Predicate Logic - Syntax

Syntax

Predicate calculus symbols may represent either variables, constants, functions or predicates.

1. Constants name specific objects or properties in the domain of discourse. Thus George, tree, tall and blue are examples of well formed constant symbols. The constants (true) and (false) are sometimes included.
2. Variable symbols are used to designate general classes or objects or properties in the domain of discourse.
3. Functions denote a mapping of one or more elements in a set (the domain of the function) into a unique element of another set (the range of the function). Elements of the domain and range are objects in the world of discourse. Every function symbol has an associated arity, indicating the number of elements in the domain mapped onto each element of range.

A function expression is a function symbol followed by its arguments. The arguments are elements from the domain of the function; the number of arguments is equal to the arity of the function. The arguments are enclosed in parentheses and separated by commas. e.g.:

• f(X,Y)
• father(david)
• price(apple)

are all well-formed function expressions.

Predicate logics may be viewed syntactically as Chomsky grammars. As such, predicate logics (as well as modal logics and mixed modal predicate logics) may be viewed as context-sensitive, or more typically as context-free, grammars. As each one of the four Chomsky-type grammars have equivalent automata, these logics can be viewed as automata just as well.