On the Logical Content of Knowledge Bases

Standard epistemic logics introduce a modal operator K to represent knowledge, but in doing so they presuppose the logical apparatus they aim to explain. By contrast, this paper explores how logic may be derived from the structure of knowledge itself. We begin from a pre-logical notion of a knowledge base understood as a network of inferential connections between atomic propositions. Logical constants are then defined in terms of what is supported by such a base: intrinsically, by relations that hold within it, and extrinsically, by the behaviour of those relations under extension. This yields a general semantic framework in which familiar systems (classical, intuitionistic, and various intermediate logics) arise naturally from different assumptions about the form of knowledge. This offers a reversal of the traditional explanatory order: rather than treating logic as a precondition for the articulation of knowledge, it shows how logical structure can emerge from epistemic organisation.