Explanatory Belief Ascription Notes and Premature Formalization

In this paper we discuss the problenl of ascribing beliefs to an agent, given partial knowledge of his beliefs. The particular kind of ascription we are interested in we call explanatory ascription, since it ascribes beliefs to an agent as a means of explaining the beliefs we already know he has. We explore two approaches to explanatory ascription. In the first, we develop a model of belief called the derivational model, in which the derivation of one belief fl'om another is made explicit. This model and its proof theory are formalized and used to solve a variation of the Wise Man Puzzle. For comparison, a second approach using a.n abductive framework and a standard modal logic of belief is developed. This approach leads to weaker conclusions than the derivational model, because closure conditions on derivations cannot be stated. On the other hand, the representational power-of the two approaches differs, the abductive system being more expressive with respect to disjunctive information about belief, and the derivationM model allowing nonmonotonic reasoning by the believer. The next section of the paper gives some background in the area of belief ascription. The third section describes the problem of explanatory ascription, and some general properties that a successful approach should have. The fourth and fifth sections develop the derivational model and its proof theory, while the sixth describes an abductive framework and compares it to the derivational approach. Finally, we discuss some extensions to the language of the derivational model.