Ontologies, Misunderstood

Forms, Instances, Logic, Reasoning and Inference

Abstract Logic: Forms Not Data

Logic is the study of valid inference. It tells you which conclusions can be derived from which premises. A logician does not check whether Socrates is in fact mortal before accepting that he is, given that all men are mortal and Socrates is a man. This is the example the discipline has used to teach abstract logic for centuries. The conclusion follows from the form of the premises, and the content is interchangeable. Replace men with integers, Socrates with seven, mortal with prime and the inference runs the same, returning the same verdict about validity. The indifference to content is the whole point.

Abstract logic reasons over forms, not data — over the relationships amongst classes rather than the membership of any one thing. The objects drop away and the structure remains. That operation is what separates an ontology from a schema, a graph, or a pile of confident text.

A thread crossed my feed this week that demonstrates what happens when abstract logic is absent from a conversation about ontologies. Five claims appeared in threaded comments in response to my last essay, each of them pointing towards misunderstandings as to the very nature of ontologies. The comments clearly demonstrated reasoning about data or instances, but they believed they were reasoning about forms.

I will dispel each of the myths expressed in each of the claims, and map the distance between relational logic and ontological logic. It is clear that the majority of misunderstandings about ontologies exist because of assumptions, that ontology logic is the same as relational logic, and it is not. By the end of the essay, I hope to shed light on how these two forms of logic are distinct, serving different purposes, each enabling unique machine functions.