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Type of mathematical variable
In mathematical logic, a predicate variable is a predicate letter which functions as a "placeholder" for a relation (between terms), but which has not
Predicate_variable
Type of logical system
where "for all x" is a quantifier, x is a variable, and "... is a human" and "... is mortal" are predicates. This distinguishes it from propositional
First-order_logic
Symbol representing a property or relation in logic
truth. Free variables and bound variables Hypostatic abstraction Multigrade predicate Opaque predicate Philosophical predication Predicate functor logic
Predicate_(logic)
Variable that can either be true or false
{\displaystyle \gamma } . Propositional variables with no object variables such as x and y attached to predicate letters such as Px and xRy, having instead
Propositional_variable
Mathematical use of "for all"
domain. It asserts that a predicate within the scope of a universal quantifier is true of every value of a predicate variable. It is usually denoted by
Universal_quantification
Mathematical use of "there exists"
by the logical operator symbol ∃, which, when used together with a predicate variable, is called an existential quantifier ("∃x" or "∃(x)" or "(∃x)"), read
Existential_quantification
Form of logic that allows quantification over predicates
notable that while we have variables for predicates in second-order logic, we don't have variables for properties of predicates. We cannot say, for example
Second-order_logic
Mathematical theory
defined as Predicate symbols F {\displaystyle F} , G {\displaystyle G} , etc. (with appropriate arities, which are left implicit) Singular variable symbols
Plural_quantification
Syntactically correct logical formula
In mathematical logic, propositional logic, and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence
Well-formed_formula
Database model
corresponds to a predicate variable; the contents of a table to a relation; key constraints, other constraints, and SQL queries correspond to predicates. However
Relational_model
Overview of and topical guide to logic
Monadic predicate calculus Predicate (mathematical logic) Predicate logic Predicate variable Quantification Second-order predicate Sentence (mathematical
Outline_of_logic
Being present, not nothing
scope of an existential quantifier is true of at least one value of a predicate variable. Eli Hirsch, Quantifier Variance and Realism: Essays in Metaontology
Something_(concept)
Symbol representing a mathematical concept
symbols.) This schema states (in one form), for any functional predicate F in one variable: ∀ A , ∃ B , ∀ C , C ∈ A → F ( C ) ∈ B . {\displaystyle \forall
Function_symbol
Symbol representing a mathematical object
that the variable represents or denotes the object, and that any valid candidate for the object is the value of the variable. The values a variable can take
Variable_(mathematics)
In logic, a statement which is always true
sentences of predicate logic that can be reduced to propositional tautologies by substitution. Propositional logic begins with propositional variables, atomic
Tautology_(logic)
Algebraization of first-order logic
i.e., without quantified variables. PFL employs a small number of algebraic devices called predicate functors (or predicate modifiers) that operate on
Predicate_functor_logic
Assignment of meaning to the symbols of a formal language
variables. Then, terms can be combined into an atomic formula using a predicate symbol (relation symbol) from the signature or the special predicate symbol
Interpretation_(logic)
Mathematical logic concept
formal expression that denotes an atomic formula. For predicate logic, the atoms are predicate symbols together with their arguments, each argument being
Atomic_formula
Reformulation of Floyd-Hoare logic
Predicate transformer semantics were introduced by Edsger Dijkstra in his seminal paper "Guarded commands, nondeterminacy and formal derivation of programs"
Predicate transformer semantics
Predicate_transformer_semantics
Study of correct reasoning
Q(John))} ". In this case, the existential quantifier is applied to the predicate variable " Q {\displaystyle Q} ". The added expressive power is especially
Logic
Mathematical use of "for all" and "there exists"
"quantifier rank". If D is a domain of x and P(x) is a predicate dependent on object variable x, then the universal proposition can be expressed as ∀
Quantifier_(logic)
Variable used for specification
be made to avoid variable capture). Others (maybe most) just call parameters passed to (or operated on by) an open predicate variables, and when defining
Parameter
3-volume treatise on mathematics, 1910–1913
"⊃"), "&" (and), "∨" (or), "¬" (not), "∀" (for all), "∃" (there exists); predicate symbol: "=" (equals); function symbols: "+" (arithmetic addition), "∙"
