On Perfect Introspection with Quantifying-In1

Abstract

Agents with perfect introspection may have incomplete beliefs about the world, but they possess complete knowledge about their own beliefs. This fact suggests that the beliefs of introspective agents should be completely determined by their objective beliefs, that is, those beliefs that are only about the domain in question and not about other beliefs. Introspection and logical reasoning alone should suffice to reconstruct all other beliefs from the objective ones. While this property has been shown to hold for propositional belief logics, there have so far only been negative results in the case of first-order belief logics with quantifying-in. In this paper we present a logic of belier with quantifying-in, where the beliefs of a perfectly introspective agent are indeed uniquely determined by the objective beliefs. The result is obtained by weakening the notion of belief of an existing logic that does not have this property.