Introducing Justification into Epistemic Logic

Plato's tripartite definition of knowledge as justified true belief (JTB) is generally regarded as a set of necessary conditions for the possession of knowledge. The true belief components the JTB definition are represented in formal epistemology by modal logic and its possible worlds semantics. At the same time, the justification component of Plato's definition did not have a formal representation. This paper introduces the notion of justification into formal epistemology. Epistemic logic with justification, along with the usual knowledge operator □F (F is known), contains assertions t:F (t is a justification for F). We study two basic systems, S4LP and S4LPN, of epistemic logic with justification and show completeness with respect to natural epistemic semantics, which augments Kripke models with a natural Fitting-style treatment of justification assertions t:F. Some new specific properties of epistemic logic with justification are established.