Meiri, I.: Combining Qualitative and Quantitative Constraints in Temporal Reasoning. Artificial Intelligence 87 (1996) 343--385  Home/Search   Document Details and Download   Summary   Related Articles   Check

....reasoning is an important task in many areas of computer science and artificial intelligence (see, e.g. Golumbic and Shamir, 1993; Nokel, 1991] Allen s algebra allows us to specify qualitative information about time intervals. This algebra has also become the kernel of some other formalisms [Meiri, 1996; Angelsmark and Jonsson, 2000] The interval algebra and some of its extensions are closely related with a number of interval based temporal logics used for real time system specification [Bellini et al. 2000] The basic satisfiability problem in Allen s algebra is NPcomplete [Vilain et al. ....

Itay Meiri. Combining qualitative and quantitative constraints in temporal reasoning. Artificial Intelligence, 87(1-2):343--385, 1996.

....representatives. Quantitative constraints: This class of constraints was originally studied by Dechter et al. 3] Combination of qualitative and quantitative constraints: Two important approaches that integrate both types of constraints were presented by Kautz and Ladkin [11] and Meiri [13]. To tackle our problem we concentrated on the work on combined qualitative and quantitative constraints as well as purely quantitative constraints. We did this for the following reason: In our guideline representation language both types of constraints are possible. Temporal scheduling ....

....relevant for our problem. As we will see in sections 4.3.2 and 4.3.3, the spectrum of qualitative constraints we may expect is reduced to the relations = and # between two time points. These 6 constraints may easily be translated to quantitative ones using the functions described by Meiri [13]. Thus, translating qualitative into quantitative constraints and working only with the latter type was also a reasonable option for us. Several authors have focused on the propagation of combined qualitative and quantitative constraints in temporal networks: Kautz and Ladkin [11] use separate ....

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I. Meiri, Combining qualitative and quantitative constraints in temporal reasoning, Artificial Intelligence 87 (1996) 343-385.

....instance, the point algebra [16] is only useful for time points and Allen s interval algebra [1] is only useful for time intervals. Such restricted languages may not be sufficient for modelling realworld problems so several formalisms for multisorted temporal reasoning have been proposed [2, 7, 9, 13, 15]. However, the basic temporal formalisms are much easier to analyse from a complexity theoretic standpoint; all tractable subclasses of Allen s interval algebra are known, for instance [10] The goal of this paper is to study the computational complexity of Meiri s [13] Qualitative Algebra which ....

.... been proposed [2, 7, 9, 13, 15] However, the basic temporal formalisms are much easier to analyse from a complexity theoretic standpoint; all tractable subclasses of Allen s interval algebra are known, for instance [10] The goal of this paper is to study the computational complexity of Meiri s [13] Qualitative Algebra which is a temporal formalism able to represent both time points and time intervals. Thus, we can relate points with points, points with intervals and intervals with intervals using an expressive set of qualitative relations. In contrast with Allen s algebra and the ....

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I. Meiri. Combining qualitative and quantitative constraints in temporal reasoning. Artificial Intelligence, 87(1-2):343--385, 1996.

....the Semantic Web have been developed from a functionality centered perspective, e.g. ontology reasoning such as with DAML Time . Temporal knowledge representation and temporal reasoning have been investigated since long, e.g. in (temporal) databases [15, 14, 8, 9] and in Artificial Intelligence [18, 6, 17, 19, 16, 5, 20]. Arguably, http: www.cs.rochester.edu ferguson daml temporal reasoning on the Web requires forms of reasoning inherently di#erent from traditional reasoning forms used in databases and Artificial Intelligence because the Web is heterogeneous: The Web can be seen as a (very large) ....

....on the components of a non convex interval o#ered by TemPTo. In this table, REL denotes anyone of the relations given in Table 2. Table 2, Table 3, and Table 4 give the relation and functions o#ered by the qualitative layer. The definitions of these relations and functions are as usual (cf. [19]) and supplemented with a core set of functions and relations on non convex time intervals according to [17, 5] Quantitative Layer. The second layer of TemPTo, the quantitative Layer, o#ers origins of time, time durations, and additional quantitative and or metric operations on the basic TemPTo ....

Itay Meiri. Combining Qualitative and Quantitative Constraints in Temporal Reasoning. In Proceedings of the 9 National Conference on Artificial Intelligence, July, AAAI Press / The MIT Press, 1991.

