Formula

logic

Definition

Formula

A formula is a well-formed expression of a formal language that can be evaluated to a truth value.

In first-order logic, formulas are built from terms, predicates, logical connectives, and quantifiers.

Satisfaction

Satisfaction Set

Definition

Formula Satisfaction Set

Let $F$ be a formula and let $\mathcal{A}$ be the set of all variable assignments. The formula satisfaction set of $F$ is the set of all assignments under which $F$ is true:

$$\{F\}\stackrel{\mathrm{def}}{=}\{\sigma \in \mathcal{A}\mid [F]\sigma =\text{true}\}$$

In other words, $\{F\}$ contains exactly the assignments that satisfy $F$.

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