How does epistemic logic represent the claim that a person knows something?

In epistemic logic, the claim that a person knows something is represented using a formal symbolic notation. The basic construction, "P knows that A," is expressed as $K_{P}A$, where $P$ represents the person and $A$ represents the proposition being known.1

The semantic foundation for this representation relies on the concept of "possible worlds." A person $P$ knows that $A$ if and only if $A$ is true in all of $P$’s "epistemic alternatives"—the set of possible worlds that are compatible with what that person knows. By knowing $A$, the individual is effectively entitled to disregard any scenarios in which $A$ is not true.1

This framework allows for more complex constructions:
* Knowledge of alternatives: "P knows whether A or B" is represented as $(K_{P}A\vee K_{P}B)$.1
* Wh-constructions: "P knows who satisfies condition A[x]" is expressed as $(\exists x)K_{P}A[x]$.1

Because epistemic logic is a form of intensional logic, it accounts for the fact that standard inferences—such as the substitutivity of identity—do not always hold unless the person specifically knows the identities involved.1