Learning to Assign Degrees of Belief in Relational Domains

Abstract

As uncertainty pervades the real world, it seems obvious that the decisions we make, the conclusions we reach, and the explanations we offer are usually based on our judgements of the probability of uncertain events such as success in a new medical treatment or the state of the market. For example, if an agent wishes to employ the expected-utility paradigm of decision theory in order to guide its actions, it must assign subjective probabilities to various assertions. Less obvious, however, is the question of how to elicit such degrees of beliefs.

The standard knowledge representation approach claims that the agent starts its life-cycle by acquiring a pool of knowledge expressing several constraints about its environment, such as properties of objects and relationships among them. This information is stored in some knowledge base using a logical representation language [1,4,8] or a graphical representation language [3,9,11]. After this period of knowledge preparation, the agent is expected to achieve optimal performance by evaluating any query with perfect accuracy. Indeed, according to the well-defined semantics of the representation language, a knowledge base provides a compact representation of a probability measure that can be used to evaluate queries. For example, if we select first-order logic as our representation language, the probability measure is induced by assigning equal likelihood to all models of the knowledge base; the degree of belief of any given query is thus the fraction of those models which are consistent with the query.