In First Order Logic is it possible to define a formula as :
p(X,a)
where X is a variable and a a constant ? Or i must use quantifiers if i use a variable in a predicate ?
2026-03-25 14:18:24.1774448304
First order logic variable without quantifiers
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It's a formula, yes. It's just not sentence.
A sentence is a formula without any free variables. But syntactically, we build up sentences using formulas. For example, a sentence like $\forall x \ p(x,a)$ starts with the formula $p(x,a)$, and then adds a quantifier.