Zeroth-order logic

Truth-functional propositional logic and systems isomorphic to it are considered to be zeroth-order logic.

Zeroth-order logic with axiom schema is a more expressive system than propositional logic.

A finitely axiomatizable zeroth-order logic is isomorphic to a propositional logic.

Zeroth-order logic is first-order logic without quantifiers.

Thus, it makes sense to refer to propositional logic as "zeroth-order logic", when comparing it with these logics.

Nicod's axiom is an axiom in propositional calculus that can be used as a sole wff in a two-axiom formalization of zeroth-order logic.

Many aspects of inquiry can be recognized and usefully studied in very basic logical settings, even simpler than the level of syllogism, for example, in the realm of reasoning that is variously known as Boolean algebra, propositional calculus, sentential calculus, or zeroth-order logic.