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Syntactically correct logical formula
propositional logic, and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence of symbols from a given
Well-formed_formula
Topics referred to by the same term
Look up well-formed in Wiktionary, the free dictionary. Well-formed or wellformed indicate syntactic correctness and may refer to: Well-formedness, quality
Well-formed
Expression of symbolic information
(See Boolean expression) In mathematical logic, a formula (often referred to as a well-formed formula) is an entity constructed using the symbols and formation
Formula
Linguistic device in formal languages
a well-formed formula (wff) of L. If φ is a well-formed formula (wff) of L, then '~φ' is a well-formed formula (wff) of L. Nothing else is a well-formed
Quasi-quotation
Defining elements of a set in terms of other elements in the set
the basis and inductive clauses (extremal clause). The notion of a well-formed formula (wff) in propositional logic is defined recursively as the smallest
Recursive_definition
Mathematical model for deduction or proof systems
minimum: Formal language, which is a set of well-formed formulas, which are strings of symbols from an alphabet, formed by a formal grammar (consisting of production
Formal_system
In mathematics, a statement that has been proven
cannot be expressed with a well-formed formula. More precisely, if the set of all sets could be expressed with a well-formed formula, this would imply that
Theorem
Mathematical logic concept
equivalently a formula that has no strict subformulas. Atoms are thus the simplest well-formed formulas of the logic. Compound formulas are formed by combining
Atomic_formula
{\displaystyle B} are; ¬ F {\displaystyle \neg F} is Harrop for any well-formed formula F {\displaystyle F} ; F → A {\displaystyle F\rightarrow A} is Harrop
Harrop_formula
Rules used for constructing, or transforming the symbols and words of a language
constitute the well-formed formulas of a formal system. In computer science, the term syntax refers to the rules governing the composition of well-formed expressions
Syntax_(logic)
Establishment of a theorem using inference from the axioms
proof or derivation is a finite sequence of sentences (known as well-formed formulas when relating to formal language), each of which is an axiom, is
Formal_proof
Logic formula
a propositional formula is a type of syntactic formula which is well formed. If the values of all variables in a propositional formula are given, it determines
Propositional_formula
In mathematical logic, a well-formed formula with no free variables
mathematical logic, a sentence (or closed formula) of a predicate logic is a Boolean-valued well-formed formula with no free variables. A sentence can be
Sentence_(mathematical_logic)
Sequence of words formed by specific rules
of well-formed formulas (which may be interpreted as sentences, or propositions) each of which is an axiom or follows from the preceding formulas in the
Formal_language
Function in mathematical logic
a Gödel numbering is a function that assigns to each symbol and well-formed formula of some formal language a unique natural number, called its Gödel
Gödel_numbering
Formal language used to prove statements
theorems. Axioms: Formulas in L assumed to be valid. All theorems are derived from axioms. A formal proof of a well-formed formula in a proof system is
Proof_calculus
Theorem in formal logic
additional contradiction where unicorns do and do not exist), as well as any other well-formed formula. Thus, there is an explosion of provable statements. In
Principle_of_explosion
Term in logic and deductive reasoning
if) it is both valid in form and has no false premises. A formal system is sound if (and only if) every well-formed formula that can be proven in the
Soundness
Token in a mathematical or logical formula
interpretation of them. A symbol or string of symbols may comprise a well-formed formula if it is consistent with the formation rules of the language. In
Symbol_(formal)
Mathematical formula expressing equality
while an égalité does not require variables, but in English, any well-formed formula consisting of two expressions related with an equals sign is an equation
Equation
Study of the properties of logical systems
syntactic consequence of all the well formed formulae that precede it in the proof system. For a well formed formula to qualify as part of a proof, it must
