Holland's schema theorem, also called the fundamental theorem of genetic algorithms, is an inequality that results from coarse-graining an equation for...

concept lattice found in Formal concept analysis. Holland's schema theorem Formal concept analysis Holland, John Henry (1992). Adaptation in Natural and Artificial...

poker Holland's schema theorem, or the "fundamental theorem of genetic algorithms" Glivenko–Cantelli theorem, or the "fundamental theorem of statistics"...

computer science) Gap theorem (computational complexity theory) Gottesman–Knill theorem (quantum computation) Holland's schema theorem (genetic algorithm)...

framework for predicting the quality of the next generation, known as Holland's Schema Theorem. Research in GAs remained largely theoretical until the mid-1980s...

"Adaptation in Natural and Artificial Systems". He also developed Holland's schema theorem. Holland authored a number of books about complex adaptive systems...

cancer research John Henry Holland – pioneer in what became known as genetic algorithms, developed Holland's schema theorem, Learning Classifier Systems...

that modus ponens preserves truth. From these axiom schemas one can quickly deduce the theorem schema P→P (reflexivity of implication), which is used below:...

Artificial Systems" in 1975 and his formalization of Holland's schema theorem. In 1976, Holland conceptualized an extension of the GA concept to what...

paradoxes that result when the axiom schema of unrestricted comprehension is assumed in set theory. The incompleteness theorems apply only to formal systems which...

model Higher-order factor analysis Highway network Hinge loss Holland's schema theorem Hopkins statistic Hoshen–Kopelman algorithm Huber loss IRCF360...

independently proposed replacing the axiom schema of specification with the axiom schema of replacement. Appending this schema, as well as the axiom of regularity...

Tarski's undefinability theorem, stated and proved by Alfred Tarski in 1933, is an important limitative result in mathematical logic, the foundations...

The theory may not have all instances of the above schemas as axioms, but rather as derivable theorems. For example, in theories with no function symbols...

used to prove the class existence theorem, which implies every instance of the axiom schema. The proof of this theorem requires only seven class existence...

}} for the formulas permitted in one's adopted Separation schema, by Diaconescu's theorem. Similar results hold for the Axiom of Regularity existence...

In set theory, Kőnig's theorem states that if the axiom of choice holds, I is a set, κ i {\displaystyle \kappa _{i}} and λ i {\displaystyle \lambda _{i}}...

contradiction. Specifically, Frege's Basic Law V (now known as the axiom schema of unrestricted comprehension). According to Basic Law V, for any sufficiently...

arithmetic and that its consistency is therefore less controversial. Gentzen's theorem is concerned with first-order arithmetic: the theory of the natural numbers...

limitations": ...the magnitudes involved should lead one to suspect that theorems and arguments based chiefly on the mere finiteness [of] the state diagram...

It's a consequence of Gödel's completeness theorem (not to be confused with his incompleteness theorems) that a theory has a model if and only if it...

In mathematics, Tarski's theorem, proved by Alfred Tarski (1924), states that in ZF the theorem "For every infinite set A {\displaystyle A} , there is...

not requiring infinite sets, and is the weakest known set theory whose theorems include the Peano axioms. The ontology of GST is identical to that of ZFC...

incompleteness theorem, an extension of the first, shows that such a system cannot demonstrate its own consistency. The T-schema or truth schema (not to be...

compactness theorem states that a set of first-order sentences has a model if and only if every finite subset of it has a model. This theorem is an important...

by Ernst Zermelo in order to formalize his proof of the well-ordering theorem. The axiom of choice is equivalent to the statement that every partition...

some number. The axiom schema of mathematical induction present in arithmetics stronger than Q turns this axiom into a theorem. x + 0 = x x + Sy = S(x...

(see Nouveaux Essais, IV,2)" (ibid p 421) The principle was stated as a theorem of propositional logic by Russell and Whitehead in Principia Mathematica...

algebraic geometry and related fields. A key result known as Chevalley's theorem in algebraic geometry shows that the image of a constructible set is constructible...

mathematics can be formalized in terms of sets, although there are some theorems that cannot be proven in common axiom systems for set theory. Contemporary...