This paper describes new algorithms for processing quantitative and qualitative Temporal Constraint Satisfaction Problems (TCSP). In contrast to discrete Constraint Satisfaction Problems (CSP), enforcing path-consistency on quantitative TCSP is exponential, due to the fragmentation problem. Identifying the fragmentation problem allows us to design several e cient polynomial algorithms that are e ective for detecting inconsistencies and explicating some implicit constraints. We discuss the tradeo s between their e ectiveness and e ciency both theoretically and empirically.

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Temporal Constraint Satisfaction is an informationtechnology useful for representing and answering queries abouttemporal occurrences and temporal relations between them. Informationis represented as a Constraint Satisfaction Problem (CSP) wherevariables denote event times and constraints represent the possibletemporal relations between them. The main tasks are two: (i)deciding consistency, and (ii) answering queries about scenariosthat satisfy all constraints. This paper overviews resultson several classes of Temporal CSPs: qualitative interval, qualitative point, metric point, and some of their combinations. Research has progressed along three lines: (i) identifyingtractable subclasses, (ii) developing exact search algorithms,and (iii) developing polynomial-time approximation algorithms. Most available techniques are based on two principles: (i)enforcing local consistency (e.g. path-consistency) and (ii)enhancing naive backtracking search.

In this work we consider using logic programs to perform temporal reasoning. We identify some difficulties of combining constraint propagation and generalized resolution when temporal information is represented using tokens. We show that standard top-down evaluation (i.e. resolution) is incomplete due to the inability to unify constraints and ground terms. We present some syntactic restrictions that enable temporal resolution. Under these restrictions, we propose a new unification method composed of constraint unification and token fusion algorithms. Incorporating them within a generalized resolution scheme render it complete.

Describes new algorithms for processing quantitative temporal constraint satisfaction problems (TCSPs). In contrast to discrete CSPs, enforcing path consistency on TCSPs is exponential due to the fragmentation problem. We present an efficient polynomial constraint propagation algorithm, called “loose-path consistency” (LPC), which is shown to improve the performance of backtrack search algorithms by orders of magnitude. The tradeoffs between the effectiveness and efficiency of LPC are analyzed. We report the presence of a phase transition on this domain and perform an empirical evaluation on problems which lie in the transition region

Time is fundamental in representing and reasoning about changing domains. A proper temporal representation requires characterizing two notions: (1) time itself, and (2) temporal incidence, i.e. the domain-independent properties for the truth-value of fluents and events throughout time. There are some problematic issues, such as the expression of instantaneous events and instantaneous holding of fluents, the specification of the properties for the temporal holding of fluents, and the "dividing instant problem". This paper presents a theory of time and temporal incidence which is more natural than its predecessors and satisfactorily addresses the issues above. Our theory of time, called /spl Iscr//spl Pscr/ (Instants and Periods), is based on having instants and periods at equal levels. We define a theory of temporal incidence upon it, whose main original feature is the distinction between continuous and discrete fluents.

Combines logic programming and temporal constraint processing techniques in a language called TCLP (Temporal Constraint Logic Programming), which augments logic programs with temporal constraints. Known algorithms for processing disjunctions in temporal constraint networks are applied. We identify a decidable fragment called Simple TCLP, which can be viewed as extending Datalog with limited functions to accommodate intervals of occurrence and temporal constraints between them. Some of the restrictions introduced by Simple TCLP are overcome by a syntactic structure which provides it with the benefits of reification. The latter allows quantification on temporal occurrences and relation symbols.

Recent work in knowledge compilation suggests that relations which can be described precisely by either Horn theories or tree constraint networks are identi able in output polynomial time. Algorithms for computing approximations using these languages were also proposed. Upon testing such approximations on arti cially generated and real life data, it was immediately observed that they yield numerous super uous models. As a result, although certain entailment queries can be answered reliably, these methods may be ine ective for a large class of membership queries. To improve the approximation quality, we investigate here the k-decomposition problem, that is, determining whether a relation can be described by a disjunction of k tractable theories. The paper discusses the complexity of this task, outlines several algorithms for computing both exact and approximate k-decompositions, and evaluates the potential of this approach empirically. We focus on the class of tree constraint networks and Horn theories and report results on arti cially generated relations and on three real life cases. Our experiments show that for uniform random relations, the quality of upper bound approximations improves as k increases. However, when we require very high accuracy, decomposition is not e ective since k grows linearly with the size of the data. When the data comes from a near-tractable source, the approach is useful. Experiments show that for the King Rook King problem the generalizing power of such methods is comparable to that of recently developed learning algorithms.

Path-consistency algorithms, which are polynomial for discrete problems, are exponential when applied to problems involving quantitative temporal information. The source of complexity stems from specifying relationships between pairs of time points as disjunction of intervals. We propose a polynomial algorithm, called ULT, that approximates path-consistency in Temporal Constraint Satisfaction Problems (TCSPs). We compare ULT empirically to path-consistency and directional path-consistency algorithms. When used as a preprocessing to backtracking, ULT is shown to be 10 times more effective then either DPC or PC-2.

The criticism on the usage of Bayesian Networks in expert systems was centered around the claim that the use of probability requires a massive amount of data in the form of conditional probabilities. This paper shows that given information easily obtained from experts, the dependence model and some observations, the conditional probabilities can be estimated using backpropagation, such that during training the Bayesian characteristic of the network is preserved. Applying the Occam's razor principal results in defining a partial order among neural network structures. Experiments show that for the Multiplexer problem, the network compiled from the more succinct causal model generalized better than the one compiled from the less succinct model.

Path-consistency algorithms, which are polynomial for discrete problems, are exponential when applied to problems involving quantitative temporal information. The source of complexity stems from specifying rela- tionships between pairs of time points as disjunction of intervals. We propose a polynomial algorithm, called ULT, that approximates path-consistency in Temporal Constraint Satisfaction Problems (TCSPs). We com- pare ULT empirically to path-consistency and direc- tional path-consistency algorithms. When used as a preprocessing to backtracking, ULT is shown to be 10 times more effective then either DPC or PC-2.