Metalogic
Topics referred to by the same term
for infants Trinitarian formula, a Biblical phrase Well-formed formula, a word that is part of a formal language, in logic Formula fiction, literature following
Formula_(disambiguation)
Branch of logic
propositional connectives. A well-formed formula is any atomic formula, or any formula that can be built up from atomic formulas by means of operator symbols
Propositional_logic
Type of logical system
"formula" to mean "well-formed formula" and have no term for non-well-formed formulas. In every context, it is only the well-formed formulas that are of interest
First-order_logic
Statement in a metalanguage
typical judgments in first-order logic would be that a string is a well-formed formula, or that a proposition is true. Similarly, a judgment may assert
Judgment_(mathematical_logic)
Subset of n-space defined by a finite sequence of polynomial equations and inequalities
semialgebraic sets are exactly those sets that can be defined by a well-formed formula built with quantifiers ∀ , ∃ {\displaystyle \forall ,\exists }
Semialgebraic_set
System responsible for combining morphemes into complex structures
mental grammars that form and interpret sentences. In logic, syntax is the study of how strings of symbols form well-formed formulas in formal languages
Syntax
logics are many-sorted logics in which the expression x = y is not a well-formed formula in general. A formal semantics can be provided using the concept
Schrödinger_logic
Symbol connecting formulas in logic
allow new well-formed formulas to be constructed by joining other well-formed formulas using truth-functional connectives, see well-formed formula. Logical
Logical_connective
Something that represents an idea, process, or physical entity
understood as representing an idea, object, relationship, or mathematical formula. Symbols allow people to go beyond what is known or seen by creating linkages
Symbol
Term that does not contain any variables
variable Sentence (mathematical logic) – In mathematical logic, a well-formed formula with no free variables Alex Sakharov. "Ground Atom". MathWorld. Retrieved
Ground_expression
Propositional logic theorem
instance of ¬¬A in a well-formed formula can be replaced by A, leaving unchanged the truth-value of the well-formed formula. Double negative elimination
Double_negation
Structure of a formal language
Grammar framework L-system Lojban Post canonical system Shape grammar Well-formed formula Meduna, Alexander (2014), Formal Languages and Computation: Models
Formal_grammar
Expression whose definition assigns it a unique interpretation
(mathematics) Uniqueness Uniqueness quantification Undefined Well-formed formula Weisstein, Eric W. "Well-Defined". From MathWorld – A Wolfram Web Resource. Retrieved
Well-defined_expression
Sufficient evidence/argument for truth
to, to correctly identify any symbol used in the proof.); for a well-formed formula to qualify as part of a formal proof, it must be the result of applying
Proof_(truth)
Argument whose conclusion must be true if its premises are
clearly expressed by means of sentences called well-formed formulas (also called wffs or simply formulas). The validity of an argument can be tested, proved
Validity_(logic)
In linguistics, conformity with grammar
Validator Well-formed document Well-formed element Well-formed formula Breiss, Canaan (2021). "Inside the wug-test: phonological well-formedness and processing
Well-formedness
Motorsport championship held worldwide
Formula One (F1) is the highest class of worldwide racing for open-wheel, single-seater formula racing cars run by the Formula One Group and sanctioned
Formula_One
Mathematical study of the meaning of programming languages
semantics makes no distinction between a phrase's meaning and the logical formulas that describe it; its meaning is exactly what can be proven about it in
Semantics (programming languages)
Semantics_(programming_languages)
Standard system of axiomatic set theory
property as one that could be formulated as a well-formed formula in a first-order logic whose atomic formulas were limited to set membership and identity
Zermelo–Fraenkel_set_theory
formula with another, maintaining logical consistency. substitution-instance The well-formed formula which results from a given well-formed formula by
Glossary_of_logic
Ongoing Formula One season
