Polyadic algebras (more recently called Halmos algebras[1]) 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[1] (when equality is part of the logic) and Lawvere's functorial semantics (a categorical approach).[2]
^ abMichiel Hazewinkel (2000). Handbook of algebra. Vol. 2. Elsevier. pp. 87–89. ISBN 978-0-444-50396-1.
^Jon Barwise (1989). Handbook of mathematical logic. Elsevier. p. 293. ISBN 978-0-444-86388-1.
Polyadicalgebras (more recently called Halmos algebras) are algebraic structures introduced by Paul Halmos. They are related to first-order logic analogous...
quantification and equality. They differ from polyadicalgebras in that the latter do not model equality. A cylindric algebra of dimension α {\displaystyle \alpha...
term dyadic to related terms triadic, tetradic and polyadic. Kronecker product Bivector Polyadicalgebra Unit vector Multivector Differential form Quaternions...
different from what is now meant by a tensor. Gibbs introduced Dyadics and Polyadicalgebra, which are also tensors in the modern sense. The contemporary usage...
Boolean algebras form a variety. They are to monadic predicate logic what Boolean algebras are to propositional logic, and what polyadicalgebras are to...
1962 Algebraic Logic, Halmos devised polyadicalgebras, an algebraic version of first-order logic differing from the better known cylindric algebras of...
and algebraic description of models appropriate for the study of various logics (in the form of classes of algebras that constitute the algebraic semantics...
abstract algebraic logic is the study of the algebraization of deductive systems arising as an abstraction of the well-known Lindenbaum–Tarski algebra, and...
cylindric algebras (Henkin, Monk & Tarski 1971) or polyadicalgebras are information algebras related to predicate logic (Halmos 2000). Module algebras: (Bergstra...
variable number of arguments are called multigrade, anadic, or variably polyadic. Latinate names are commonly used for specific arities, primarily based...
In mathematics, a polyadic space is a topological space that is the image under a continuous function of a topological power of an Alexandroff one-point...
In mathematics, especially in abstract algebra, a quasigroup is an algebraic structure resembling a group in the sense that "division" is always possible...
The polyadicalgebra of Paul Halmos. By virtue of its economical primitives and axioms, this algebra most resembles PFL; Relation algebraalgebraizes the...
Carol cooperate. are said to involve a multigrade (also known as variably polyadic, also anadic) predicate or relation ("cooperate" in this example), meaning...
this decomposition is an open problem.[clarification needed] Canonical polyadic decomposition (CPD) is a variant of the tensor rank decomposition, in which...
contrasted with polyadic predicate calculus, which allows relation symbols that take two or more arguments. The absence of polyadic relation symbols...
In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative internal binary operation on it. The binary operation...
1989. Revised Sept. 1990 and Oct. 1990 respectively. Robin Milner. The Polyadic pi-Calculus: A Tutorial Edinburgh University. LFCS report ECS-LFCS-91-180...
his work on model theory, metamathematics, and algebraic logic, he also contributed to abstract algebra, topology, geometry, measure theory, mathematical...
it is homeomorphic to a separable and complete metric space. Polyadic A space is polyadic if it is the continuous image of the power of a one-point compactification...
Double Polyadics, with Application to the Linear Matrix Equation, Proceedings AAAS 58(10): 355 to 395. 1923: Identities Satisfied by Algebraic Point Functions...
eliminating the need for parentheses to indicate order of operation. polyadic first-order logic First-order logic extended to include predicates with...
continuous. Here N {\displaystyle \mathbb {N} } has the discrete topology. Polyadic spaces are defined as topological spaces that are the continuous image...
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