On the Logical Content of Knowledge Bases
Alexader V. Gheorghiu, Tao Gu
TL;DR
This paper argues that logic can be derived from the structure of knowledge rather than assumed a priori. By modeling knowledge as atomic systems—networks of inferential rules—the authors define intrinsic and extrinsic logical connectives that reveal how conjunction, disjunction, and negation operate both within a knowledge base and under its extensions. The base-extension semantics show that, depending on the chosen basis, the resulting logic can be classical, intuitionistic, or intermediate, recasting epistemic logic as an emergent property of epistemic organization. This reframes traditional logic as a formal articulation of knowledge dynamics and suggests directions for richer models of knowledge in AI and semantics.
Abstract
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.