Principia_Mathematica
Number of arguments required by a function
that accepts a variable number of arguments is called variadic. In logic and philosophy, predicates or relations accepting a variable number of arguments
Arity
Logical statement with variables, predicates, and quantifiers over objects
first-order predicate is a predicate that takes only individual(s) constants or variables as argument(s). Compare second-order predicate and higher-order
First-order_predicate
Form of second-order logic
predicate variables only. In the variant considered in automata theory and the Büchi–Elgot–Trakhtenbrot theorem, all predicates, constant or variable
Monadic_second-order_logic
Object or module in concurrent programming
precondition that our predicate // must be true. // This code might make cv's condition false, and/or make other condition variables' // predicates true. // Call
Monitor_(synchronization)
Mathematical-logic system based on functions
expressing computation based on function abstraction and application using variable binding and substitution. Untyped lambda calculus, the topic of this article
Lambda_calculus
Rule defining the correct structure of expressions in formal grammar
and α as a variable then we can take ( ∀ {\displaystyle \forall } α)Φ and ( ∃ {\displaystyle \exists } α)Φ each to be formulas of our predicate calculus
Formation_rule
Measure of the structural complexity of a software program
compound predicates like those found in high-level languages like IF cond1 AND cond2 THEN ... should be counted in terms of predicate variables involved
Cyclomatic_complexity
Axiomatic set theories based on the principles of mathematical constructivism
or predicate variable in axiom schemas and P {\displaystyle P} or Q {\displaystyle Q} is used for particular such predicates. The word "predicate" is
Constructive_set_theory
Logical formalism using combinators instead of variables
of quantified variables in logic, essentially by eliminating them. Another way of eliminating quantified variables is Quine's predicate functor logic
Combinatory_logic
Term in logic
be predicate letters; let a, b, c be individual constants; let x, y, z be variables. These wffs are atomic sentences; they contain no free variables or
Atomic_sentence
Term that does not contain any variables
operators, and P {\displaystyle P} the set of predicate symbols. A ground term is a term that contains no variables. Ground terms may be defined by logical
Ground_expression
System of formal deduction in logic
ponens, for propositional logics – or two – with generalisation, to handle predicate logics, as well – and several infinite axiom schemas. Hilbert systems
Hilbert_system
Set of tuples consisting of values indexed by attributes
extension of some n-adic predicate: all and only those n-tuples whose values, substituted for corresponding free variables in the predicate, yield propositions
Relation_(database)
Method of deriving conclusions
analyzing how the internal structure of propositions, like names and predicates, influences reasoning. Other logical systems explore inferential patterns
Rule_of_inference
Programming language that uses first order logic
and higher-order programming. A higher-order predicate is a predicate that takes one or more other predicates as arguments. Although support for higher-order
Prolog
Index of articles associated with the same name
mathematical logic, stratification is any consistent assignment of numbers to predicate symbols guaranteeing that a unique formal interpretation of a logical
Stratification_(mathematics)
Set of rules defining correctly structured Prolog programs
anonymous variable and means "any term". Unlike other variables, the underscore does not represent the same value everywhere it occurs within a predicate definition
Prolog_syntax_and_semantics
Concept in mathematics or computer science
this notation: λx is the lambda operator that binds the variable x. x hurt x is the predicate, a function that takes an argument and states that this
Free variables and bound variables
Free_variables_and_bound_variables
Fragment of first-order logic
logic, the monadic predicate calculus (also called monadic first-order logic) is the fragment of first-order logic (also called predicate calculus) in which
Monadic_predicate_calculus
Formal system of logic
term "higher-order logic" is commonly used to mean higher-order simple predicate logic. Here, "simple" indicates that the underlying type theory is the
Higher-order_logic
Approach to logic
with the advent of new logic, remaining dominant until the advent of predicate logic in the late nineteenth century. However, even if eclipsed by newer
Term_logic
Use of braces for specifying sets
