1 FINDING OUT = ACHIEVING DECIDABILITY Manny Rayner and Sverker Janson Swedish Institute of Computer Science Box 1263, S-164 28 KISTA, Sweden manny@sics.se, sverker@sics.se ABSTRACT We present a framework for reasoning about the concepts of "knowing what" and "finding out", in which the key concept is to identify "finding out the answer to question Q" with "achieving a situation in which Q is decidable". We give examples of how the framework can be used to formulate non-trivial problems involving the construction of plans to acquire and use information, and go on to demonstrate that these problems can often be solved by systematic application of a small set of goal-directed backward-chain- ing rules. In conclusion, it is suggested that systems of this kind are potentially imple- mentable in λ-Prolog, a logic programming language based on higher-order logic. 1. INTRODUCTION The goal of this paper is to construct a framework which will allow us to describe prob- lems which involve acquisition and use of knowledge. The first, and most immediate, demand that we will make on this formalism is that it should be well-defined, that is to say possessed of a clear formal semantics; the second is that it should, at least in many of the cases where this seems intuitively reasonable, be able to support efficient goal- directed reasoning about these concepts. Before we go any further, however, we will pause a moment to give an example of the kind of thing we want to achieve. At this stage, we will present the problem informally: later in the paper, we will demonstrate how to describe and solve it in terms of the formalism we will be proposing. Problem 1: finding a squash racket I want a squash racket. I know Keith has one, and I know that he knows where it is. I can find out where it is if I can ask him. I can do this if I can find out where he is. I don't know where he is, but I know that his secretary does, at least during office hours. I can ring his secretary and ask her if I know her number, which I do during office hours. Merely from the way the problem is described, it is obvious to a human that a simple solution exists. We can reason backwards from the initial goal "find out where Keith's racket is", producing a goal-tree like the one in diagram 1: what we are trying to do, then, is to justify this kind of reasoning in formal terms. The basic notions we will use have already been described by us in an earlier paper [Rayner & Janson 88], and are closely related to Levesque's work on incomplete databases [Levesque 81, 84]. To summarize, we follow Levesque in extending first-order