Observational Advantages and Occurrence Referentiality

Logical diagrams are known to have certain advantages over sentential notations for particular reasoning tasks: using a diagram may make logical consequences directly evident, when these consequences are “hidden” in an equivalently expressive sentential language. This phenomenon is known as a “free ride” or “observational advantage”. Where does this advantage come from, and why? We answer this question by distinguishing two general kinds of logical languages: occurrence-referential languages, in which sameness of reference (for sentential and predicate variables) is determined by the sameness of variable occurrence, and type-referential languages, in which sameness of variable type determines sameness of reference. We explain that it is the occurrence-referential nature of some languages that explains for their observational advantage over equivalently expressive type-referential languages.