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Formal grammar

Definition

A formal grammar is a set of symbols and the production rules for rewriting some of them into every possible string of a formal language over an alphabet. A grammar does not describe the meaning of the strings—only their form.

Related concepts

Abstract logic Abstract machine Abstract syntax tree Ackermann set theory Adaptive grammar Affix grammar Aleph number Algebraic logic Alphabet (formal languages)Ambiguous grammar Aperiodic finite state automaton Applied mathematics Argument Arity Atomic formula Atomic model (mathematical logic)Atomic sentence Attribute grammar Automata theory Automated theorem proving Axiom Axiom of choice Axiom schema Axiomatic system Axiomatization of Boolean algebras Backus–Naur form Banach–Tarski paradox Big O notation Bijection Binary operation Boolean algebra Boolean algebras canonically defined Boolean function Cantor's diagonal argument Cantor's paradox Cantor's theorem Cardinality Cartesian product Categorial grammar Categorical theory Category (mathematics)Category of sets Category theory Chomsky hierarchy Church encoding Church–Turing thesis Class (set theory)Classical logic Codomain Compactness theorem Compiler Complement (set theory)Complete theory Compositional semantics Computability theory Computable function Computable set Computably enumerable set Computational complexity of matrix multiplication Computational linguistics Concrete category Concrete syntax tree 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 Continuum hypothesis Countable set Decidability (logic)Decider (Turing machine)Decision problem Deductive system Deep structure and surface structure Deterministic acyclic finite state automaton Deterministic context-free grammar Deterministic context-free language Deterministic pushdown automaton Diagram (mathematical logic)Disjoint sets Domain of a function Donald Knuth Earley parser Element (mathematics)Elementary diagram Elementary equivalence Elementary function arithmetic Embedded pushdown automaton Empty set Empty string Enumeration Equiconsistency Equivalence relation Euclid's Elements Euclidean geometry Existential quantification Expression (mathematics)Expressivity (computer science)Extended Backus–Naur form Extension by definitions Extension by new constant and function names Extensionality Finitary relation Finite-state machine Finite-valued logic Finite language Finite model theory Finite set First-order logic Fixed-point logic Forcing (mathematics)Formal language Formal languages Formal methods Formal proof Formal semantics (logic)Formal system Formal verification Formation rule Foundations of geometry Foundations of mathematics Free logic Free variables and bound variables Function (mathematics)Functional predicate Fuzzy set General set theory Generative grammar Grammar Grammar framework Grothendieck universe Ground expression Ground formula Gödel's completeness theorem Gödel's incompleteness theorems Gödel numbering Halting problem Hereditary set Higher-order logic Hilbert's axioms Hilbert system History of logic History of mathematical logic IRE Transactions on Information Theory Image (mathematics)Inaccessible cardinal Independence (mathematical logic)Indexed grammar Indexed language Inference Infinite-valued logic Infinite set Information theory Inhabited set Injective function Interpretation (logic)Interpretation (model theory)Interpretation function Intersection (set theory)Isomorphism JPR02 Kleene star Kolmogorov complexity Kripke's theory of truth Kripke–Platek set theory L-system LL parser LR parser Lambda calculus Large cardinal Left recursion Lemma (mathematics)Lindström's theorem Linear bounded automaton Linear context-free rewriting language Linear context-free rewriting system Linguistics Link grammar 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 Logic Logical biconditional Logical conjunction Logical connective Logical consequence Logical constant Logical disjunction Logical equality Logical equivalence Logical truth Logicism Lojban Löwenheim–Skolem theorem Many-valued logic Map (mathematics)Material conditional Mathematical linguistics Mathematical logic Mathematical notation Mathematical object 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 Mouton de Gruyter NP (complexity)Naive set theory Natural deduction Natural language processing 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 Nonterminal symbol Open formula Operation (mathematics)Ordinal analysis Ordinal number PTIME P (complexity)P versus NP problem Paradoxes of set theory Parse tree Parser Parsing algorithm Parsing expression grammar Partition of a set Peano axioms Philosophy of mathematics Phrase structure grammar 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 Pumping lemma for context-free languages Pushdown automaton Quantifier (logic)Quantifier rank Range concatenation grammars Range concatenation language Recursion Recursion (computer science)Recursive language Recursive set Recursively enumerable language Reflexive transitive closure Regular expression Regular grammar Regular language Relation (mathematics)Reverse mathematics Rewriting system 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 Semi-Thue system Sentence (mathematical logic)Sequent calculus Set-builder notation Set (mathematics)Set theory Seymour Ginsburg Shape grammar Signature (logic)Singleton (mathematics)Skolem arithmetic Soundness Spectrum of a sentence Spectrum of a theory Square of opposition Star-free language Strength (mathematical logic)String (computer science)String (formal languages)Structure (mathematical logic)Substitution (logic)Substructure (mathematics)Supertask Surjective function Syllogism Symbol (formal)Syntactic sugar Syntax (logic)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 Terminal and nonterminal symbols Terminal symbol Theorem Theoretical computer science Theoretical linguistics Theories of truth Theory (mathematical logic)Thread automaton Three-valued logic Timeline of mathematical logic Top-down parsing Top-down parsing language Transfer principle Transitive set Tree-adjoining grammar Tree stack automaton True arithmetic Truth predicate Truth table Truth value Tuple Turing machine Type (model theory)Type theory Ultrafilter (set theory)Ultraproduct Uncountable set Undecidable problem Uninterpreted function Union (set theory)Uniqueness quantification Universal quantification Universal set Universe (mathematics)Unrestricted grammar Urelement Validity (logic)Variable (mathematics)Venn diagram Von Neumann universe Von Neumann–Bernays–Gödel set theory Well-formed formula Zermelo–Fraenkel set theory

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