A Survey of Probabilistic Reasoning in Justification Logic

Submitted by admin on Thu, 01/09/2022 - 14:30
Thomas Pipilikas
Date of Defense
Three-member Committee
Lefteris Kirousis
Ioannis Kokkinis (Co-Advisor)
Costas D. Koutras
Stathis Zachos (Co-Advisor)

In this thesis, we study the notion of justification, interpreted in a logical formalism. Specifically, we study the epistemic/doxastic interpretation of justification logic; i.e., an expansion of classical logic with formulae of the form t:F , which translate as “t is an evidence of the truth of F .”. We present the basic semantics for justification logic, along with the corresponding theorems of soundness and completeness, and analyze how each one of them perceives the notion of justification.

Moreover, we examine the notion of justification in relation to the notion of uncer­ tainty, by presenting the fundamental probabilistic justification logics. We present the corresponding semantics, accompanied with the corresponding soundness and (sort of) completeness and we investigate how each one of these perceives the uncertainty in the context of justification.

Last but not least, we define the subset models, a recent semantics for justification logic proposed and studied by E. Lehmann and T. Studer. We analyze the ontology of justification, as it is expressed in this framework, and we examine how subset models could probably combine with the notion of uncertainty, in a way that distinguishes be­ tween the suasiveness of the evidence t, the conclusiveness of evidence t over assertion F , and the certainty of F .