2026 FIA Formula One World Championship Previous 2025 Next 2027 Races by country Races by venue Support series: Formula 2 Championship FIA Formula 3 Championship
2026 Formula One World Championship
2026_Formula_One_World_Championship
Summary of a mathematical proof
of the form x*, x**, x***, ... This is the language of Peano arithmetic. A well-formed formula is a sequence of these symbols that is formed so as to
Proof sketch for Gödel's first incompleteness theorem
Proof_sketch_for_Gödel's_first_incompleteness_theorem
Term in logic
language, and it can be defined as follows. In a formal language, a well-formed formula (or wff) is a string of symbols constituted in accordance with the
Atomic_sentence
Symbol representing a property or relation in logic
Predicate functor logic Predicate variable Truthbearer Truth value Well-formed formula Lavrov, Igor Andreevich; Maksimova, Larisa (2003). Problems in Set
Predicate_(logic)
Class of non-classical logics
systems of logic. In these logics: the set of well-formed formulas generated equals the set of well-formed formulas generated by classical logic. the set of
Deviant_logic
Motor racing championship held in 2025
Parent series: Formula One World Championship Support series: FIA Formula 3 Championship F1 Academy Porsche Supercup The 2025 FIA Formula 2 Championship
2025_Formula_2_Championship
Topics referred to by the same term
Logical expression may refer to: Well-formed formula Boolean expression This disambiguation page lists articles associated with the title Logical expression
Logical_expression
degree of a polynomial, or other recursively defined objects such as well-formed formulas. (Also written as ∂.) del – del, a differential operator. (Also written
List of mathematical abbreviations
List_of_mathematical_abbreviations
Formula One constructor
manufacturer General Motors (GM) has been a Formula One constructor under the luxury Cadillac brand as Cadillac Formula 1 Team since 2026 and is expected to
Cadillac_in_Formula_One
Topics referred to by the same term
1968) Wallops Flight Facility, a NASA launch site in Virginia, US Well-formed formula, in logic World's Funniest Fails, a 2015 American TV series WFF 'N
WFF
Concept in logic
(b){\bigr ]}} For every a {\textstyle a} and b {\textstyle b} , and any well-formed formula ϕ ( x ) {\textstyle \phi (x)} (with a free variable x). For example:
Substitution_(logic)
Form of logic that allows quantification over predicates
A sentence in second-order logic, as in first-order logic, is a well-formed formula with no free variables (of any sort). It's possible to forgo the
Second-order_logic
Motor racing championship held in 2024
Parent series: Formula One World Championship Support series: FIA Formula 3 Championship F1 Academy Porsche Supercup The 2024 FIA Formula 2 Championship
2024_Formula_2_Championship
Type of mathematical function
some formal language to the natural numbers. This associates each well-formed formula with a unique natural number, called its Gödel number. If a Gödel
Ordinal_notation
as Craig's trick) states that any recursively enumerable set of well-formed formulas of a first-order language is recursively axiomatizable, and even
Craig's_theorem
Type of mathematical variable
variables correspond to propositional variables which can stand for well-formed formulas of the same logic, and such variables can be quantified by means
Predicate_variable
Formal systems of logic that significantly differ from standard logical systems
extensions of a logic, the set of well-formed formulas generated is a proper superset of the set of well-formed formulas generated by classical logic. the
Non-classical_logic
Standard form of a boolean function
In boolean logic, a disjunctive normal form (DNF) is a normal form of a logical formula consisting of a disjunction of conjunctions; it can also be described
Disjunctive_normal_form
Open-wheeled single-seater motorsport
best known are Formula One, Formula E, Formula Two, Formula Three, regional Formula Three and Formula Four. Common usage of "formula racing" encompasses
Formula_racing
Rule defining the correct structure of expressions in formal grammar
In mathematical logic, formation rules are rules for describing well-formed words over the alphabet of a formal language. These rules only address the
Formation_rule
Application of logical methods to philosophical problems
