Translation in Polyadic QL
 

Mixed quantification, which we just covered, is the hardest part of translation in Polyadic QL. Apart from that, translation in Polyadic QL works just like it did in Monadic QL. There are singular propositions, quantified propositions, categorical propositions, negations of quantified propositions, and categorical propositions. Remember to classify the proposition before translating. Here are some examples.

 
This is a categorical sentence, really an A-type categorical sentence, with polyadic subject and predicate. The propositional functions are "Txy" for "x is taller than y" and "Hxy" for "x is happier than y."   Our translation is:

Notice that our universal quantifier ranges over both the "x" in the subject and the "x" in the predicate.  Now let's look at an I-type categorical proposition:

This is an existentially quantified sentence:

We can also have categorical propositions without constants. Consider:

which we can translate as:

We're certainly not limited to categorical propositions. We can translate the full complement of proposition types, and the following exercise indeed offers you just that! While you're at it,  translate some arguments.