# first order logic representations question

I want to know if these two alternative formulations for English sentences are well represented in first order logic.

"Caracas and Valencia are located in Venezuela."

LOCATED_IN (Caracas ^ Valencia, Venezuela)

"There is a state that borders Indiana and Washington."

Exists s: State(s) ^ Borders (s, Indiana) ^ Borders (s, Washington)

I'm particularly doubtful about my second interpretation, should it have a biconditional <=> to make it not axiomatic and more like a theorem?

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It depends a lot on you particular formulation; for example, the predicate "LOCATED_IN" is not a common first order logic operator, but I don't know if it is allowed in your setting. That said, I would expect you to need to give the statement as "LOCATED_IN(Caracas, Venezuela)$\land$LOCATED_IN(Valencia, Venezuela)", rather than as you have done it. – Arturo Magidin Nov 7 '11 at 3:57

## 1 Answer

In my experience with first order logic, one wouldn't put an 'and' inside a predicate. Concretely, for "Caracas and Valencia are located in Venezuela" I'd prefer (as Arturo Magidin also said)

LOCATED_IN(Caracas, Venezuela) $\bigwedge$ LOCATED_IN(Valencia, Venezuela)

The second interpretation seems correct to me. In fact, I think a biconditional would make it incorrect because an implication is true if both sides are false.

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