534 articles
Business rules engine
A business rules engine, also known as a rule engine, is software that executes business rules like IF/THEN policies separately from application code, so policy changes need no reprogramming.
Busy beaver
The busy beaver function, defined by Tibor Radó in 1962, maps a Turing machine's states to the most steps a halting machine of that size can run.
Cantor space
Cantor space, written 2^N, is the space of infinite binary sequences with the product topology; it is compact, perfect, and totally disconnected, and homeomorphic to the middle-thirds Cantor set introduced by Georg Cantor in 1883.
Cantor's theorem
Cantor's theorem is the set-theory result that every set is strictly smaller than the set of all its subsets, proved by Georg Cantor in 1891 using the diagonal argument.
Cardinal number
A cardinal number is a number that measures the size of a set by counting its elements; Georg Cantor developed the concept in the nineteenth century.
Cardinality
Cardinality is the size of a set, written |A|, defined through one-to-one correspondence. Georg Cantor showed in 1873 that infinite sets come in different sizes.
Cartesian closed category
A cartesian closed category is a category with finite products and, for each pair of objects, an exponential object B^A behaving like a function space, as in the category of sets.
Cartesian product
The Cartesian product of two sets A and B, written A × B, is the set of all ordered pairs (a, b) with a in A and b in B.
Catch-22 (logic)
The Catch-22 problem is a situation in which a desired outcome is impossible to attain because of inherently contradictory rules, coined by Joseph Heller in his 1961 novel.
Categorical logic
Categorical logic is the study of logic using category theory, interpreting logical systems as objects and morphisms in categories and unifying syntax, semantics, and proof theory.
Categoricity
Categoricity is the model-theoretic property that a theory has exactly one model of a given cardinality up to isomorphism; Morley's 1965 theorem made it central.
Categorification
Categorification is a mathematical technique that replaces set-theoretic notions with category-theoretic analogs: sets become categories, functions become functors, and equations become natural isomorphisms between functors.
Causal inference
Causal inference is the process of drawing conclusions about cause and effect from data, using tools such as potential outcomes, causal graphs, and the do-operator, since causal effects cannot be measured directly.
Choice function
A choice function, introduced by Ernst Zermelo in 1904, is a function that selects exactly one element from each set in a family of nonempty sets.
Church encoding
Church encoding is a method of representing data values, such as booleans and natural numbers, purely as functions in the lambda calculus, devised by Alonzo Church in the 1930s.
Church–Turing thesis
The Church–Turing thesis is the claim that every effectively calculable function is computable by a Turing machine, proposed independently by Church and Turing in the 1930s.
Church's thesis (constructive mathematics)
Church's thesis (CT) in constructive mathematics asserts that every constructible function on the natural numbers is recursive, and can be adopted as an axiom of the theory.
Cirquent calculus
Cirquent calculus is a proof-theoretic framework introduced by Giorgi Japaridze in 2006, in which proofs are built from circuit-style structures called cirquents that allow sharing of components.
Class (set theory)
A class in set theory, also called a proper class when it is not a set, is a collection defined by a property, such as the class of all sets.
Clock (model checking)
In model checking, a clock is a real-valued variable that advances with time and can be reset to zero, turning a finite automaton into a timed automaton.
Closed monoidal category
A closed monoidal category, also called a monoidal closed category, is a monoidal category in which tensoring with any fixed object has a right adjoint, yielding an internal hom object.
Combinatory logic
Combinatory logic, also known as combinatory algebra, is a formal system for describing functions without variable binding, using only combinators such as S and K.
Common knowledge (logic)
Common knowledge is a property of a proposition among a group: everyone knows it, everyone knows that everyone knows it, and so on without end.
Compactness theorem
The compactness theorem is a theorem of first-order logic stating that a set of sentences has a model if every finite subset does, first proved by Gödel in 1930.
Complement (set theory)
In set theory, the complement of a set is the elements, drawn from a fixed universe, that do not belong to the set, such as A \ B.
Complete numbering
A complete numbering is a numbering in computability theory where any partial computation can be effectively totalized, mapping divergences to a special element, introduced by Mal'tsev in 1963.
Complete theory
A complete theory is a first-order theory that decides every sentence of its language: either the sentence or its negation is provable from the theory.
Complex question
The complex question, also called the fallacy of many questions (plurium interrogationum), is an informal fallacy where a question's wording presupposes an unestablished claim, so any direct answer concedes it.
Computability logic
Computability logic (CoL) is a formal theory of interactive computability introduced by logician Giorgi Japaridze in 2003, treating computational problems as games won by a machine.
Computable analysis
Computable analysis is the branch of mathematical logic and theoretical computer science that studies computability and complexity for real numbers, continuous functions, and differential equations.