Maintaining knowledge about temporal intervals

“One of the most seminal works is constituted by Allen’s interval algebra [2] and has found many adoptions in the above fields [38].”

“Expectations and observations are defined by the specification of a type (based on the classification of activity types) and timing, expressed using time intervals (Allen 1983).”

“Several quantitative and qualitative constraint-based temporal formalisms have been proposed, stemming from pioneering works by Allen (Allen 1983) and by Dechter, Meiri, and Pearl (Dechter, Meiri, & Pearl 1991).”

“Concurrently with the seven relations which can exist between two activities in [ 20 ], we define seven types of links between two use cases UCi and UCj (Table 1). The links introduced in our approach are different from those which have previously been defined in the sense that they are not established for the same pu…”

“Ordering constraints are expressible in SOMA through a sequence pattern based on Allen’s interval calculus [27].”

“Together with these parameters, the layout specifications can capture all possible Allen relations [3] for intervals.”

“Formal studies of the temporal aspects of both non-spatial and spatial systems can be found since the early 1980s (Allen 1983; Clifford and Warren 1983; Ariav 1986; Rolland et al. 1987; Snodgrass 1987; Armstrong 1988) (see Figure 1). Nonetheless, time as a research subject has been specifically studied long before in…”

“The 13 interval relations (Allen, 1983). an object may have several or many di ff erent SBRs or main directions.”

“Allen’s interval algebra consists of binary relations between intervals which are disjunctions of 13 basic interval relations (such as before, meets, includes, overlaps, starts, finishes or equals) [3].”

“HS features one modality for each of the 13 possible ordering relations between pairs of intervals (the so-called Allen’s relations [1]), apart from the equality relation.”

“…with D and for the logic with ¯ D is that in linear discrete orders all intervals have either 0 or 2 subintervals with the maximal size, while an interval may have only one superinterval with the minimal size (e.g. over the naturals, the interval [1 , 5] has only one such superinterval — [1 , 6] ).”

“, 15Days of Months can be defined as “[1-5] / Days NSDur Months”) and”

“Second, Allen defines the operations of converse and composition on : and Æ Æ and .”

“These relations between intervals in a string are very similar to Allen’s relations for intervals in time [1].”

“Multiple hot objects in a video sequence can have any one or more of the 13 temporal interval relations [3] based on their LTIs.”

“A Complete Classi cation ofTractability in Allen's AlgebraRelative to Subsets of Basic RelationsThomas Drakengren and Peter JonssonDepartment of Computer and Information ScienceLink oping University, S-581 83 Link oping, Swedenemail: fthodr, petejg@ida.liu.seSeptember 3, 1998AbstractWe characterise…”

“For specifying qualitative temporal information about relations between intervals, Allen's interval algebra [ 1] is often considered a convenient tool.”

“An alternative approach, developed by Allen [3], and by Halpern and Shoham [15], regards intervals as primitive.”

“With regard to mining the temporal relations between patterns in multivariate data, Allen's interval algebra [1] is particularly useful in modeling sequence information.”

“We remark that Allen’s all relations [18] between two distinct intervals can be expressed by means of these modal operators.”

“In the past, several qualitative spatial and temporal calculi have been introduced, first and foremost as a reasoning tool: the Interval Algebra (Allen 1983), the Point Algebra (Vilain & Kautz 1986), the Cardinal Direction Calculus (Frank 1991), the Doublecross Calculus (Freksa 1992b), the Region Connection Calculus (…”

“The possible RELTYPE values for a TLINK are based on Allen’s thirteen relations (Allen 1983).”

“Considered temporal relations are starts, meets, during, o6erlaps, equal, finishes [2].”

“Indeed, what was needed was a combination of a vocabulary tailored for intervals [Allen 1983] (e.g., interval A should coiltai)l interval B), timing constraints [Lutz,& Wong 1992] (e.g., X must occur within 10 seconcls after a Y has occurred), etc. 5.”

“In these last years, the temporal knowledge representation scene has been dominated by the debate about the ‘Interval Algebra’ (IA) proposed by James Allen, (1981, 1983, 1984), for applications such as automated planning and plan synthesis .”

“Note that most of the existing temporal query languages violate both of the above principles, mainly by introducing constructs for explicit manipulation of the actual timestamp representation: both ATSQL [5] and SQL/Temporal [18] use the BEGIN and END keywords to extract the endpoints of intervals, PERIOD keyword to c…”

“Allen [10] defines thirteen temporal relations between two intervals of time.”

“• Temporal and qualitative reasoning (Allen, 1983; Allen, 1984; Kowalski and Sergot, 1986; Kuipers, 1984; Kuipers, 1986; Kuipers, 1987; Shoham, 1987; Williams, 1986) are not supported.”

“Some of these results (e.g., all results before Theorem 15) can also be applied to other qualitative calculi (like Inter-val Algebra (Allen 1983), Point Algebra (Vilain and Kautz 1986), and Cardinal Relation Algebra (Ligozat 1998)) immediately, but some others (including Proposition 19 and Theorem…”

“Domain #BR RM 9-Intersection [8] simple 2D regions 8 I [11, 15] Allen’s interval relations [1] intervals (order) 13 A [41] Block Algebra [2] n-dimensional blocks 13 A [2] Cardinal Dir.”

