Polyadic algebra

Polyadic algebras (more recently called Halmos algebras) are algebraic structures introduced by Paul Halmos, designed to study first-order logic. Polyadic algebras form one of the main algebraic frameworks used in algebraic logic to study the syntax and model theory of first-order logic.

The relationship between polyadic algebra and first-order logic is analogous to the relationship between Boolean algebras and propositional logic (see Lindenbaum–Tarski algebra). There are other ways to relate first-order logic to algebra, including Tarski's cylindric algebras (when equality is part of the logic) and Lawvere's functorial semantics (a categorical approach).

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