Conditional Inference in Subjective Logic

The interpretations of conditionals and conditional inference are often disputed. The classic logic conditional called material implication can easily be proven to be invalid, and the conditional inference rule Modus Ponens represents a tautology that becomes invalid in the face of contrary evidence from realistic scenarios. The foundations of conditionals and conditional inference seem plagued with problems and also seem unable to realistically model causal relationships in the world around us. Now introduce the concepts of ignorance and uncertainty into the framework and it seems to get even fuzzier because the traditional tools of logic or probabilistic conditional inference can no longer be applied. This paper introduces a conditional inference operator that explicitly incorporates ignorance and uncertainty, thereby making it suitable in situations of partial ignorance and imperfect information.