“Several quantitative and qualitative constraint-based temporal formalisms have been proposed, stemming from pioneering works by Allen (1983) and by Dechter et al .”

“…with a 3-DOF Inertial Measurement Unit (IMU) from Xsens, allowing drift-free measurements of the three Euler angles yaw, roll, and pitch, and two Hokuyo URG-X004 Laser Range Finders (LRFs), one for scan matching, and one for elevation mapping, which can be tilted in the pitch angle within 90◦.”

“The resulting labeled tableau systems capture the accessibility relation by means of labeled formulas, and they provide suitable notions of closed branches and tableaux.”

“REFERENCES [1] J.F. Allen (1983) Maintaining Knowledge about Temporal Intervals, Communications of the ACM, Vol. 26, No. 11, pp 832-843.”

“Existing interval-based temporal models are mainly based on some or all of the 13 binary temporal relations between time intervals as defined by Allen (Allen, 1983).”

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

“For instance, Figure 2 gives an Echidna program for scheduling tasks using some of the relations on temporal intervals described in ( Allen, 1983 ).”

“The kind of analysis required is a simplified version of the temporal reasoning framework presented by Allen (Allen 1983), where the 13 basic different temporal relations among events were identified.”

“Allen [1983] defines five relationships between a point and an interval: ahead, front-touch, in, back-touch, and behind.”

“A mutex constraint is a relationship between two tasks, a i and a j , that ensures that either a j must finish before a i starts or a i must finish before a j starts (Allen, 1983).”

“Furthermore, events are related with temporal interval, logical, and spatial constraints [6].”

“The earliest approach to add temporal support to relational query languages, such as SQL, was to introduce new data types with associated predicates and functions that were strongly influenced by Allen’s interval relationships [Allen 1983].”

“To do so, based on the visionary work of Allen (1983) who proposes 13 relationships between two intervals, the present work defines four relationships that are illustrated in Figure 2 and are suitable for the current setting as follows: (1) A direct match occurs when one inferred period is aligned…”

“Its processing pipeline is decomposed into people detection, tracking, and event recognition.”

“Excluding equality, there are 12 different non-trivial relative position relations between pairs of intervals in a linear order, often called Allen’s relations [3]: the six relations depicted in Tab.”

“We show that these conditions are satisfied by a range of calculi including the Interval Algebra (IA), Rectangle Algebra (RA) and Block Algebra (BA) [3], and Region Connection Calculus RCC8 [4] and RCC5 [5], for all of which reasoning in general is known to be NP-hard [2,6].”

“[46] J.”

“In contrast, the following query exploits SXPath that allows for extracting details of music bands by exploiting only the DOM nodes of type img and text , and their spatial relationships.”

“In our implementation of graph matching, we start the search from the vertices and find a set of matching vertices for each query vertex in each distinct database description.”

“5 0 0 0 b [1] 0.”

“However BBNs provide no direct mechanism for representing temporal dependencies [ 11 ,[2],[391.”

“Time relations are the ones defined in Allen’s time calculus [4,5]: overlap, inclusion, (direct) precedence, .”

“media items such as before, while, overlaps etc. [ Alle83 ], [WaRo94]. A summary of the”

“For example, the discussion of relationships between segments (section 3.2.3) can be seen to be an extension of crisp relationships proposed by Allen [ 1 ] others.”

“Composition table for the 12 qualitative relations (omitting the trivial relation “=”) introduced by Allen (1983). (shaded cells = multiple model cases; white cells = single model cases) .”

“Allen [1] formulated a set of 13 temporal relations that can hold between two primitive events, i.”

“If we look at the results obtained from 4-objectives onwards, it can be observed that the loss of hypervolume is higher. is because of the forth objective (the number of UAVs) which is an integer variable in the range [ 1 , 5 ] .”

“…models of spatial and temporal relations dealing with different aspects of space such topology, direction, distance, size , etc. QSTR has evolved as a specialised discipline within Artificial Intelligence [Allen, 1983, Bhatt et al., 2011a, Cohn and Renz, 2007, Freksa, 1991b, Renz and Nebel, 2007].”

“Allen introduced interval based temporal logic in [3].”

“However, the wide industrial use of configuration technologies and the increasing size and complexity of configuration problems make the field more challenging than ever. Today the mass customization paradigm has been extended from traditional physical products to the fields of software and service configuration. Conf…”

“The algebraic treatment pursued in that area originates in qualitative temporal reasoning, notably with Allen’s interval algebra [10].”

“Now, we can use the basic Allen’s interval relations [2] depicted in Figure 2 to place constraints over the anonymous intervals.”

“, [6], or some other domain which support the RCC5 and RCC8 CT (see [26]); on the other hand, this approach is applicable to other formal theories of binary relations, for example, the 13 interval relations given in [1] or the RCC11 theory developed in [13].”

“However, representing the spatial relations between objects is also an important component of image content description and access.”

“In addition, approaches like that of Allen [ 14 ] that treat intervals as primitive temporal elements can successfully overcome or bypass the DIP, which, as discussed [21], only arises when one insists on the existence of time points.”

“Allen’s relations can be first-order defined using < and ≺ [1].”

“Allen [ 26 ] defines 13 possible relationships between intervals, and this may be an indication of the order of magnitude of the number of types of causal expression that is required.”