set-builder notation has three parts: a variable, a colon or vertical bar separator, and a predicate. Thus there is a variable on the left of the separator, and
Set-builder_notation
Mathematical function characterizing set membership
Laplacian of the indicator Dirac delta Extension (predicate logic) Free variables and bound variables Heaviside step function Identity function Iverson
Indicator_function
Programming paradigm based on formal logic
function fibonacci(N) = M, and the predicate N is Expression is Prolog notation for the predicate that instantiates the variable N to the value of Expression
Logic_programming
Statement that is taken to be true
sufficient for proving all tautologies in the language; in the case of predicate logic more logical axioms than that are required, in order to prove logical
Axiom
all". If E is a logical predicate, ∀ x E {\displaystyle \forall x\;E} means that E is true for all possible values of the variable x. 2. Often used in plain
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
Paradox in set theory
y\forall x(x\in y\iff \varphi (x))} for any predicate φ {\displaystyle \varphi } with x as a free variable inside φ {\displaystyle \varphi } . Substitute
Russell's_paradox
Mathematical logic concept
to the predicate of the inferred proposition, it is permissible that it could be the original subject or its contradictory, and the predicate term of
Contraposition
{\displaystyle m} are fixed constants and x {\displaystyle x} is a variable. A predicate is regular if and only if it can be defined in the language of congruence
Regular_numerical_predicate
Kind of transfinite induction
stated in terms of a negated predicate ¬ S {\displaystyle \neg S} is then just as strong as one in terms of a predicate variable P {\displaystyle P} , as
Epsilon-induction
Variable that stores data about other variables or program structure
In logic, a metavariable (also metalinguistic variable or syntactical variable) is a symbol or symbol string which belongs to a metalanguage and stands
Metavariable
Type of logical argument that applies deductive reasoning
some academic contexts, syllogism has been superseded by first-order predicate logic following the work of Gottlob Frege, in particular his Begriffsschrift
Syllogism
Graphical method to simplify Boolean expressions
(2004) [2003-11-05]. "Karnaugh Maps". Switching Theory: Insight Through Predicate Logic. Berlin, Heidelberg, New York: Springer-Verlag. pp. 57–76. ISBN 3-540-40343-4
Karnaugh_map
Basic notion of sameness in mathematics
through set theory. In logic, equality is a primitive predicate (a statement that may have free variables) with the reflexive property (called the law of identity)
Equality_(mathematics)
Words joined with underscores
identifiers. Prolog, for both atoms (predicate names, function names, and constants) and variables Python, for variable names, function names, method names
Snake_case
Formula that contains at least one free variable
An open formula is a formula that contains at least one free variable. An open formula does not have a truth value assigned to it, in contrast with a closed
Open_formula
Model that describes the programmable interface of a computer processor
instruction sets include a predicate field in every instruction. Having predicates on instructions is called predication, and can include conditional-branches
Instruction_set_architecture
Impossible task in computing
15), thus undecidable. The monadic predicate calculus is the fragment where each formula contains only 1-ary predicates and no function symbols. Its S a
Entscheidungsproblem
Function computable with bounded loops
primitive recursive in ψ. #C: A predicate P obtained by substituting functions χ1,..., χm for the respective variables of a predicate Q is primitive recursive
Primitive_recursive_function
Theory of truth in the philosophy of language
assignment of values to the variables x1, ..., xn)) if the corresponding values of variables bear the relation expressed by the predicate F. Tarski himself defined
Semantic_theory_of_truth
Components of a mathematical or logical formula
constructed from constant symbols, variable symbols, and function symbols. An expression formed by applying a predicate symbol to an appropriate number of
Term_(logic)
Constructed language
verbs, adjectives and adverbs. A predicate may act as any of these, depending on its position in a sentence. Each predicate has its own argument structure
Loglan
In mathematical logic, a well-formed formula with no free variables
a sentence (or closed formula) of a predicate logic is a Boolean-valued well-formed formula with no free variables. A sentence can be viewed as expressing
Sentence_(mathematical_logic)
Standard system of axiomatic set theory
common. The signature has a single predicate symbol, usually denoted ∈ {\displaystyle \in } , which is a predicate symbol of arity 2 (a binary relation
