Polyadic algebras (more recently called Halmos algebras) are algebraic structures introduced by Paul Halmos. They are related to first-order logic 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).
Further reading
- Paul Halmos, Algebraic Logic, Chelsea Publishing, New York (1962)
References
Michiel Hazewinkel (2000). Handbook of algebra. Vol. 2. Elsevier. pp. 87–89. ISBN 978-0-444-50396-1. 978-0-444-50396-1 ↩
Michiel Hazewinkel (2000). Handbook of algebra. Vol. 2. Elsevier. pp. 87–89. ISBN 978-0-444-50396-1. 978-0-444-50396-1 ↩
Jon Barwise (1989). Handbook of mathematical logic. Elsevier. p. 293. ISBN 978-0-444-86388-1. 978-0-444-86388-1 ↩