Complete Axiomatizations of Finite Syntactic Epistemic States

An agent who bases his actions upon explicit logical formulae has at any given point in time a finite set of formulae he has computed. Closure or consistency conditions on this set cannot in general be assumed – reasoning takes time and real agents frequently have contradictory beliefs. This paper discusses a formal model of knowledge as explicitly computed sets of formulae. It is assumed that agents represent their knowledge syntactically, and that they can only know finitely many formulae at a given time. In order to express interesting properties of such finite syntactic epistemic states, we extend the standard epistemic language with an operator expressing that an agent knows at most a particular finite set of formulae, and investigate axiomatization of the resulting logic. This syntactic operator has also been studied elsewhere without the assumption about finite epistemic states [5]. A strongly complete logic is impossible, and the main results are non-trivial characteriza...

• Type: Conference
• Year: 2005
• Where: DALT
• Authors: Thomas Ågotnes, Michal Walicki
• Keywords: DALT 2005, Epistemic States, Formulae, finite Sets