The problem of representing temporal knowledge arises in many areas of computer science. In applications in which such knowledge is imprecise or relative, current representations based on date lines or time instants are inadequate. An interval-based temporal logic is introduced, together WiUl a computationally effective reasoning algorithm based on constraint- propagation. This system is notable in offering a delicate balance between expressive power and the efficiency of its deductive engine. A notion of reference intervals is introduced which captures the temporal hierarchy implicit in many domains, and which can be used to precisely control the amount of deduction performed automatically by the system. Examples.are provided for a data base containing historical data, a d<lta base. used for modeling processes and process interaction, and a data base for an interactive system where the present moment is continually being updated.

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Belief networks are directed acyclic graphs in which the nodes represent propositions (or variables), the arcs signify direct dependencies between the linked propositions, and the strengths of these dependencies are quantified by conditional probabilities. A network of this sort can be used to represent the generic knowledge of a domain expert, and it turns into a computational architecture if the links are used not merely for storing factual knowledge but also for directing and activating the data flow in the computations which manipulate this knowledge. The first part of the paper deals with the task of fusing and propagating the impacts of new information through the networks in such a way that, when equilibrium is reached, each proposition will be assigned a measure of belief consistent with the axioms of probability theory. It is shown that if the network is singly connected (e.g. tree-structured), then probabilities can be updated by local propagation in an isomorphic network of parallel and autonomous processors and that the impact of new information can be imparted to all propositions in time proportional to the longest path in the network. The second part of the paper deals with the problem of finding a tree-structured representation for a collection of probabilistically coupled propositions using auxiliary (dummy) variables, colloquially called "hidden causes. " It is shown that if such a tree-structured representation exists, then it is possible to uniquely uncover the topology of the tree by observing pairwise dependencies among the available propositions (i.e., the leaves of the tree). The entire tree structure, including the strengths of all internal relationships, can be reconstructed in time proportional to n log n, where n is the number of leaves.

Abstract: This paper revises and expands upon a paper presented by two of the present authors at AAAI 1986 [Vilain & Kautz 1986]. As with the original, this revised document considers computational aspects of intervalbased and point-based temporal representations. Computing the consequences of temporal assertions is shown to be computationally intractable in the interval-based representation, but not in the point-based one. However, a fragment of the interval language can be expressed using the point language and benefits from the tractability of the latter. The present paper departs from the original primarily in correcting claims made there about the point algebra, and in presenting some closely related results of van Beek [1989]. The representation of time has been a recurring concern of Artificial Intelligence researchers. Many representation schemes have been proposed for temporal reasoning; of these, one of the most attractive is James Allen's algebra of temporal intervals [Allen 1983]. This representation scheme is particularly appealing for its simplicity and for its ease of implementation with constraint propagation algorithms. Reasoners based on

problem (csp), namely, naive backtracking (BT), backjumping (BJ), conflict-directed backjumping

In order to deal with over-constrained Constraint Satisfaction Problems, various extensions of the CSP framework have been considered by taking into account costs, uncertainties, preferences, priorities...Each extension uses a specific mathematical operator (+, max...) to aggregate constraint violations. In this paper, we consider a simple algebraic framework, related to Partial Constraint Satisfaction, which subsumes most of these proposals and use it to characterize existing proposals in terms of rationality and computational complexity. We exhibit simple relationships between these proposals, try to

Bucket elimination is an algorithmic framework that generalizes dynamic programming to accommodate many problem-solving and reasoning tasks. Algorithms such as directional-resolution for propositional satisfiability, adaptive-consistency for constraint satisfaction, Fourier and Gaussian elimination for solving linear equalities and inequalities, and dynamic programming for combinatorial optimization, can all be accommodated within the bucket elimination framework. Many probabilistic inference tasks can likewise be expressed as bucket-elimination algorithms. These include: belief updating, finding the most probable explanation, and expected utility maximization. These algorithms share the same performance guarantees; all are time and space exponential in the inducedwidth of the problem's interaction graph. While elimination strategies have extensive demands on memory, a contrasting class of algorithms called "conditioning search" require only linear space. Algorithms in this class split a problem into subproblems by instantiating a subset of variables, called a conditioning set, or a cutset. Typical examples of conditioning search algorithms are: backtracking (in constraint satisfaction), and branch and bound (for combinatorial optimization). The paper presents the bucket-elimination framework as a unifying theme across probabilistic and deterministic reasoning tasks and show how conditioning search can be augmented to systematically trade space for time.

Introduction 1.1 Preliminaries Constraint programming is an alternative approach to programming in which the programming process is limited to a generation of requirements (constraints) and a solution of these requirements by means of general or domain specific methods. The general methods are usually concerned with techniques of reducing the search space and with specific search methods. In contrast, the domain specific methods are usually provided in the form of special purpose algorithms or specialised packages, usually called constraint solvers. Typical examples of constraint solvers are: ffl a program that solves systems of linear equations, ffl a package for linear programming, ffl an implementation of the unification algorithm, a cornerstone of automated theorem proving. Problems that can be solved in a natural way by means of constraint programming are usually those for which efficient algorithms are

... quickly across a wide range of hard SAT problems than any other SAT tester in the literature on comparable platforms. On a Sun SPARCStation 10 running SunOS 4.1.3 U1, POSIT can solve hard random 400-variable 3-SAT problems in about 2 hours on the average. In general, it can solve hard n-variable random 3-SAT problems with search trees of size O(2 n=18:7 ). In addition to justifying these claims, this dissertation describes the most significant achievements of other researchers in this area, and discusses all of the widely known general techniques for speeding up SAT search algorithms. It should be useful to anyone interested in NP-complete problems or combinatorial optimization in general, and it should be particularly useful to researchers in either Artificial Intelligence or Operations Research.

We compare tractable classes of constraint satisfaction problems (CSPs). We first give a uniform presentation of the major structural CSP decomposition methods. We then introduce a new class of tractable CSPs based on the concept of hypertree decomposition recently developed in Database Theory. We introduce a framework for comparing parametric decomposition-based methods according to tractability criteria and compare the most relevant methods. We show that the method of hypertree decomposition dominates the others in the case of general (nonbinary) CSPs.