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Formal language

Definition

In logic, mathematics, computer science, and linguistics, a formal language is a set of strings whose symbols are taken from a set called "alphabet".

Related concepts

ASCII Abstract family of languages Abstract logic Abstract machine Abstract syntax tree Ackermann set theory Aleph number Algebraic logic Algorithm Alphabet Alphabet (formal languages)Alphanumeric Aperiodic finite state automaton Argument Arity Arto Salomaa Atomic formula Atomic model (mathematical logic)Atomic sentence Automata theory Automated theorem proving Axel Thue Axiom Axiom of choice Axiom schema Axiomatic system Axiomatization of Boolean algebras Backus–Naur form Banach–Tarski paradox Begriffsschrift Bijection Binary operation Boolean algebra Boolean algebras canonically defined Boolean function Cambridge University Press Cantor's diagonal argument Cantor's paradox Cantor's theorem Cardinality Carl Friedrich Gauss Cartesian product Categorical theory Category (mathematics)Category of sets Category theory Character encoding Characteristica universalis Chomsky Chomsky hierarchy Church encoding Church–Turing thesis Class (set theory)Classical logic Closure (mathematics)Codomain Colorless green ideas sleep furiously Combinatorics on words Compactness theorem Compiler-compiler Complement (set theory)Complete theory Complexity class Computability theory Computable function Computable set Computably enumerable set Computational complexity theory Computational linguistics Computer science Concatenation Concrete category Cone (formal languages)Conservative extension Consistency Constructible universe Construction of the real numbers Constructive set theory Context-free grammar Context-free language Context-sensitive grammar Context-sensitive language Context free language Context sensitive language Continuum hypothesis Countable set DCFL Decidability (logic)Decider (Turing machine)Decision problem Decision procedure Deductive apparatus Deductive system Degeneracy (mathematics)Deterministic acyclic finite state automaton Deterministic context-free grammar Deterministic context-free language Deterministic pushdown automaton Diagram (mathematical logic)Domain of a function Element (mathematics)Elementary diagram Elementary equivalence Elementary function arithmetic Embedded pushdown automaton Emil Post Empty set Encyclopedia of Mathematics Enumeration Equiconsistency Equivalence relation Euclid's Elements Euclidean geometry European Mathematical Society Executable Existential quantification Expression (mathematics)Extension by definitions Extension by new constant and function names Extensionality FORTRAN Finitary relation Finite-state automaton Finite-state machine Finite-valued logic Finite language Finite model theory Finite set First-order logic Fixed-point logic Forcing (mathematics)Formal grammar Formal languages Formal method Formal methods Formal proof Formal semantics (logic)Formal semantics (natural language)Formal system Formal verification Formalism (philosophy of mathematics)Formation rule Foundations of geometry Foundations of mathematics Free logic Free monoid Free variables and bound variables Function (mathematics)Functional predicate Fuzzy set Gauss notation General set theory George Boole Gottfried Leibniz Gottlob Frege Grammar framework Grothendieck universe Ground expression Ground formula Grzegorz Rozenberg Gödel's completeness theorem Gödel's incompleteness theorems Gödel numbering Halting problem Heinz Zemanek Hereditary set Higher-order logic Hilbert's axioms Hilbert system History of logic History of mathematical logic Identifier Image (mathematics)Inaccessible cardinal Independence (mathematical logic)Indexed grammar Indexed language Inference Infinite-valued logic Infinite set Information theory Inhabited set Injective function Intermediate code Interpretation (logic)Interpretation (model theory)Interpretation function Intersection (set theory)Introduction to Automata Theory, Languages, and Computation Isomorphism Jeffrey Ullman John Backus John Hopcroft Keyword (computer programming)Kleene star Kolmogorov complexity Kripke's theory of truth Kripke–Platek set theory Lambda calculus Large cardinal Lemma (mathematics)Leonardo Torres Quevedo Lex programming tool Lexical analyzer Lindström's theorem Linear bounded automaton Linear context-free rewriting language Linear context-free rewriting system Linguistics List of Hilbert systems List of axioms List of first-order theories List of formal systems List of mathematical theories List of set identities and relations List of statements independent of ZFC Literary language Logic Logical biconditional Logical conjunction Logical connective Logical consequence Logical constant Logical disjunction Logical equality Logical equivalence Logical truth Logicism Löwenheim–Skolem theorem Machine code Many-valued logic Map (mathematics)Material conditional Mathematical linguistics Mathematical logic Mathematical notation Mathematical object Mathematics Metalanguage Michael A. Harrison Minimal axioms for Boolean algebra Model complete theory Model theory Monadic predicate calculus Monadic second-order logic Morse–Kelley set theory NP (complexity)Naive set theory Natural deduction Natural language Natural language processing Natural number Negation Nested stack automaton Nested word New Foundations Noam Chomsky Non-Euclidean geometry Non-logical symbol Non-recursive grammar Non-standard model Non-standard model of arithmetic Open formula Operation (mathematics)Ordinal analysis Ordinal number PTIME P (complexity)P versus NP problem Paradoxes of set theory Parser Parser generator Parsing Partition of a set Peano axioms Peter Naur Philosophy of mathematics Pictographs Post canonical system Power set Predicate (mathematical logic)Predicate logic Predicate variable Prime model Primitive recursive arithmetic Primitive recursive function Principia Mathematica Production (computer science)Programming language Programming language theory Proof of impossibility Proof theory Proper subset Proposition Propositional calculus Propositional formula Propositional variable Pushdown automaton Quantifier (logic)Quantifier rank Range concatenation grammars Range concatenation language Recursion Recursive language Recursive set Recursively enumerable language Regular expression Regular expressions Regular grammar Regular language Relation (mathematics)Reverse mathematics Robinson arithmetic Rule of inference Russell's paradox Satisfiability Saturated model Schröder–Bernstein theorem Second-order arithmetic Second-order logic Self-verifying theories Semantic theory of truth Semantics Semantics (computer science)Semantics of logic Sentence (mathematical logic)Sequent calculus Set (mathematics)Set theory Seymour Ginsburg Signature (logic)Singleton (mathematics)Skolem arithmetic Soundness Spectrum of a sentence Spectrum of a theory Springer Science+Business Media Springer Verlag Square of opposition Star-free language Strength (mathematical logic)String (computer science)String (formal languages)String homomorphism String operations Structure (mathematical logic)Subset Substitution (logic)Substructure (mathematics)Supertask Surjective function Syllogism Symbol (formal)Syntactic Syntax Syntax (logic)Syntax (programming languages)Syntax analysis T-schema Tarski's axiomatization of the reals Tarski's axioms Tarski's theory of truth Tarski's undefinability theorem Tarski–Grothendieck set theory Tautology (logic)Term (logic)Term logic The Laws of Thought Theorem Theories of truth Theory (mathematical logic)Thread automaton Three-valued logic Timeline of mathematical logic Transfer principle Transformation rule Transitive set Tree-adjoining grammar Tree stack automaton True arithmetic Truth predicate Truth table Truth value Turing machine Type (model theory)Type theory Ultrafilter (set theory)Ultraproduct Uncountable set Undecidable problem Unicode Uninterpreted function Union (set theory)Uniqueness quantification Universal quantification Universal set Universe (mathematics)University of Maryland, Baltimore Unrestricted grammar Urelement Validity (logic)Variable (mathematics)Venn diagram Vienna Virtual machine Von Neumann universe Von Neumann–Bernays–Gödel set theory Well-formed formula Wolfgang Rautenberg Yacc Zermelo–Fraenkel set theory ∅

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