Definition:Basic WFF of Predicate Logic

Definition

Let $\LL$ be the language of predicate logic.

A WFF $\mathbf A$ of $\LL$ is called basic if and only if it does not start with a logical connective.

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Basic WFFs are useful to consider as atoms when analysing propositional logic within the larger context of predicate logic.

Expressed more formally, we can take the basic WFFs as the vocabulary of the language of propositional logic.

Do note that e.g. $\forall x: x = x \land x = x$ is considered basic even though it contains the logical connective $\land$.

This is because $\land$ is not the main connective.

Also see

• Definition:Atom (Logic)

Sources

• 2009: Kenneth Kunen: The Foundations of Mathematics ... (previous) ... (next): $\text{II}.9$ Tautologies: Definition $\text{II}.9.1$