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

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...

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...

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...

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

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;...

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

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...

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,...

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...

Ockham algebras form a variety. Examples of Ockham algebras include Boolean algebras, De Morgan algebras, Kleene algebras, and Stone algebras. Berman...

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

Standard First Order Logic. University of California Press. ISBN 0-520-01822-2 Kleene, S. C. (1967). Mathematical Logic. Reprinted 2002, Dover. ISBN 0-486-42533-9...

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

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

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]...

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...

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...

Cole Kleene, and John Horton Conway have preferred to include 0. Mathematicians have noted tendencies in which definition is used, such as algebra texts...

following table for "P ⊃ (Q ∨ R ⊃ (R ⊃ ¬P))", produced by Stephen Cole Kleene: Colin Howson, on the other hand, believes that "it is a good practical...

simplified system close to von Neumann's original one". Kleene 1952, pp. 143–145. N.Bourbaki (1954). Elements de Mathematique, Theorie des Ensembles. Hermann &...

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

matched. For example, x+ means "one or more of the letter x". This is the Kleene plus notation. There is no concept of negative zero in mathematics, but...

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":...

universally valid. It is common in presentations after this (such as Stephen Kleene 1967 and Herbert Enderton 2002) to use tautology to refer to a logically...

or constructivism, as exemplified in the extreme by Brouwer and Stephen Kleene, requires proofs to be "constructive" in nature – the existence of an object...

who included Paul Bernays, Wilhelm Ackermann, and John von Neumann (cf. Kleene (1952), p. 46–59). A variety of constructive mathematics, intuitionism is...

provability), are Kurt Gödel’s dialectica interpretation, Stephen Cole Kleene’s realizability, Yurii Medvedev’s logic of finite problems, or Giorgi Japaridze’s...