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First-Order Predicate Logic

The underlying logical framework used to formally define and reason about relational data structures and operations.
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The statement of the theorem

Let L\text{L} be a first-order language defined by a set of predicate symbols P=P1,P2,...\text{P} = \text{P}_1, \text{P}_2, \text{...} and a set of function symbols F\text{F}. A formula A\text{A} is constructed recursively: A::=p(xˉ) ∣ ¬A ∣ A1  A2 ∣∀x A ∣ A → A\text{A} ::= p(\bar{x}) \text{ } | \text{ } \neg \text{A} \text{ } | \text{ } \text{A}_1 \text{ } \text{ } \text{A}_2 \text{ } | \forall x \text{ } \text{A} \text{ } | \text{ } \text{A} \text{ } \rightarrow \text{ } \text{A}. The truth value of A\text{A} is evaluated relative to an interpretation I\text{I} mapping symbols in L\text{L} to sets and functions over a domain D\text{D}.