definition of Kleene algebra. The simplest Kleene algebra that is not Boolean is Kleene's three-valued logic K3. K3 made its first appearance in Kleene's On notation...

science. Kleene's work grounds the study of computable functions. A number of mathematical concepts are named after him: Kleene hierarchy, Kleene algebra, the...

values. It is also a special case of a De Morgan algebra and a Kleene algebra (with involution). Every Boolean algebra gives rise to a Boolean ring, and vice...

fragment of the Kleene K3 logic, restricted to AND, OR, and NOT tables. Philosophy portal Binary logic (disambiguation) Boolean algebra (structure) Boolean...

expressions began in the 1950s, when the American mathematician Stephen Cole Kleene formalized the concept of a regular language. They came into common use...

set of all possible finite-length strings of an alphabet generated by the Kleene star). The use of channels for communication is one of the features distinguishing...

Rosser 1939 in Davis 1965:226. Kleene 1943, p. 60 in Davis 1965:274. Footnotes omitted. Kleene 1952:300. Kleene 1952:376. Kleene 1952:382, 536 Gandy 1980:123ff...

Kleene and Emil Leon Post. Kleene introduced the concepts of relative computability, foreshadowed by Turing, and the arithmetical hierarchy. Kleene later...

later repeat this thesis (in Kleene 1952:300) and name it "Church's Thesis"(Kleene 1952:317) (i.e., the Church thesis). Kleene, Stephen C. (1991) [1952]...

most popular in the literature are three-valued (e.g., Łukasiewicz's and Kleene's, which accept the values "true", "false", and "unknown"), four-valued,...

infinite-dimensional spaces Injective metric space Kakutani fixed-point theorem Kleene fixed-point theorem Knaster–Tarski theorem Lefschetz fixed-point theorem...

power set of a topological space to itself are idempotent; the Kleene star and Kleene plus functions of the power set of a monoid to itself are idempotent;...

Completeness Result for Relation Algebra with Binders." Peter Jipsen: Relation algebras "Foundations of Relations and Kleene Algebra." "Computer Aided Investigations...

matched. For example, x+ means "one or more of the letter x". This is the Kleene plus notation. Hyphen-minus usually indicates a range ([A-Z] - any capital...

Morgan algebra Kleene algebra (with involution) Łukasiewicz–Moisil algebra Boolean algebra (structure) Boolean ring Complete Boolean algebra Orthocomplemented...

symbols is called a "word over A", and the free monoid A∗ is called the "Kleene star of A". Thus, the abstract study of formal languages can be thought...

Metaphysics Research Lab, Stanford University. Retrieved 20 January 2025. Kleene 1967, pp. 158–161. Suppes, Patrick (1957). Introduction to Logic (PDF)....

embedding theorem (ordered groups) Hausdorff maximality theorem (set theory) Kleene fixed-point theorem (order theory) Knaster–Tarski theorem (order theory)...

monoid Green's relations Monad (functional programming) Semiring and Kleene algebra Star height problem Vedic square Frobenioid If both e1 and e2 satisfy...

1 + a a ∗ = 1 + a ∗ a . {\displaystyle a^{*}=1+aa^{*}=1+a^{*}a.} A Kleene algebra is a star semiring with idempotent addition and some additional axioms...

apply. Example of a 3-valued logic applied to vague (undetermined) cases: Kleene 1952 (§64, pp. 332–340) offers a 3-valued logic for the cases when algorithms...

Kenneth (eds.). "Some Philosophical Aspects of Combinatory Logic". The Kleene Symposium: Proceedings of the Symposium Held June 18-24, 1978 at Madison...

give equivalent results"(Kleene 1967:33). This foundational choice, and their equivalence also applies to predicate logic (Kleene 1967:318). In his introduction...

related to several results about undecidable sets in recursion theory. Kleene (1943) presented a proof of Gödel's incompleteness theorem using basic results...

the left of the scanned symbol. A variant of this is seen in Kleene (1952) where Kleene shows how to write the Gödel number of a machine's "situation":...

intuitionistic linear logic" Dexter Kozen, "A completeness theorem for Kleene algebras and the algebra of regular events" Thomas Henzinger, Xavier Nicollin, Joseph...

{\displaystyle A} and B {\displaystyle B} was used here. The ∗ denotes the Kleene star operation, while Σ∗ denotes the set of words formed from the alphabet...

allied notions in an abstract formal system. Revue philosophique de Louvain 50, 251–269. Kleene, S. C. (1967). Mathematical Logic. Reprinted 2002, Dover. ISBN 0-486-42533-9...

expressed using generalized regular expressions with limited nesting depths of Kleene stars? For which number fields does Hilbert's tenth problem hold? Kueker's...

Stephen Kleene. Both Kurt Gödel and Kleene believed that the classical paradoxes are uniformly examples of this sort of definition. But Kleene went on...