Categorical Propositions in Quantificational Logic

 
  When we introduced QL back in Chapter 7,  we looked a quantified propositions where the quantifier ranged only over a single propositional function. That placed a severe limit on what we could express. We could express "Everything is lovely" and there are no unicorns" but we could not express a quantified relation among two or more propositional functions.

We now show how to translate categorical propositions into QL. From there, we will provid the formal semantics for QL and then its proof theory, following the order we used for PL.