if two conditions are fulfilled: (1) all well-formed formulas of classical logic are also well-formed formulas in it and (2) all valid inferences in classical
Philosophical_logic
Mathematical system
X ) {\displaystyle \forall n(n\in X\rightarrow Sn\in X)} , is a well-formed formula of second-order arithmetic that is arithmetical, has one free set
Second-order_arithmetic
3-volume treatise on mathematics, 1910–1913
starts with "0" and specifies how to build acceptable strings or "well-formed formulas" (wffs). This includes a rule for "substitution" of strings for the
Principia_Mathematica
Complex exponential in terms of sine and cosine
Euler's formula is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the
Euler's_formula
Topics referred to by the same term
of finitely-additive measures Valuation (logic), an operation on well-formed formulas with the semantics of evaluation Valuation (measure theory), a tool
Valuation
Range of application for a quantifier or connective in a logical formula
within a formula is the smallest well-formed formula that contains the connective in question. The connective with the largest scope in a formula is called
Scope_(logic)
Standard form of Boolean function
In Boolean algebra, a formula is in conjunctive normal form (CNF) or clausal normal form if it is a conjunction of one or more clauses, where a clause
Conjunctive_normal_form
Kind of proof calculus
tree notation, by writing well-formed formulas below the inference line and any schematic variables used by those formulas above it. For instance, the
Natural_deduction
beginning, because Ψ {\displaystyle \Psi } would not have been a well-formed formula in that case. This is why we cannot naively use the argument appearing
Original proof of Gödel's completeness theorem
Original_proof_of_Gödel's_completeness_theorem
Study of correct reasoning
in well-formed formulas. For instance, the syntactic rules of propositional logic determine that " P ∧ Q {\displaystyle P\land Q} " is a well-formed formula
Logic
Quantifier elimination for semi-algebraic sets
computational algebraic geometry. A formula of the first-order theory of the real numbers is a well-formed formula involved only the quantifier ∀ , ∃
Tarski–Seidenberg_theorem
Single-seater racing championship
The FIA Formula 2 Championship (F2) is a second tier single-seater championship organised by the Fédération Internationale de l'Automobile. The championship
FIA_Formula_2_Championship
Race car class
Europe, Australia, South America and Asia form an important step for many prospective Formula One drivers. Formula Three (adopted by the FIA in 1950) evolved
Formula_Three
Formula One activities of Mercedes-Benz
German automotive brand of the Mercedes-Benz Group, has been involved in Formula One as both team owner and engine manufacturer for various periods since
Mercedes-Benz_in_Formula_One
Axiomatic system
well-formed formulas, and provided that no variable which is free in one is quantified in the other, then the following are all well-formed formulas <x∧y>
Typographical_Number_Theory
Former motor racing team
the chequered flag only twice out of 20 total entries. Benetton Formula Limited was formed in 1985 when the Toleman team was sold to the Benetton family
Benetton_Formula
French motorsport executive (born 1968)
Renault Sport as team principal of the newly formed Renault Sport Formula One Team during the 2016 Formula One season. He resigned at the end of the 2016
Fred_Vasseur
60th season of the FIA Formula One World Championship
Supercup Formula BMW Europe The 2009 FIA Formula One World Championship was the 63rd season of FIA Formula One motor racing. It featured the 60th Formula One
2009 Formula One World Championship
2009_Formula_One_World_Championship
Open-wheel racing car category intended for junior drivers
FIA Formula 4, also known as "F4", is an open-wheel racing car category intended for junior drivers. There is no global championship; instead, individual
Formula_4
Motorsport championship held in Japan
The Japanese Super Formula Championship (全日本スーパーフォーミュラ選手権) is a formula racing series held primarily in Japan. It is considered to be the pinnacle of single-seater
Super_Formula_Championship
Theory in computer science
a well-formed CTL formula: EF ( EG p ⇒ AF r ) {\displaystyle {\mbox{EF }}({\mbox{EG }}p\Rightarrow {\mbox{AF }}r)} The following is not a well-formed
Computation_tree_logic
Notation for chemical compounds