.... but it implies a higher computational cost [6] The main classical disjunctive temporal models are point based [12] interval based [3] metric (quantitative) point based models [7] Moreover, some efforts have been made to integrate qualitative and quantitative temporal information, as [9] among others. However, many application domains (scheduling, causal reasoning, etc. need to manage disjunctive assertions of temporal constraints, as well as conjunctive and hypothetical queries, one to many constraints, etc. This gives rise to the need to manage nonbinary constraints. Although ....

I. Meiri. Combining qualitative and quantitative constraints in temporal reasoning. Art. Intellig., 87(1-2):343--385, 1996.

....Problems (DTPs) Stergiou and Koubarakis 1998; Armando, Castellini et al. 1999; Oddi and Cesta 2000] The class of DTPs is significantly more expressive than other problems already studied in constraint based temporal reasoning. It extends the well known Simple Temporal Problem (STP) Dechter, Meiri et al. 1991] by allowing disjunctions and the Temporal Constraint Satisfaction Problem (TCSP) ibid. by removing restrictions on the form of allowable disjunctions. Formally, a Disjunctive Temporal Problem (DTP) is a pair 1, z, C where V is a set of temporal variables and Cis a set of constraints among ....

....problem to one of selecting one disjunct, x i xs N bsi from each constraint Ci C and then checking that the set of selected disjuncts forms a consistent STP. Checking the consistency of and finding a solution to an STP can be performed in polynomial time using shortest path algorithms [Dechter, Meiri et al. 1991]. The computational complexity in DTP solving defives from fact that there are exponentially many sets of selected disjuncts that may need to be considered; the challenge is to find ways to efficiently explore the space of disjunct combinations. This has been done by casting the disjunct selection ....

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Meiri, I. (1991). Combining qualitative and quantitative constraints in temporal reasoning. National Conference in Artificial Intelligence (AAAI'91).

.... determining whether a formula is a tautology, denoted j= is PSPACE complete [11] Formulae of this form occur in many areas of mathematics and computer science, some examples are logical formalisms for time, actions, events, and persistence [20, 7, 12, 3] reasoning with temporal constraints [17], and planning and scheduling [2, 10] However, there are very few tools for performing quanti er elimination and validity checking for this logic e ciently. The primary focus has been on tools for either more expressive theories such as integers or reals with addition and order (e.g. Omega ....

I. Meiri. Combining qualitative and quantitative constraints in temporal reasoning. Articial Intelligence, 87(12):343385, 1996.

....marco.falda ladseb.pd.cnr.it, giacomin ing.unibs.it Abstract. This paper describes a model for temporal reasoning that handles both quantitative and qualitative information affected by vagueness and uncertainty. Starting from two existing models, namely the Meiri s system [9] and IA [2, 3] the proposed approach generalizes the first to a fuzzy framework and extends the second in order to handle qualitative constraints. The system uses the Fuzzy Constraint Satisfaction Problem theory to formulate reasoning tasks and so it takes advantage of traditional solving ....

....temporal information can be both vague and uncertain, so that this aspect should be taken into account by means of an explicit representation. Furthermore, agents can have conflicting goals, so that they should be able to express preferences on temporal constraints regarding their activities. In [9] an integrated model capable of handling both quantitative and qualitative constraints is proposed but this approach is not appropriate for those domains where knowledge about time is pervaded with vagueness and uncertainty. The notions of vagueness and uncertainty can be represented in the ....

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I. Meiri., Combining qualitative and quantitative constraints in temporal reasoning, Artificial Intelligence, num. 87 (1996) 343--385.

....used. The STP framework only takes into account conjunctions (sets) of distances [9] and can be used to model precise or imprecise temporal locations (dates) durations, delays between points, and different forms of qualitative temporal constraints between time points and or time intervals (see [13, 5]) The STP framework has very nice computational properties: correct and complete propagation of the constraints (e.g. for consistency checking) can be performed in cubic time, and can give as output the minimal network of the constraints (i.e. the minimal constraints between each pair of ....

I. Meiri. Combining qualitative and quantitative constraints in temporal reasoning. In Proceedings of the National Conference on Artificial Intelligence, pages 260--267, 1991.

.... whether an expression is a tautology, denoted j= is PSPACE complete [11] Expressions of this form occur in many areas of mathematics and computer science, some examples are logical formalisms for time, actions, events, and persistence [19, 6, 12, 3] reasoning with temporal constraints [16], and planning and scheduling [2, 9] However, there are very few tools for performing quanti er elimination and validity checking for this logic e ciently; the primary focus has been on tools for either more expressive theories such as integers or reals with addition and order (e.g. Omega ....

