Inspired by game theory representations, Bayesian networks, influence diagrams, structured Markov decision process models, logic programming, and work in dynamical systems, the independent choice logic (ICL) is a semantic framework that allows for independent choices (made by various agents, including nature) and a logic program that gives the consequence of choices. This representation can be used as a specification for agents that act in a world, make observations of that world and have memory, as well as a modelling tool for dynamic environments with uncertainty. The rules specify the consequences of an action, what can be sensed and the utility of outcomes. This paper presents a possible-worlds semantics for ICL, and shows how to embed influence diagrams, structured Markov decision processes, and both the strategic (normal) form and extensive (game-tree) form of games within the Thanks to Craig Boutilier and Holger Hoos for detailed comments on this paper. This work was supporte...

Introduction The introduction of Bayesian networks (Pearl 1986b) and associated local computation algorithms (Lauritzen and Spiegelhalter 1988, Shenoy and Shafer 1990, Jensen, Lauritzen and Olesen 1990) has initiated a renewed interest for understanding causal concepts in connection with modelling complex stochastic systems. It has become clear that graphical models, in particular those based upon directed acyclic graphs, have natural causal interpretations and thus form a base for a language in which causal concepts can be discussed and analysed in precise terms. As a consequence there has been an explosion of writings, not primarily within mainstream statistical literature, concerned with the exploitation of this language to clarify and extend causal concepts. Among these we mention in particular books by Spirtes, Glymour and Scheines (1993), Shafer (1996), and Pearl (2000) as well as the collection of papers in Glymour and Cooper (1999). Very briefly, but fundamentally,

To model decision problems involving uncertainty and probability, we propose stochastic constraint programming. Stochastic constraint programs contain both decision variables (which we can set) and stochastic variables (which follow some probability distribution), and combine together the best features of traditional constraint satisfaction, stochastic integer programming, and stochastic satisfiability. We give a semantics for stochastic constraint programs, and propose a number of complete algorithms and approximation procedures. Using these algorithms, we observe phase transition behavior in stochastic constraint programs. Interestingly, the cost of both optimization and satisfaction peaks in the satisfaction phase boundary. Finally, we discuss a number of extensions of stochastic constraint programming to relax various assumptions like the independence between stochastic variables. Introduction Many real world decision problems contain uncertainty. Data about event...

This paper studies a variant of axioms originally developed by Shafer and Shenoy (1988). It is investigated which extra assumptions are needed to perform the local computations in a HUGIN-like architecture (Jensen et al. 1990) or in the architecture of Lauritzen and Spiegelhalter (1988). In particular it is shown that propagation of belief functions can be performed in these architectures. Keywords: articial intelligence, belief function, constraint propagation, expert system, probability propagation, valuation-based system. 1 Introduction An important development in articial intelligence is associated with an abstract theory of local computation known as the Shafer{Shenoy axioms (Shafer and Shenoy 1988; Shenoy and Shafer 1990). These describe in a very general setting how computations can be performed eciently and locally in a variety of problems, just if a few simple conditions are satised. Even though the axioms were developed to formalize computation with belief functions (Shaf...

this paper is to review the research about the latter.

INTRODUCTION This chapter surveys the development of graphical models known as Bayesian networks, summarizes their semantical basis and assesses their properties and applications to reasoning and planning. Bayesian networks are directed acyclic graphs (DAGs) in which the nodes represent variables of interest (e.g., the temperature of a device, the gender of a patient, a feature of an object, the occurrence of an event) and the links represent causal influences among the variables. The strength of an influence is represented by conditional probabilities that are attached to each cluster of parents-child nodes in the network. Figure 1 illustrates a simple yet typical Bayesian network. It describes the causal relationships among the season of the year (X 1 ), whether rain falls (X 2 ) during the season, whether the sprinkler is on (X 3 ) during that season, whether the pavement would get wet (X<F28.21

To model combinatorial decision problems involving uncertainty and probability, we introduce scenario based stochastic constraint programming. Stochastic constraint programs contain both decision variables, which we can set, and stochastic variables, which follow a discrete probability distribution. We provide a semantics for stochastic constraint programs based on scenario trees. Using this semantics, we can compile stochastic constraint programs down into conventional (nonstochastic) constraint programs. This allows us to exploit the full power of existing constraint solvers. We have implemented this framework for decision making under uncertainty in stochastic OPL, a language which is based on the OPL constraint modelling language [Hentenryck et al., 1999]. To illustrate the potential of this framework, we model a wide range of problems in areas as diverse as portfolio diversification, agricultural planning and production/inventory management.

This article provides a guide to source material for practitioners interested in applying decision analysis methods. Specifically, applications of decision analysis are surveyed that were published from 1990 through 1999 in major English language operations research journals and other closely related journals. In addition, references are presented for recently developed useful decision analysis methods that are not yet included in many introductory textbooks. As used in this article, decision analysis refers to a set of quantitative methods for analyzing decisions that use expected utility as the criterion for identifying the preferred alternative. The paper classifies the applications into six main areas (with sub-areas in parentheses): energy (bidding and pricing, environmental risk, product and project selection, strategy, technology choice, and miscellaneous), manufacturing and services (finance, product planning, R&D project selection, strategy, and miscellaneous), medical, military, public policy, and general. A list is also included of application articles that present significant details about methodological and implementation issues, which are classified into the areas of strategy and/or objectives generation, problem structuring/formulation, probability assessment, utility/value assessment, sensitivity analysis, co mmunication/facilitation, group issues, and implementation. Decision Analysis Applications in the Operations Research Literature,

Introduction The work reported here began with the desire to find a network architecture that shared with Boltzmann machines [6, 1, 7] the capacity to learn arbitrary probability distributions over binary vectors, but that did not require the negative phase of Boltzmann machine learning. It was hypothesized that eliminating the negative phase would improve learning performance. This goal was achieved by replacing the Boltzmann machine's symmetric connections with feedforward connections. In analogy with Boltzmann machines, the sigmoid function was used to compute the conditional probability of a unit being on from the weighted input from other units. Stochastic simulation of such a network is somewhat more complex than for a Boltzmann machine, but is still possible using local communication. Maximum likelihood, gradient-ascent learning can be done with a local Hebb-type rule.

The mathematical theory of evidence has been introduced by Glenn Shafer in 1976 as a new approach to the representation of uncertainty. This theory can be represented under several distinct but more or less equivalent forms. Probabilistic interpretations of evidence theory have their roots in Arthur Dempster's multivalued mappings of probability spaces. This leads to random set and more generally to random lter models of evidence. In this probabilistic view evidence is seen as more or less probable arguments for certain hypotheses and they can be used to support those hypotheses to certain degrees. These degrees of support are in fact the reliabilities with which the hypotheses can be derived from the evidence. Alternatively, the mathematical theory of evidence can be founded axiomatically on the notion of belief functions or on the allocation of belief masses to subsets of a frame of discernment. These approaches aim to present evidence theory as an extension of probability theory. Evidence theory has been used to represent uncertainty in expert systems, especially in the domain of diagnostics. It can be applied to decision analysis and it gives a new perspective for statistical analysis. Among its further applications are image processing, project planing and scheduling and risk analysis. The computational problems of evidence theory