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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?

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    $\begingroup$ You example uses different vocabularies: Large and Computer are not logical terms. $\endgroup$
    – Mauro ALLEGRANZA
    Commented Mar 23, 2020 at 15:57
  • $\begingroup$ @MauroALLEGRANZA I see. What about in the latter example? $\endgroup$
    – 24n8
    Commented Mar 23, 2020 at 16:24
  • $\begingroup$ 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. $\endgroup$
    – Mauro ALLEGRANZA
    Commented Mar 23, 2020 at 16:45
  • $\begingroup$ @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. $\endgroup$
    – 24n8
    Commented Mar 23, 2020 at 17:36
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    $\begingroup$ See Logical constants: connectives, quantifiers. $\endgroup$
    – Mauro ALLEGRANZA
    Commented Mar 23, 2020 at 17:40

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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

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