534 articles
Material conditional
The material conditional, or logical conditional, is the truth-functional "if A then B" connective of classical logic, false only when A is true and B is false.
Mathematical induction
Mathematical induction, also called proof by induction, is a proof technique that establishes a statement holds for every natural number from a base case onward.
Mathematical logic
Mathematical logic, also known as formal logic, is the branch of mathematics that builds formal languages and proof systems, comprising proof theory, model theory, set theory, and computability theory.
Mathematical operators and symbols in Unicode
Mathematical operators and symbols in Unicode, also called Unicode mathematical symbols, are the characters Unicode encodes for mathematical notation, centered on the Mathematical Operators block.
Mathematical Platonism
Mathematical Platonism is the metaphysical view that abstract mathematical objects, such as numbers, sets, and functions, exist independently of us, our language, and our practices, so mathematical truths are discovered, not invented.
Mathematical proof
A mathematical proof is a deductive argument establishing a statement as true from accepted starting points such as axioms and definitions, tracing to Euclid's Elements.
Max-product algorithm
The max-product algorithm, also called min-sum or max-sum, is a message-passing method that computes the most probable assignment of a distribution over a factor graph, exactly on trees.
Measurable cardinal
A measurable cardinal is an uncountable cardinal carrying a nontrivial two-valued measure, introduced by Stanisław Ulam in 1930; its existence cannot be proved in ZFC and contradicts V = L.
Metabolic network modelling
Metabolic network modeling, also known as metabolic network reconstruction and simulation, is the mathematical representation of biochemical reactions in a cell, used to predict metabolite and flux behavior.
Method of analytic tableaux
The method of analytic tableaux, also called semantic tableaux, is a tree-shaped proof procedure for logic introduced by Evert Beth and Jaakko Hintikka in 1955, testing satisfiability by searching for counterexamples.
Metric interval temporal logic
Metric interval temporal logic (MITL) is a real-time temporal logic, introduced by Alur, Feder, and Henzinger in 1996, whose temporal operators carry non-singular time intervals, making satisfiability decidable in EXPSPACE.
Metric temporal logic
Metric temporal logic (MTL) is a formal specification language that extends linear temporal logic with time bounds, letting requirements such as 'every request must be answered within 5 seconds' be checked mechanically.
Mice (set theory)
In inner model theory, a mouse is an iterable premouse, a canonical fine-structural model introduced by Dodd and Jensen in the 1970s to measure consistency strength.
Michael Dummett
Michael Dummett (1925–2011) was a British philosopher, Wykeham Professor of Logic at Oxford from 1979 to 1992, known for his work on Frege and anti-realism.
Minimal degree (computability theory)
A minimal degree in computability theory is an incomputable Turing degree with no degree strictly between it and the computable sets, first constructed by Spector in 1956.
Modal logic
Modal logic is a family of formal logics extending classical logic with operators for necessity and possibility, plus logics of obligation, time, and belief, originating with C.I. Lewis in 1912.
Modal logic D
Modal logic D, also written KD, adds to K the axiom that what is necessary is possible, making it the modal basis of Standard Deontic Logic.
Modal logic of agency
The modal logic of agency formalizes what agents do, can do, and are responsible for, chiefly through Belnap and Perloff's "seeing to it that" (stit) operator.
Modal realism
Modal realism is the metaphysical thesis that possible worlds are concrete entities like our own world, associated above all with David Lewis's 1986 book On the Plurality of Worlds.
Modal μ-calculus
The modal μ-calculus is a temporal logic of programs extending modal logic with least and greatest fixed-point operators, used to model check recursive correctness properties.
Model checking
Model checking is a formal verification technique that automatically checks whether a finite model of a system satisfies a temporal logic property, producing counterexamples on failure.
Model companion
A model companion of a first-order theory T is a model complete theory whose models each embed in models of T and vice versa, introduced by Abraham Robinson.
Model theory
Model theory, also called the theory of models, is the branch of mathematical logic studying how formal languages are interpreted, especially first-order languages and their structures.
Modest set
A modest set is a set whose elements have computational realizers, each realizer determining at most one element, serving as a notion of data type in realizability.
Modus ponens
Modus ponens, also called the law of detachment, is a valid rule of inference in propositional logic: from if A then B, and A, infer B.
Modus tollens
Modus tollens, or denying the consequent, is a valid rule of inference in propositional logic: from a conditional p → q and the denial ¬q, one infers ¬p.
Monad (functional programming)
In functional programming, a monad is an abstraction that structures computations, letting pure languages represent effects such as state, exceptions, and input and output behind a uniform interface.
Monadic second-order logic
Monadic second-order logic (MSO logic) extends first-order logic by quantifying over sets of elements, and over words, trees, and bounded graphs it has the power of finite automata.
Morley rank
Morley rank is an ordinal-valued dimension assigned to definable sets in a model, introduced by Michael Morley in 1965; in algebraically closed fields it equals Zariski dimension.
Morse–Kelley set theory
Morse–Kelley set theory (MK), also called Kelley–Morse set theory, is an axiomatic set theory with sets and classes whose class comprehension allows quantification over proper classes.