534 articles
Free logic
Free logic, named by Karel Lambert in 1960, is a family of first-order systems that drops the classical assumption that every singular term denotes an existing object.
Free variables and bound variables
In formal logic, a free variable is not bound by a quantifier and a bound variable is; the distinction applies to occurrences, and formulas without free variables are sentences.
Frege system
A Frege system, also called a Frege proof system, is a standard axiomatic proof system for propositional logic, named after Gottlob Frege and central to proof complexity.
Frege's propositional calculus
Frege's propositional calculus is the axiomatic system for propositional logic in Gottlob Frege's 1879 Begriffsschrift, using only negation and the conditional, with six key axioms and modus ponens.
Functional calculus (logic)
Functional calculus, or first-order predicate logic, is a formal system in which statements about individuals are proved from axioms, and the standard logical framework of mathematics.
Functional completeness
Functional completeness, also called expressive adequacy, is the property of a set of logical connectives that can express every truth function; NAND and NOR are each complete alone.
Functor
A functor is a structure-preserving map between categories that sends objects to objects and morphisms to morphisms, introduced by Eilenberg and Mac Lane in 1945.
Fundamenta Mathematicae
Fundamenta Mathematicae is a Polish mathematics journal published in Warsaw by the Polish Academy of Sciences, founded in 1920 as the world's first specialized mathematical journal, devoted to set theory.
Fuzzy control system
A fuzzy control system is a control system whose controller uses fuzzy logic and linguistic rules, converting a human operator's heuristic knowledge into automatic control strategy.
Fuzzy logic
Fuzzy logic, also called mathematical fuzzy logic, is a form of reasoning that assigns propositions degrees of truth between 0 and 1, introduced by Lotfi A. Zadeh in 1965.
Fuzzy set
A fuzzy set is a class in which membership is a matter of degree from 0 to 1, a concept introduced by Lotfi Zadeh in his 1965 paper "Fuzzy sets."
Game semantics
Game semantics is a style of denotational semantics interpreting types as games and programs as strategies, arising in the early 1990s from the full abstraction problem for PCF.
Generalization
Generalization is extending a finding from the studied sample to a broader population, a component of external validity in research and a key goal in machine learning.
Generic structure
A generic structure, also called a Fraïssé limit or rich model, is a countable homogeneous structure containing every finite structure from a given class, unique up to isomorphism.
Gentzen's consistency proof
Gentzen's consistency proof, also known as Gentzen's theorem, is Gerhard Gentzen's 1936 proof that Peano arithmetic is consistent, using transfinite induction up to the ordinal ε0.
Geometric logic
Geometric logic is a fragment of infinitary first-order logic allowing finite conjunctions, arbitrary set-indexed disjunctions, and existential quantification; it underlies the theory of classifying toposes.
Geometry of interaction
The geometry of interaction is a semantic framework for linear logic, introduced by Jean-Yves Girard in the late 1980s, which models cut elimination by operators on Hilbert spaces rather than syntactic rewriting.
Georg Cantor
Georg Cantor, in full Georg Ferdinand Ludwig Philipp Cantor (1845–1918), was a German mathematician at the University of Halle who created set theory as a mathematical discipline.
George Boole
George Boole (1815–1864) was an English mathematician who reduced logic to an algebra; his Boolean logic, applied to circuits by Claude Shannon, underlies modern digital computing.
Gerhard Gentzen
Gerhard Gentzen (Gerhard Karl Erich Gentzen, 1909–1945) was a German mathematician and logician who created natural deduction and the sequent calculus, the two main logical calculi in proof theory.
Giorgi Japaridze (გიორგი ჯაფარიძე)
Giorgi Japaridze (გიორგი ჯაფარიძე), also published as Giorgie Dzhaparidze, is a Georgian-born logician and full professor at Villanova University in Pennsylvania, known for creating computability logic and cirquent calculus.
Giuseppe Peano
Giuseppe Peano (1858–1932) was an Italian mathematician and logician at the University of Turin who formulated the Peano axioms and found the first space-filling curve.
Gödel numbering
Gödel numbering is a method assigning a unique natural number to each symbol, formula, and proof of a formal language, introduced by Kurt Gödel in his 1931 incompleteness paper.
Gödel, Escher, Bach
Gödel, Escher, Bach is a 1979 book by Douglas Hofstadter exploring self-reference and consciousness through mathematics, art, and music, and it won the Pulitzer Prize.
Gödel's completeness theorem
Gödel's completeness theorem, proved in Kurt Gödel's 1929 doctoral thesis, states that every valid formula of first-order predicate logic is provable, answering a 1928 question of Hilbert and Ackermann.
Gödel's incompleteness theorems
Gödel's incompleteness theorems are two results of mathematical logic published by Kurt Gödel in 1931, showing that any consistent formal system with elementary arithmetic contains undecidable statements.
Gödel's ontological proof
Gödel's ontological proof, also known as Gödel's ontological argument, is a formal modal argument for the existence of God written by Kurt Gödel around 1970.
Goodstein's theorem
Goodstein's theorem is a statement in number theory, proved by Reuben Goodstein in 1944, that every Goodstein sequence eventually reaches 0 but cannot be proved in Peano Arithmetic.
Gradual typing
Gradual typing is a programming language design approach where parts of a program are statically type checked and others dynamically, introduced by Jeremy Siek and Walid Taha in 2006.
Grothendieck construction
The Grothendieck construction turns an indexed category, a functor assigning a category to each object of a base category, into a single total category over the base, giving an equivalence between indexed categories and Grothendieck fibrations.