A New Approach to Epistemic Logic

A new language for epistemic logic is introduced in which the epistemic operators are of the form | x : x_1 ...x_n | with the intended reading ``x knows of x_1 ... x_n that ...''. Analogously we can express ``t knows of t_1 ... t_n that ... '', where t, t_1 ... t_n are terms. An advantage of this approach is that we can quantify on the agents, ``every y knows of x_1 ... x_n that A'' or ``some expert knows of t_1 ... t_n that A'' can easily be expressed. The semantics we present for this language is a generalization of the transition semantics, called 'epistemic transition semantics' in which the possible worlds are states of affairs compatible with the epistemic state of some agent. A calculus is presented and shown to be complete with respect to epistemic transition semantics.