Term (Logic)

A term in predicate logic refers to any symbol that is not a logical formula (so not a predicate or a proposition, or a logical quantifier. Terms include functions and their variables, as well as any constants.

Definition §

Term

In the formal language of predicate logic, a term is defined, recursively in Backus-Naur form as:

$$t::=x|c|f(t_1,t_2,\dots )$$

• $::=$ : Is defined to be
• $x$ : Any variable
• $c$ : Any constant
• $f(t_1,t_2,\dots )$ : A function operating over one or more terms.

Convention §

Functions (which are terms) and predicates (which are formulas) can be easily misinterpreted:

$\text{killer}(x)$ could mean: If we need a way to say

• A function which returns the killer of $x$
• A predicate which states whether $x$ is a killer

As such, convention states that functions start with lowercase letters, while predicates start with uppercase letters: $\text{killer}(x)$ is a function, while $\text{Killer}(x)$ is a predicate.