INDu: An Interval & Duration Network

Weak Composition for Qualitative Spatial and Temporal Reasoning

“…However, weak composition has also been used in cases where composition could have been computed because the domain is well-structured and consists of pairs of ordered points, but where the authors did not seem to be aware that R is not closed under composition (e.g. INDU, PDN, or PIDN [17,16,18]) Example 1 (Region Connection Calculus RCC8 [19]). RCC8 is a topological constraint language based on eight atomic relations between extended regions of a topological space.…”

“…For analysing the effects of weak composition, we will mainly focus on its effects on the most commonly studied reasoning problem, the consistency problem, i.e., whether a-closure sufficient a-closure not sufficient weak composition = composition Interval Algebra [1] STAR calculus [21] rectangle algebra [9] containment algebra [10] block algebra [3] cyclic algebra [2] weak composition = composition RCC8 [19], discrete IA INDU [17],PDN [16], PIDN [18] a given set Θ of spatial or temporal constraints has a solution. Recall that consistency means that there is at least one instantiation for each variable of Θ with a value from its domain which satisfies all constraints.…”

“…Although we know the composition and all relations are closed under composition, it is possible to refine atomic relations using networks with more than three nodes. [17]). Allen's 13 interval relations are combined with relative duration of intervals given in the form of a point algebra, i.e., INDU relations are of the form R = I δ where I is an interval relation (precedes p, meets m, during d, starts s, overlaps o, finishes f, equal =, and the converse relations fi,oi,si,di,mi,pi) and δ a duration relation (<, >, =).…”

An Occlusion Calculus Based on an Interval Algebra

“…The interval sizes could be considered by using the INDU calculus [13], instead of Allen's algebra, as the underlying theory. This issue is left for further research.…”

A survey of qualitative spatial representations

“…The set of basic relations includes lef t of, right of, behind, in f ront of, above, below, inside, outside and overlaps, and it has been proven that its deductive system is complete for 3D space but is not complete for 2D space. The IN DU calculus (Pujari et al, 1999) can be seen as a tight combination of Interval Algebra with Point Algebra, i.e., each basic relation includes not only the interval relations but Pujari et al, 2006) also the size information represented by the point algebra, and it forms a JEPD relation set including 25 basic relations, as shown in Figure 27. The detailed analysis of its consistency is in (Balbiani et al, 2006).…”