---++++ Sorted logic

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

Let %$S$% 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 %$n$% of places, each predicate symbol has a list %$s_{1},\dotsc ,s_n$% 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 %$\mathcal L$% followed by a list of variables and constant symbols from %$\mathcal L$% such that the %$i$%th item on the list is of the %$i$%th sort in the list of sorts associated with the relation symbol is a formula.