Belief, Awareness, and Two-Dimensional Logic

Belief has been formally modelled using doxastic logics in recent decades. The possible worlds model provides an intuitive semantics for these log­ ics. But it also commits us to the problem of logical omniscience. A number of logics have been intro­ duced to circumvent the problem. Of particular in­ terest is the logic of awareness. In this paper we present a new method to put awareness into doxastic logic so as to get a flexible way to model actual belief. The underlying logics are two-dimensional logics. Two two-dimensional doxastic logics are given. In the first logic, a quite limited concept of actual belief is presented. In the second logic, twodimensional and classical semantics are combined into a hybrid system.