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I took a statement like

"Caracas and Valencia are located in Venezuela"

and expressed it as:

LocatedIn (Caracas, Venezuela) ^ LocatedIn(Valencia, Venezuela)

Is this a statement in propositional logic, first order logic or both?

I'm inclined to say it's first order logic due to its use of predicates, with an implied for all quantifier before it.

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I believe this is zeroth-order logic. – goblin Sep 27 '13 at 0:26

1 Answer 1

up vote 6 down vote accepted

Your analysis is correct. Propositional logic in general deals with combinations of "atomic" propositions that are not analyzed further.

However, there is no implied universal quantifier. The various countries, cities are most naturally though of as constant symbols. So we are dealing here with a language that has at least one binary predicate symbol, and a large number of constant symbols. If $P$ is a binary predicate symbol, and $a$ and $b$ are constant symbols, then $P(a,b)$ is a sentence, and requires no quantification.

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