Mathematical Logic of Justification

Since Plato, the notion of justification has been an essential component of epistemic studies. However, until recently, the notion of justification has been conspicuously absent from mathematical models of knowledge within the epistemic logic framework. Commencing from seminal works by von Wright and Hintikka, the notions of Knowledge and Belief have acquired formalization by means of modal logic with modals ‘F is known’ and ‘F is believed.’ Within this approach, the following analysis was adopted: For a given agent, F is known ~ F holds in all epistemically possible situations. The deficiency of this approach is displayed most prominently, in the Logical Omniscience feature of the modal logic of knowledge.

Justification Logic had been anticipated by Goedel as the logic of explicit mathematical proofs and has been first developed as the Logic of Proofs. It introduces a mathematical notion of justification, making epistemic logic more expressive. We now have the capacity to reason about justifications, simple and compound. We can compare different pieces of evidence pertaining to the same fact. We can measure the complexity of justifications, which leads to a coherent theory of logical omniscience. Justification Logic provides a novel mechanism of evidence-tracking which seems to be a key ingredient in the analysis of knowledge. Finally, Justification Logic furnishes a new, evidence-based foundation for the logic of knowledge, according to which F is known ~ F has an adequate justification.