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...

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

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...

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

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;...

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...

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...

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...

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

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

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]...

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

called lambda expressions, were introduced by Alonzo Church and Stephen Kleene for formalizing functions and their evaluation. They form the basis for...

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

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...

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

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...

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

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...

supremum of the iterates (⊥, f (⊥), f (f (⊥)), … f n(⊥), …) of ⊥ (see also the Kleene fixed-point theorem). Another fixed point theorem is the Bourbaki-Witt theorem...

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

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":...

simpler variant of the deductive systems employed for first-order logic (see Kleene 1967, Sec 1.9 for one such system). A proof of a tautology in an appropriate...

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

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