This paper presents a simple framework for Horn-clause abduction, with probabilities associated with hypotheses. The framework incorporates assumptions about the rule base and independence assumptions amongst hypotheses. It is shown how any probabilistic knowledge representable in a discrete Bayesian belief network can be represented in this framework. The main contribution is in finding a relationship between logical and probabilistic notions of evidential reasoning. This provides a useful representation language in its own right, providing a compromise between heuristic and epistemic adequacy. It also shows how Bayesian networks can be extended beyond a propositional language. This paper also shows how a language with only (unconditionally) independent hypotheses can represent any probabilistic knowledge, and argues that it is better to invent new hypotheses to explain dependence rather than having to worry about dependence in the language. Scholar, Canadian Institute for Advanced...

Bayesian networks provide a modeling language and associated inference algorithm for stochastic domains. They have been successfully applied in a variety of medium-scale applications. However, when faced with a large complex domain, the task of modeling using Bayesian networks begins to resemble the task of programming using logical circuits. In this paper, we describe an object-oriented Bayesian network (OOBN) language, which allows complex domains to be described in terms of inter-related objects. We use a Bayesian network fragment to describe the probabilistic relations between the attributes of an object. These attributes can themselves be objects, providing a natural framework for encoding part-of hierarchies. Classes are used to provide a reusable probabilistic model which can be applied to multiple similar objects. Classes also support inheritance of model fragments from a class to a subclass, allowing the common aspects of related classes to be defined only once. Our language h...

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...

Knowledge representation languages invariably reflect a trade-off between expressivity and tractability. Evidence suggests that the compromise chosen by description logics is a particularly successful one. However, description logic (as for all variants of first-order logic) is severely limited in its ability to express uncertainty. In this paper, we present P-CLASSIC, a probabilistic version of the description logic CLASSIC. In addition to terminological knowledge, the language utilizes Bayesian networks to express uncertainty about the basic properties of an individual, the number of fillers for its roles, and the properties of these fillers. We provide a semantics for P-CLASSIC and an effective inference procedure for probabilistic subsumption: computing the probability that a random individual in class C is also in class D. The effectiveness of the algorithm relies on independenceassumptions and on our ability to execute lifted inference: reasoning about similar individuals as a gr...

We define a language for representing context-sensitive probabilistic knowledge. A knowledge base consists of a set of universally quantified probability sentences that include context constraints, which allow inference to be focused on only the relevant portions of the probabilistic knowledge. We provide a declarative semantics for our language. We present a query answering procedure which takes a query Q and a set of evidence E and constructs a Bayesian network to compute P (QjE). The posterior probability is then computed using any of a number of Bayesian network inference algorithms. We use the declarative semantics to prove the query procedure sound and complete. We use concepts from logic programming to justify our approach. Keywords: reasoning under uncertainty, Bayesian networks, Probability model construction, logic programming Submitted to Theoretical Computer Science special issue on Uncertainty in Databases and Deductive Systems. This work was partially supported by NSF g...

We define the probabilistic planning problem in terms of a probability distribution over initial world states, a boolean combination of goal propositions, a probability threshold, and actions whose effects depend on the execution-time state of the world and on random chance. Adopting a probabilistic model complicates the definition of plan success: instead of demanding a plan that provably achieves the goal, we seek plans whose probability of success exceeds the threshold. This paper describes a probabilistic semantics for planning under uncertainty, and presents a fully implemented algorithm that generates plans that succeed with probability no less than a user-supplied probability threshold. The algorithm is sound (if it terminates then the generated plan is sufficiently likely to achieve the goal) and complete (the algorithm will generate a solution if one exists).

We propose a logical/mathematical framework for statistical parameter learning of parameterized logic programs, i.e. de nite clause programs containing probabilistic facts with a parameterized distribution. It extends the traditional least Herbrand model semantics in logic programming to distribution semantics, possible world semantics with a probability distribution which is unconditionally applicable to arbitrary logic programs including ones for HMMs, PCFGs and Bayesian networks. We also propose a new EM algorithm, the graphical EM algorithm, thatrunsfora class of parameterized logic programs representing sequential decision processes where each decision is exclusive and independent. It runs on a new data structure called support graphs describing the logical relationship between observations and their explanations, and learns parameters by computing inside and outside probability generalized for logic programs. The complexity analysis shows that when combined with OLDT search for all explanations for observations, the graphical EM algorithm, despite its generality, has the same time complexity as existing EM algorithms, i.e. the Baum-Welch algorithm for HMMs, the Inside-Outside algorithm for PCFGs, and the one for singly connected Bayesian networks that have beendeveloped independently in each research eld. Learning experiments with PCFGs using two corpora of moderate size indicate that the graphical EM algorithm can signi cantly outperform the Inside-Outside algorithm. 1.

To coordinate with other agents in its environment, an agent needs models of what the other agents are trying to do. When communication is impossible or expensive, this information must be acquired indirectly via plan recognition. Typical approaches to plan recognition start with a specification of the possible plans the other agents may be following, and develop special techniques for discriminating among the possibilities. Perhaps more desirable would be a uniform procedure for mapping plans to general structures supporting inference based on uncertain and incomplete observations. In this paper, we describe a set of methods for converting plans represented in a flexible procedural language to observation models represented as probabilistic belief networks. 1 Introduction Decisions about what to do should be based on knowledge of the current situation and expectations about possible future actions and events. Anticipating the actions that others might take requires models of their de...

Most probabilistic inference algorithms are specified and processed on a propositional level. In the last decade, many proposals for algorithms accepting first-order specifications have been presented, but in the inference stage they still operate on a mostly propositional representation level. [Poole, 2003] presented a method to perform inference directly on the first-order level, but this method is limited to special cases. In this paper we present the first exact inference algorithm that operates directly on a first-order level, and that can be applied to any first-order model (specified in a language that generalizes undirected graphical models). Our experiments show superior performance in comparison with propositional exact inference. 1

This paper will focus exclusively on the problem solving activity. The other activities are described in Martin and VanLehn (1993, in press). This section describes OLAE's input (student behavior) and output (assessment presentation), and the way that OLAE uses the behavioral data to calculate the assessments