# Uniqueness of first order logic representation

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?

• You example uses different vocabularies: Large and Computer are not logical terms. Commented Mar 23, 2020 at 15:57
• @MauroALLEGRANZA I see. What about in the latter example?
– 24n8
Commented Mar 23, 2020 at 16:24
• Obviously you can define: $\text {LargeComputer}(x) \Leftrightarrow (\text {Large}(x) \land \text {Computer}(x))$ and it's done: you have defined a translation between the two vocabularies. Commented Mar 23, 2020 at 16:45
• @MauroALLEGRANZA What is a "logical term" specifically? I don't think I've seen this terminology used, and I couldn't find any information on this on Google.
– 24n8
Commented Mar 23, 2020 at 17:36
• See Logical constants: connectives, quantifiers. Commented Mar 23, 2020 at 17:40