Zermelo–Fraenkel_set_theory
Study of the semantics, or interpretations, of formal and natural languages
introduced, and that made it impossible to perform the kind of subject–predicate analysis in Aristotle's logic. Term logic is an attempt to modernize Aristotle's
Semantics_(logic)
Problem in computer science
we can read a definite answer, 'Yes' or 'No,' to the question, 'Is the predicate value true?'." 1952 (1952): Kleene includes a discussion of the unsolvability
Halting_problem
Subfield of automated reasoning and mathematical logic
both a complete propositional calculus and what is essentially modern predicate logic. His Foundations of Arithmetic, published in 1884, expressed (parts
Automated_theorem_proving
Symbolic description of a mathematical object
syntactic conventions of mathematical notation. Symbols can denote numbers, variables, operations, and functions. Other symbols include punctuation marks and
Expression_(mathematics)
Any one of the distinct objects that make up a set in set theory
makes this definition well-defined by ensuring that x is a bound variable in its predication of membership in y. In this case, the domain of Px, which is
Element_of_a_set
Data having only values "true" or "false"
Booleans can store all logical values resulting from the evaluation of predicates in SQL. A column of Boolean type can be restricted to just TRUE and FALSE
Boolean_data_type
Non-monotonic logic created by John McCarthy
propositional variable with a predicate of zero arity (i.e., a predicate with no arguments). Therefore, minimization is done on predicates in the first-order
Circumscription_(logic)
Abstract model
first-order predicate logic. Its core idea is to describe a database as a collection of predicates over a finite set of predicate variables, describing
Data_model
Characteristic of some logical systems
an inconsistency. Truth-functional propositional logic and first-order predicate logic are semantically complete, but not syntactically complete (for example
Completeness_(logic)
Logical operator in modal logic
existential quantifiers only binds to the propositional variables or the predicate variables following the quantifiers, since the modal operators ◻ {\displaystyle
Modal_operator
Logical formulation of recursion
formulas formed from X using first-order connectives and predicates, second-order variables as well as a partial fixed point operator PFP {\displaystyle
Fixed-point_logic
syntactic predicate specifies the syntactic validity of applying a production in a formal grammar and is analogous to a semantic predicate that specifies
Syntactic_predicate
Mathematical function that can be computed by a program
ground open Free/bound variable Language Metalanguage Logical connective ¬ ∨ ∧ → ↔ = Predicate functional variable propositional variable Proof Quantifier ∃
Computable_function
Form of mathematical proof
(}P(n){\bigr )}{\Bigr )},} where P(·) is a variable for predicates involving one natural number and k and n are variables for natural numbers. In words, the base
Mathematical_induction
Expression in propositional calculus
or a predicate is a sentence expressed in a way that would assume the value of true or false, except that within the sentence there is a variable (x) that
Propositional_function
Whether a decision problem has an effective method to derive the answer
validities in any signature that includes equality and at least one other predicate symbol with two or more arguments is not decidable. Logical systems extending
Decidability_(logic)
Typed lambda calculus
will do. A predicate is a function which returns a B o o l e a n {\displaystyle {\mathsf {Boolean}}} -typed value. The most fundamental predicate is ISZERO
System_F
Logic formula
discourse) and (ii) a predicate (a verb or possibly verb-clause that asserts a quality or attribute of the object(s)). The predicate calculus then generalizes
Propositional_formula
Reasoning for mathematical statements
ground open Free/bound variable Language Metalanguage Logical connective ¬ ∨ ∧ → ↔ = Predicate functional variable propositional variable Proof Quantifier ∃
Mathematical_proof
makes S2S second order, with "monadic" indicating absence of k-ary predicate variables for k>1. Concatenation of strings s and t is denoted by st, and is
S2S_(mathematics)
Axiom of set theory
ground open Free/bound variable Language Metalanguage Logical connective ¬ ∨ ∧ → ↔ = Predicate functional variable propositional variable Proof Quantifier ∃
Axiom_of_choice
In mathematical logic, an atomic formula or its negation
propositional variable or its negation. In predicate calculus a literal is an atomic formula or its negation, where an atomic formula is a predicate symbol applied
Literal_(mathematical_logic)
Non-contradiction of a theory
