Zeroth-order logic is first-order logic without quantifiers. A finitely axiomatizable zeroth-order logic is isomorphic to a propositional logic. Zeroth-order logic with axiom schema is a more expressive system than propositional logic. An example is given by the system Primitive recursive arithmetic, or PRA.
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“Histories make men wise; poets witty; the mathematics subtle; natural philosophy deep; moral grave; logic and rhetoric able to contend.”
—Francis Bacon (1561–1626)