Itay Meiri. Combining qualitative and quantitative constraints in temporal reasoning. Articial Intelligence, 87(12):343385, 1996.

.... 1988] quantitative indeterminacy [Dyreson and Snodgrass, 1993] lower and upper bounds on an interval [Gadia et al. 1992] Artificial intelligence: 13 basic kinds of relationships between intervals, algebra of relationships [Allen, 1983] disjunctive information metric information [Meiri, 1991], Kautz and Ladkin, 1991] Example: I1 before, after I2 equivalent to Iz I v I I The qualitative part of these can be recast using Koubarakis approach. Functional Dependencies and Normal Forms Constraint Dependencies Temporal Integrity Constraints in Relational DBs l,mporal ....

Meiri, I. (1991). Combining Qualitative and Quantitative Constraints in Temporal Reasoning. In National Conference on Artificial Intelligence.

....I Introduction Research on temporal reasoning has produced many different temporal reasoning systems. These systems differ in expressive power and in computational complexity. While the theoretical complexity of these techniques has been explored in depth (e,g, Vilain et al. 1990] [Meiri, 1991]) there has been no systematic study of their actual performance. This is especially important since it is the behavior of these systems in practice that determine their usefulness in actual implementations. In this paper, we evaluate six different temporal reasoning systems on a range of ....

I. Meiri, "Combining qualitative and quantitative constraints in tem- poralreasoning," In Proceedings of the Ninth National Conference on Artificial Intlligence (AAAI-91), pages 260-267, 12-19 July 1991.

....points) the point interval algebra [33] for expressing relations between time points and intervals) and the famous Allen s algebra [1] for expressing relations between time intervals. This algebra has proven to be useful and convenient and it has also become the kernel of some other formalisms [3, 21] . Due to computational hardness (the basic satis ability problem in Allen s algebra is NP complete [34] it is unlikely that ecient algorithms exists for reasoning in the full algebra. The computational diculty has motivated the search for e ective heuristics, e.g. 17, 22, 32] and the study of ....

Itay Meiri. Combining qualitative and quantitative constraints in temporal reasoning. Articial Intelligence, 87(1-2):343-385, 1996.

.... and Van Hentenryck s algorithm for a successor to CHIP [5] and on identifying the trade offs between representational adequacy and computational complexity, e.g. Meiri s clarification of the effort required to answer consistency questions for classes of temporal reasoning problems [13]. Another interesting follow on result was that although arc consistency is achievable in linear sequential time there is apparently no polylogarithmic time parallel algorithm in the general case: it is log space complete for P [9] and, hence, unlikely to be in NC. There are, though, ....

Meiri, I. Combining qualitative and quantitative constraints in temporal reasoning. In Proc. 9th National Conference on Artificial Intelligence (1991), pp. 260--267.

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Meiri, I.: Combining Qualitative and Quantitative Constraints in Temporal Reasoning. Artificial Intelligence 87 (1996) 343--385

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Meiri, I. (1995): "Combining qualitative and quantitative constraints in temporal reasoning." Artificial Intelligence 87: 343 - 385.

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I. Meiri, Combining qualitative and quantitative constraints in temporal reasoning, Artificial Intelligence 87 (1996), 343--385.

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Itay Meiri. Combining Qualitative and Quantitative Constraints in Temporal Reasoning. In Proceedings of the 9 National Conference on Artificial Intelligence, July, AAAI Press / The MIT Press, 1991.

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I. Meiri, `Combining qualitative and quantitative constraints in temporal reasoning ', Artificial Intelligence, 87, 343--385, (1996).

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I. Meiri. Combining qualitative and quantitative constraints in temporal reasoning. Artificial Intelligence, 87:343--385, 1996.

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Meiri I.: Combining qualitative and quantitative constraints in temporal reasoning. Artificial Intelligence 87 (1996) 343-385

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I. Meiri, `Combining qualitative and quantitative constraints in temporal reasoning', Artificial Intelligence, 87, 343--385, (1996).

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I. Meiri, Combining Qualitative and Quantitative Constraints in Temporal Reasoning, AAAI 91, pp 260-267.

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Meiri, I., Combining Qualitative and Quantitative Constraints in Temporal Reasoning, Proceedings of AAAI-91, the 9th National Conference on AI, AAAI Press 1991, pp260--267.

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Meiri I., Combining qualitative and quantitative constraints in temporal reasoning, Arti - cial Intelligence, 87(1-2):343-385, 1996.

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