresponding to Allen's interval relations.”

“In the majority of cases,including the models introduced by Allen [ 1 ],Balbiani and Condotta [2],Balbiani,Condotta and Fari˜ nas del Cerro [3],Cristani [7],Ligozat [11],Ligozat [12] and Vilain and Kautz [19]:”

“The Lrformula ANet(xy : i, j e A) is defined to be /\{xu < Id) A f\ (xij;xjk > Xjk). i€A i,j,keA Roughly, this formula means that the graph formed by the variables xy is an atomic network.”

“We note that operation delay constraints are general and can be used to capture durational and deadline constraints in specifying real-time systems [14] and all possible binary timing relationships between operations [15] as shown in Figure 7.”

“Angle 0.1 0.3 0.4 0.5 0.7 0.9 Outcome ok ok ok fail fail fail 13 possible temporal relations between time intervals can be used to constrain the query (Allen, 1983).”

“Though the authors do not consider algebras of relations, this work suggests to use them, since Allen’s constraint propagation algorithm [1] is an instance of a constraint propagation algorithm (which can be generalised as arc-consistency).”

“Following a natural or man made disaster, rescue workers risk their lives searching for survivors in a race against time.”

“Temporal predicates and operators of this language would be interpreted in terms of arithmetic functions like those presented, for instance, in Allen’s temporal logic (Allen, 1983).”

“In the area of reasoning about temporal relations between events [2], it was possible to identify tractable special cases that are natural for uncertain observations and text understanding [30, 34].”