needed] and Emil Post in 1921, while the completeness of (first order) predicate calculus was proved by Kurt Gödel in 1930, and consistency proofs for
Consistency
One-to-one correspondence
ground open Free/bound variable Language Metalanguage Logical connective ¬ ∨ ∧ → ↔ = Predicate functional variable propositional variable Proof Quantifier ∃
Bijection
Theorem that arithmetical truth cannot be defined in arithmetic
metalanguage capable of expressing the semantics of some object language (e.g. a predicate is definable in Zermelo–Fraenkel set theory for whether formulae in the
Tarski's undefinability theorem
Tarski's_undefinability_theorem
Logical connective AND
ground open Free/bound variable Language Metalanguage Logical connective ¬ ∨ ∧ → ↔ = Predicate functional variable propositional variable Proof Quantifier ∃
Logical_conjunction
Sequence of words formed by specific rules
contains infinitely many elements x0, x1, x2, … that play the role of variables. See e.g. Reghizzi, Stefano Crespi (2009). Formal Languages and Compilation
Formal_language
Measure of algorithmic complexity
ground open Free/bound variable Language Metalanguage Logical connective ¬ ∨ ∧ → ↔ = Predicate functional variable propositional variable Proof Quantifier ∃
Kolmogorov_complexity
System of mathematical set theory
one-sorted theory, this notational convention is only mnemonic. The monadic predicate M x , {\displaystyle Mx,} whose intended reading is "the class x is a
Morse–Kelley_set_theory
Set whose elements all belong to another set
ground open Free/bound variable Language Metalanguage Logical connective ¬ ∨ ∧ → ↔ = Predicate functional variable propositional variable Proof Quantifier ∃
Subset
Topological model
When testing two geometries against a scheme, the result is a spatial predicate named by the scheme. The model was developed by Clementini and others
DE-9IM
RDF query language
"intermediate" variables ?vendor and ?owner # would be part of the output. SELECT ?slbl ?vlbl ?lei ?lname WHERE { # ?sw is unbound. Set predicate to rdf:type
SPARQL
Logic for proving computer program correctness
program state. The assertions are logical statements—predicates with variables, where the variables define the state of the program. Algebraic semantics
Axiomatic_semantics
PREDICATE VARIABLE
PREDICATE VARIABLE
Girl/Female
Arabic
Dark Night; Dedicate
Surname or Lastname
English
English : from a medieval male personal name (from Latin Hilarius, a derivative of hilaris ‘cheerful’, ‘glad’, from Greek hilaros ‘propitious’, ‘joyful’). The Latin name was chosen by many early Christians to express their joy and hope of salvation, and was borne by several saints, including a 4th-century bishop of Poitiers noted for his vigorous resistance to the Arian heresy, and a 5th-century bishop of Arles. Largely due to veneration of the first of these, the name became popular in France in the forms Hilari and Hilaire, and was brought to England by the Norman conquerors.English : from the much rarer female personal name Eulalie (from Latin Eulalia, from Greek eulalos ‘eloquent’, literally well-speaking, chosen by early Christians as a reference to the gift of tongues), likewise introduced into England by the Normans. A St. Eulalia was crucified at Barcelona in the reign of the Emperor Diocletian and became the patron of that city. In England the name underwent dissimilation of the sequence -l-l- to -l-r- and the unfamiliar initial vowel was also mutilated, so that eventually the name was considered as no more than a feminine form of Hilary (of which the initial aspirate was in any case variable).
Girl/Female
Indian
Dedicate, Presenting
Girl/Female
Bengali, Indian
Dedicate
Girl/Female
Hindu, Indian, Malayalam, Marathi, Tamil, Telugu
Devotee of God; Daughter of God; Dedicated; Tribute; To Dedicate Something
Girl/Female
Biblical
According to variable songs or tunes.
Girl/Female
Indian
One who Willingly Dedicate Herself
Biblical
respiration; conversion; taking captive;man sitting in Nob;dweller on the mount, he that predicts;
Girl/Female
Tamil
Arpita | à®…à®°à¯à®ªà®¿à®¤à®¾
Dedicate, Presenting
Arpita | à®…à®°à¯à®ªà®¿à®¤à®¾
Biblical
according to variable songs or tunes,
Boy/Male
Hindu, Indian, Tamil
Sun; Moon; Dedicate
Surname or Lastname
English
English : topographic name for someone living on (and farming) a hide of land, Old English hī(gi)d. This was a variable measure of land, differing from place to place and time to time, and seems from the etymology to have been originally fixed as the amount necessary to support one (extended) family (Old English hīgan, hīwan ‘household’). In some cases the surname is habitational, from any of the many minor places named with this word, as for example Hyde in Greater Manchester, Bedfordshire, and Hampshire.English : variant of Ide, with inorganic initial H-. Compare Herrick.Jewish (American) : Americanized spelling of Haid.
