Hyperderivations for Epistemic Logic

The existing tradition of specifying an epistemic situation by a single model covers only complete descriptions. Such descriptions require determening truth values of knowledge assertions of any nested depth, which is usually not feasible. Epistemic descriptions are often partial and cannot be adequately specified by a single model.
However, an appropriate tool for partial specifications, epistemic theory incorporated into the possible worlds environment, has been conspicuously absent. This situation can be compared with the depleted fraction of mathematical logic which considers only complete theories whereas most of the theories of interest are incomplete: arithmetic, set theory, group theory, etc.
We suggest a framework of epistemic theories, hypertheories, which fills in this void. Hypertheories and their classes of models offer a well-principled foundation for epistemic reasoning with partial information.