------++++ Sorted logic

---++++++ Syntax of sorted logic

Let be a set of sorts. Instead of one set of variables, we have one set for each sort. Each constant symbol has a sort. Instead of having a number of places, each predicate symbol has a list of sorts. The first two clauses in the definition of a formula become

1. A variable or a constant symbol followed by = followed by a variable or a constant symbol is a formula if the variable or constant symbol on the left is of the same sort as that of the variable or constant symbol on the right.
1. A relation symbol from followed by a list of variables and constant symbols from such that the th item on the list is of the th sort in the list of sorts associated with the relation symbol is a formula.