We argue that rather than representing an agent's knowledge as a collection of formulas, and then doing theorem proving to see if a given formula follows from an agent's knowledge base, it may be more useful to represent this knowledge by a semantic model, and then do model checking to see if the given formula is true in that model. We discuss how to construct a model that represents an agent's knowledge in a number of different contexts, and then consider how to approach the model-checking problem.

Despite their different perspectives, artificial intelligence (AI) and the disciplines of decision science have common roots and strive for similar goals. This paper surveys the potential for addressing problems in representation, inference, knowledge engineering, and explanation within the decision-theoretic framework. Recent analyses of the restrictions of several traditional AI reasoning techniques, coupled with the development of more tractable and expressive decisiontheoretic representation and inference strategies, have stimulated renewed interest in decision theory and decision analysis. We describe early experience with simple probabilistic schemes for automated reasoning, review the dominant expert-system paradigm, and survey some recent research at the crossroads of AI and decision science. In particular, we present the belief network and influence diagram representations. Finally, we discuss issues that have not been studied in detail within the expert-systems sett...

Two or more Bayesian network structures are Markov equivalent when the corresponding acyclic digraphs encode the same set of conditional independencies. Therefore, the search space of Bayesian network structures may be organized in equivalence classes, where each of them represents a different set of conditional independencies. The collection of sets of conditional independencies obeys a partial order, the so-called “inclusion order.” This paper discusses in depth the role that the inclusion order plays in learning the structure of Bayesian networks. In particular, this role involves the way a learning algorithm traverses the search space. We introduce a condition for traversal operators, the inclusion boundary condition, which, when it is satisfied, guarantees that the search strategy can avoid local maxima. This is proved under the assumptions that the data is sampled from a probability distribution which is faithful to an acyclic digraph, and the length of the sample is unbounded. The previous discussion leads to the design of a new traversal operator and two new learning algorithms in the context of heuristic search and the Markov Chain Monte Carlo method. We carry out a set of experiments with synthetic and real-world data that show empirically the benefit of striving for the inclusion order when learning Bayesian networks from data.

This paper presents a logical formalism for representing and reasoning with statistical knowledge. One of the key features of the formalism is its ability to deal with qualitative statistical information. It is argued that statistical knowledge, especially that of a qualitative nature, is an important component of our world knowledge and that such knowledge is used in many different reasoning tasks. The work is further motivated by the observation that previous formalisms for representing probabilistic information are inadequate for representing statistical knowledge. The representation mechanism takes the form of a logic that is capable of representing a wide variety of statistical knowledge, and that possesses an intuitive formal semantics based on the simple notions of sets of objects and probabilities defined over those sets. Furthermore, a proof theory is developed and is shown to be sound and complete. The formalism offers a perspicuous and powerful representational tool for stat...

Bayesian networks originated as a framework for distributed reasoning. In singlyconnected networks, there exists an elegant inference algorithm that can be implemented in parallel having a processor for every node. It can be extended to take profit of the OR--gate, a model of interaction among causes which simplifies knowledge acquisition and evidence propagation. We also discuss two exact and one approximate methods for dealing with general networks. All these algorithms admit distributed implementations.

Data dependencies are used in database schema design to enforce the correctness of a database as well as to reduce redundant data. These dependencies are usually determined from the semantics of the attributes and are then enforced upon the relations. This paper describes a bottom-up procedure for discovering multivalued dependencies (MVDs) in observed data without knowing `a priori the relationships amongst the attributes. The proposed algorithm is an application of the technique we designed for learning conditional independencies in probabilistic reasoning. A prototype system for automated database schema design has been implemented. Experiments were carried out to demonstrate both the effectiveness and efficiency of our method. 1

Two or more Bayesian Networks are Markov equivalent when their corresponding acyclic digraphs encode the same set of conditional independence (# CI) restrictions. Therefore, the search space of Bayesian Networks may be organized in classes of equivalence, where each of them consists of a particular set of CI restrictions. The collection of sets of CI restrictions obeys a partial order, the graphical Markov model inclusion partial order, or inclusion order for short.

It follows from the known relationships among the dierent classes of graphical Markov models for conditional independence that the intersection of the classes of moral directed acyclic graph models (or decomposable {DEC models), and transitive directed acyclic graph {TDAG models (or lattice conditional independence {LCI models) is non-empty. This paper shows that the conditional independence models in the intersection can be characterized as labeled trees, where every vertex on the tree corresponds to a single random variable. This fact leads to the de nition of a speci c Markov property for trees and therefore to the introduction of trees as part of the family of graphical Markov Models.

Based on the elegant theory of relational databases, the present investigation establishes a unified model for both relational databases and Bayesian networks. This is in contradiction to the argument that relational databases and Bayesian networks are different, where it was shown that the implication problem does not coincide for embedded multivalued dependency (EMVD) and probabilistic conditional independence (CI). The main result of this thesis, however, is that the implication problem coincides on the solvable subclasses of EMVD and CI, but differs on the unsolvable general classes of EMVD and CI. This means that there is no practical difference between relational databases and Bayesian networks, since only the solvable subclasses are useful in the design of both of these knowledge systems.

This extended abstract presents a logic, called Lp, that is capable of representing and reasoning with a wide variety of both qualitative and quantitative statistical information. The advantage of this logical formalism is that it offers a declarative representation of statistical knowledge; knowledge represented in this manner can be used for a variety of