Uniqueness of first order logic representation

137 Views Asked by At

My understand of first order logic and logic in general is that the representation of a sentence may not be unique.

For example, if we were to represent the sentence "Every large computer is a Dell computer," I believe any of the following representations are correct:

$$ \forall x \ \ \ Large(x) \land Computer(x) \implies Dell(x) \land Computer(x) \\ \forall x \ \ \ LargeComputer(x) \implies DellComputer(x) \\ $$

The former involves a conjunction because it separates the adjectives (large, dell) from the nouns (computer), and the latter does not. Is there some common understanding in the community on which representation might be more preferable?

1

There are 1 best solutions below

0
On

I think you need to look into the Syntax of First-Order Logic to understand better. Formal Logic is a fundamental subject to the point that there is no scope for preference. So, in my opinion, there are no preferences for any representation in First-Order Logic itself. Now once you have picked a Signature depending on your application, the communities in those application domains may have preferences but it is surely nothing axiomatic. The two examples you give have two different signatures and hence these formulas are simply not comparable. For reference, I am adding these notes, which describe the syntax of FOL. https://www.cs.ox.ac.uk/people/james.worrell/lecture9-2015.pdf