Subjective Logic: A Formalism of Reasoning Under Uncertainty

Abstract

Subjective logic is a type of probabilistic logic that allows probability values to be ex- pressed with degrees of uncertainty. Probabilistic logic combines the strengths of logic and probability calculus, meaning that it has binary logics capacity to express struc- tured argument models, and it has the power of probabilities to express degrees of truth of those arguments. Subjective logic makes it possible to express uncertainty about the probability values themselves, meaning that it is possible to reason with argument models in presence of uncertain or partially incomplete evidence. This manuscript de- scribes the central elements of subjective logic. More specifically, it first describes a set of equivalent representations of uncertain probabilities with their interpretations. It then describes the most important subjective logic operators. Finally, it describes how subjective logic can be applied in trust modelling and for analysing Bayesian networks. Subjective logic is directly compatible with binary logic, probability calculus and clas- sical probabilistic logic. The advantage of using subjective logic is that real world situations can be more realistically modelled, and that conclusions more correctly re- flect the ignorance and uncertainties that accompany the input arguments.