534 articles
Motion estimation
Motion estimation is the computer vision task of computing the displacement of image content between video frames, producing motion vectors or dense optical flow fields.
Multimodal logic
Multimodal logic is a modal logic with several modal operators, each with its own accessibility relation, built from unimodal components by combination methods such as fusion and product.
Multiset
A multiset, also called a bag, is a mathematical collection in which elements may appear more than once, each carrying a multiplicity, unlike an ordinary set where repeats collapse.
Natural deduction
Natural deduction is a logical proof system, described by Gentzen and Jaśkowski in 1934, built by assuming temporary premises and discharging them, with an introduction and elimination rule for each connective.
Necessity and sufficiency
Necessity and sufficiency, also called necessary and sufficient conditions, are concepts in logic and mathematics: a sufficient condition guarantees a statement, and a necessary condition must hold for it.
Neuro-fuzzy
Neuro-fuzzy, also called a fuzzy neural network, is a hybrid intelligent system combining neural networks with fuzzy logic, whose landmark model is ANFIS from 1993.
New Foundations
New Foundations, also called typed set theory, is an axiomatic set theory proposed by W. V. Quine in 1937, known for admitting a universal set.
Nicolas Bourbaki
Nicolas Bourbaki is the collective pseudonym of a semi-secret, self-renewing society of mathematicians, founded by young French mathematicians in 1935, whose monumental treatise Éléments de mathématique reshaped mathematics.
NIP theory
NIP theory, also called a dependent theory, is a first-order theory in which no formula has the independence property. Introduced by Saharon Shelah, it is a central tameness dividing line in model theory.
Nominalism
Nominalism, also called via moderna, is the metaphysical view that only particular, concrete things exist, denying universals and abstract entities; William of Ockham was its key medieval exponent.
Non-normal modal logic
A non-normal modal logic is a modal logic weaker than the smallest normal logic K, lacking necessitation or the K axiom, and interpreted over neighborhood (Scott–Montague) models.
Non-standard model
A non-standard model is a mathematical structure satisfying the same first-order axioms as a standard structure like the natural numbers, yet containing extra elements such as infinite integers.
NOR logic
NOR logic is the Boolean operation, written A ↓ B, that outputs true only when all inputs are false; its NOR gate is a universal gate.
Normal modal logic K
Normal modal logic K is the smallest normal modal logic, containing classical propositional logic, the Distribution Axiom, and the Necessitation Rule, named after Saul Kripke.
o-minimality
O-minimality is a tameness condition in model theory requiring every definable set to be a finite union of points and intervals, introduced by van den Dries.
OR gate
The OR gate, or OR circuit, is a digital logic circuit whose output is HIGH when at least one input is HIGH, implementing inclusive logical disjunction.
Ordered abelian groups
An ordered abelian group is an abelian group with a total order compatible with addition, such as the integers, rationals, and reals; it is central to model theory.
Ordered pair
An ordered pair (a, b) is a mathematical object with a first and second coordinate, so (a, b) equals (c, d) only when a = c and b = d.
Ordinal analysis
Ordinal analysis, also known as proof theoretic ordinal, is a proof theory research program assigning each formal theory a characteristic ordinal, begun with Gentzen's 1936 consistency proof of Peano arithmetic.
Ordinal collapsing function
An ordinal collapsing function is a proof theory function that assigns large uncountable ordinals smaller countable ones, introduced by Heinz Bachmann and central to analyzing impredicative theories via the Bachmann–Howard ordinal.
Ordinal notation
An ordinal notation is a formal system of finite expressions with a computable ordering that names ordinals, central to ordinal analysis in proof theory and to proving program termination.
PA degree
A PA degree is a Turing degree that computes a complete, consistent extension of Peano Arithmetic; equivalently, one computing a path through every nonempty Pi-0-1 class.
Paraconsistent logic
Paraconsistent logic is a family of formal logical systems in which a contradiction does not entail everything: explosion is invalid, so theories containing contradictions can remain non-trivial.
Paradox
A paradox is seemingly sound reasoning from apparently true assumptions that still leads to a contradiction; the Liar dates to antiquity, and Russell's paradox arose in 1901.
Paradoxes of set theory
The paradoxes of set theory are contradictions from naive comprehension, including Russell's paradox (1901), Burali-Forti's (1897), and Cantor's, which forced set theory onto axiomatic foundations.
Parametric polymorphism
Parametric polymorphism is a form of polymorphism in which one piece of code written with type variables works uniformly at many types, as in Java or Haskell generics.
Paramodulation
Paramodulation is an inference rule in automated theorem proving, introduced by George Robinson and Larry Wos in 1969 to build equality reasoning into resolution while eliminating explicit equality axioms.
Paris–Harrington theorem
The Paris–Harrington theorem, proved by Jeff Paris and Leo Harrington in 1977, strengthens the finite Ramsey theorem and is true but unprovable in Peano Arithmetic.
Peano axioms
The Peano axioms, or Dedekind–Peano axioms, are axioms characterizing the natural numbers through zero, a successor operation, and induction, introduced by Giuseppe Peano in 1889.
Permutation model
A permutation model, also called a Fraenkel–Mostowski model, is a model of Zermelo–Fraenkel set theory with atoms built by symmetric groups of permutations, devised to prove the Axiom of Choice independent.