Modal Epistemic and Doxastic Logic

Abstract

Knowledge has always been a topic central to philosophy (cf. e.g. [Glymour, 1992]). Since ancient times philosophers have been interested in the way knowledge comes to us and in what way it relates to reality, the world in which we live. As is the case with so many things, during this century also the topic of knowledge has become the subject of formal investigations. Questions arose such as what the logical properties of knowledge are, and in order to come up with answers to these, logics have been devised to study these questions in a formal setting. These logics are now generally called ‘epistemic logics’, i.e., logics pertaining to ‘knowledge’. Mostly, also the notion of ‘belief, which is sometimes thought of as a weaker form of knowledge (but this is debated among philosophers (cf. [Gettier, 1963; Pollock, 1986; Voorbraak, 1993]) is considered, and we will also incorporate this notion in our treatment. Sometimes logics of belief are referred to with the special term ‘doxastic logics’, but we will just use the term ‘epistemic logic(s)’ for logics of knowledge and belief. Jaakko Hintikka [1962] was the first who proposed a modal logic approach to knowledge and belief. We follow the tradition of most recent treatments of modal logics, including those of knowledge and belief, by adopting possible world semantics in the style of Kripke [1963].