Girl/Female
Tamil
Arpitha | à®…à®°à¯à®ªà®¿à®¤à®¾
Dedicate, Presenting
Arpitha | à®…à®°à¯à®ªà®¿à®¤à®¾
Girl/Female
Indian
Dedicate, Presenting
Boy/Male
Anglo, Australian, British, English, French, Swedish
Variable; Brave with the Spear; Spear Rule
Boy/Male
Anglo, British, English
Variable
Girl/Female
Bengali, Indian
Dedicate
Surname or Lastname
English (of Norman origin)
English (of Norman origin) : habitational name from Saint-Hilaire-du-Harcouët in La Manche, which gets its name from the dedication of its church to St. Hilary, or alternatively from either of the places, in La Manche and Somme, called Saint-Lô. Both of the latter are named from a 6th-century St. Lauto, bishop of Coutances; his name is of variable form in the sources and uncertain etymology.North German : habitational name for someone from Sandel.Jewish (eastern Ashkenazic) : occupational name for a cobbler or shoemaker, Yiddish sandler (from Hebrew sandelar, from Late Latin sandalarius, an agent derivative of sandalium ‘shoe’).
PREDICATE VARIABLE
PREDICATE VARIABLE
Male
English
Anglicized form of Hebrew Yehowash, JEHOASH means "given by the Lord" or "whom Jehovah gave." In the bible, this is the name of a son of king Ahaziah and a son of king Jehoahaz.
Boy/Male
Tamil
Lord Vishnu, Intelligent
Girl/Female
Indian, Sanskrit, Tamil
Beautiful Spring
Girl/Female
Celtic
Legendsry tale.
Girl/Female
Tamil
Girl/Female
Indian, Punjabi, Sikh
Shape
Girl/Female
Tamil
Girl/Female
Indian
Painting, Picture, A Nakshatra
Boy/Male
Arabic, Muslim
Jewel; Gold
Female
Hebrew
(×ï‹×¨Ö´×™×ª) Variant form of Hebrew Ora, ORIT means "light."
PREDICATE VARIABLE
PREDICATE VARIABLE
PREDICATE VARIABLE
PREDICATE VARIABLE
PREDICATE VARIABLE
a.
Capable of being predicated or affirmed of something; affirmable; attributable.
a.
Predicated.
v. t.
To found; to base.
p. pr. & vb. n.
of Prejudicate
a.
Expressing affirmation or predication; affirming; predicating, as, a predicative term.
a.
Joining subject and predicate; copulative.
n.
One who predicates, affirms, or proclaims; specifically, a preaching friar; a Dominican.
p. pr. & vb. n.
of Eradicate
v. t.
To root out; to destroy utterly; to extirpate; as, to eradicate diseases, or errors.
v. t.
To assert to belong to something; to affirm (one thing of another); as, to predicate whiteness of snow.
v. t.
To set apart and consecrate, as to a divinity, or for sacred uses; to devote formally and solemnly; as, to dedicate vessels, treasures, a temple, or a church, to a religious use.
imp. & p. p.
of Predict
imp. & p. p.
of Predicate
v. t.
That which is affirmed or denied of the subject. In these propositions, "Paper is white," "Ink is not white," whiteness is the predicate affirmed of paper and denied of ink.
imp. & p. p.
of Eradicate
v. t.
To tell or declare beforehand; to foretell; to prophesy; to presage; as, to predict misfortune; to predict the return of a comet.
imp. & p. p.
of Prejudicate
v. i.
To affirm something of another thing; to make an affirmation.
v. t.
The word or words in a proposition which express what is affirmed of the subject.
p. pr. & vb. n.
of Predicate