Polyadic Quantificational Logic

The propositional functions we have presented in QL so far take just one variable. For example, we have propositional functions such as "Tx" for "x is tall" and "Rx" for "x is red."  We call these monadic propositional functions, since they  are functions with one argument.  There are, however, functions of more than one argument. We may wish to say that Harry is taller than Solomon. In order to do that in QL we need to introduce polyadic predicates, such as relations. We can express the proposition that Harry is taller than Solomon by introducing the relation "Txy" for "x is taller than y". Then using names in the obvious way we can translate the sentence as "Ths".

We turn to a brief treatment of Polyadic Quantificational Logic.