Philosophical foundations of partial belief models

This paper is an attempt to put forward a new kind of partial model for representing belief states. I first introduce some philosophical motivations for working with partial models. Then, I present the standard (total) model proposed by Hintikka, and the partial models studied by Humberstone and Holliday. I then show how to reduce Hintikka's semantics in order to obtain a partial model which, however, differs from Humberstone's and Holliday's. The nature of such differences is assessed, and I provide motivations for using the newly proposed semantics rather than the existing ones. Finally, I review some promising philosophical applications of the ideas developed throughout the discussion.