chemical formula is any of several kinds of notation for expressing the composition and structure of a chemical compound. Chemical formulas use element
Chemical_formula
French-owned Formula One racing team
of the 2021 Formula One World Championship. Formerly named Renault F1 Team and owned by the French automotive company Groupe Renault as well as Renault–Nissan–Mitsubishi
Alpine_F1_Team
Study of the semantics, or interpretations, of formal and natural languages
consequence. While logical syntax concerns the formal rules for constructing well-formed expressions, logical semantics establishes frameworks for determining
Semantics_(logic)
System including an indeterminate value
tautologies (valid formulas) because whenever all of the atomic components of a well-formed formula are assigned the value Unknown, the formula itself must also
Three-valued_logic
Racing video game series by Psygnosis and Studio Liverpool
Since 2001, the Formula One series had been made by Studio Liverpool (an internal Sony Computer Entertainment Europe game studio) formed from the restructuring
Formula One (video game series)
Formula_One_(video_game_series)
Assignment of meaning to the symbols of a formal language
interpretation. For example, we can determine that (P or Q) is a well-formed formula even without knowing whether it is true or false. A formal language
Interpretation_(logic)
40th season of FIA Formula One motor racing
dominated throughout the season and formed what was dubbed as the "Gang of Four". The 1986 season also marked the final Formula One season of 1982 Drivers' Champion
1986 Formula One World Championship
1986_Formula_One_World_Championship
Computer program created in 1959
means–ends analysis. Any problem that can be expressed as a set of well-formed formulas (WFFs) or Horn clauses, and that constitutes a directed graph with
General_Problem_Solver
French and Algerian racing driver (born 2004)
French and Algerian racing driver who competes under the French flag in Formula One for Red Bull Racing. Born and raised in Paris to an Algerian family
Isack_Hadjar
Motor racing competition
2027 Formula Regional Oceania Trophy Previous 2026 Next 2028 The 2027 Castrol Toyota Formula Regional Oceania Trophy is scheduled to be the twenty-second
2027 Formula Regional Oceania Trophy
2027_Formula_Regional_Oceania_Trophy
Racing car design competition
the world. For example, Formula Student is a similar SAE-sanctioned event in the UK, as well as Formula SAE Australasia (Formula SAE-A) taking place in
Formula_SAE
Overview of and topical guide to logic
metalanguage Symbol (formal) Type–token distinction Use–mention distinction Well-formed formula Proof theory – The study of deductive systems. Axiom Deductive system
Outline_of_logic
British auto racing team
McLaren Racing Limited (/məˈklærən/ mə-KLARR-ən), currently competing in Formula One as McLaren Mastercard F1 Team, is a British motor racing team based
McLaren
Motor racing championship
GP3 Series Porsche Supercup Formula BMW Europe The 2010 FIA Formula One World Championship was the 64th season of FIA Formula One motor racing. The season's
2010 Formula One World Championship
2010_Formula_One_World_Championship
System for representing and reasoning about time
operators are well-formed formulas whenever B(φ) is well-formed. Binary operators are well-formed formulas whenever B(φ) and C(φ) are well-formed. In some
Temporal_logic
Australian racing driver (born 2001)
win the GP2/Formula 2 title in their rookie season. Piastri is the only driver in history to win Formula Renault, Formula Three, and Formula Two—or
Oscar_Piastri
59th season of the FIA Formula One World Championship
GP2 Series Porsche Supercup Formula BMW Europe The 2008 FIA Formula One World Championship was the 62nd season of Formula One motor racing, recognised
2008 Formula One World Championship
2008_Formula_One_World_Championship
Game of symbolic logic
and methods available. All players must be able to recognize a "well-formed formula" (WFF in Łukasiewicz notation), to assemble dice values into valid
WFF_'N_PROOF
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WELL FORMED-FORMULA
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WELL FORMED-FORMULA
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WELL FORMED-FORMULA
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WELL FORMED-FORMULA
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