Syntactical treatments of propositional attitudes

Abstract

Syntactical treatments of propositional attitudes are attractive to artificial intelligence researchers. But results of Montague (1974) and Thomason (1980) seem to show that syntactical treatments are not viable. They show that if representation languages are sufficiently expressive, then axiom schemes characterizing knowledge and belief give rise to paradox. Des Rivières and Levesque (1988) characterize a class of sentences within which these schemes can safely be instantiated. These sentences do not quantify over the propositional objects of knowledge and belief. We argue that their solution is incomplete, and extend it by characterizing a more inclusive class of sentences over which the axiom schemes can safely range. Our sentences do quantify over propositional objects.