PHILOS 31 Lecture Notes - Lecture 8: Atomic Formula, Prime Number, Universal Quantification
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Q r: show r, ~r, p, q ass id pr pr. Molecular formulas: p q, p ^ q, p q, ~p, p v q. If p is a formula and x a variable, then xp, xp. Xfx, x(fx gy), x(fx v gb) We can include sentence letters as well. Atomic sentence: predicate letter followed by a name letter. Atomic formula: predicate letter followed by a term letter. If p and q are formulas then, p q, p ^ q, p q, ~p, p v q are molecular formulas. A quantifier occurrence binds an occurrence of a variable if. The variable occurrence is within the scope of the quantifier occurrence. The variable occurrence is the same as the one that accompanies the quantifier. The variable occurrence is not already bound by another quantifier occurrence within the scope of the first quantifier occurrence. Universal quantifier almost always ranges over a conditional. Existential quantifier almost always ranges over a conjunction.
