Reasoning: An Introduction to Logic, Sets, and Functions

Subsection 4.1.5 Predicate Logic Well-Formed Formulas

Using these building blocks, we can now describe what a syntactically legal predicate logic expression looks like. As in Boolean logic, we’ll call such an expression a well-formed formula or wff (pronounced “woof”).

The simplest kind of wff is a single predicate applied to its required number of objects.

Examples of simple wffs:

1. Bear(Smokey) Bear is a predicate of one argument.

2. Prime(269) Prime is a predicate of one argument.

3. MotherOf(Gruffy, Smokey) MotherOf takes two arguments.

4. CurrentProjectOf(Shazaam, Chris) Also takes two arguments.

5. Bear(x)

The first four of our example wffs are logical statements. They have truth values. If we want to use them to reason about some situation, we’ll need to choose premises so that the ones that are true can be proven to be true and the ones that are false can be proven to be false.

The last of our examples contains the variable x. We’ll say that the variable x is unbound or free. Before we can assign a truth value to the wff, we need to know what actual object(s) x refers to. The terminology we’ll use is that we need to bind x. More about this in a minute.