A New Approach to Epistemic Logic

Abstract

A new language for epistemic logic is introduced in which the epistemic “x knows of $x_{1}\ldots x_{n}$ that …”.

$$\displaystyle{``x\text{ knows of }x_{1}\ldots x_{n}\text{that \ldots}".}$$

Analogously we can express “t knows of $t_{1}\ldots t_{n}$ that …”, where $t,t_{1}\ldots t_{n}$ are terms. An advantage of this approach is that we can quantify on the agents, “every y knows of $x_{1}\ldots x_{n}$ that A” or “some expert knows of $t_{1}\ldots t_{n}$ 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.