An Epistemic Logic with Quantification over Names

A sentential theory of attitudes holds that propositions (the things that agents believe and know) are sentences of a representation language. The idea has an obvious appeal to AI workers, who rely heavily on representation languages. Moore and Hendrix (1982) gave the classic statement of the case for a sentential theory of attitudes. Haas (1986), Perlis (1988), and Morgenstern (1987) among the authors who have developed sentential theories and applied them to problems in AI. Konolige (1986) proposed a resolution theorem proving algorithm for his version of the sentential theory, and he proved that this algorithm was sound and complete. This is the only known technique for reasoning efficiently in a sentential theory of attitudes. Not surprisingly, he had to limit the expressive power of his logic in order to achieve efficiency. I will criticize his treatment of one problem: quantification into the scope of attitudes. I will argue that in this area Konolige’s logic is clearly too weak. In the next section I will sketch a new logic that overcomes the limitations of Konolige’s system. Quantification into the scope of attitudes is a difficult problem for any theory of attitudes. The problem arises when a quantifier stands outside the scope of an attirude operator, and binds a variable that appears inside the scope of that operator. Suppose John knows who the president of IBM is. We might try to represent this information as follows.