Object-Role Modeling and Higher-Order Logic
Finding a Medium
The image above was selected from a set of images provided by Bing Image Creator to the prompt, “The intersection of Higher-Order Logic and First-Order Logic under Ehrenfeucht Fraisse Games” and it is fitting that the text is not accurate, subject to interpretation and where there is no defining line between first-order logic and higher-order logic. Indeed, one cannot tell from the image what the image has to do with logic at all, and where one such thing begins and the other ends.
All of which would be a sad indictment for logic if there were no purpose to logic and formal logic. But there is. The aim of logic is to at least provide scaffolding for reasoning and communication.
On the face of it one might not think of formal logic as a means of communication, but in its written form it is. The symbols for theorems of formal logic in their own way provide a logographic set of expressions, or sentences, within a medium (on paper or a computer screen) that in their interpretation have meaning to the interpreter.
In a previous article I outlined a thesis that all of logic is a game. Even if one played by one’s self, theorems on a piece of paper form but a reminder of what it is we were thinking about or a challenge as to find their proof etc under a theory. As a…
