In mathematical logic, a predicate variable is a predicate letter which functions as a "placeholder" for a relation (between terms), but which has not been specifically assigned any particular relation (or meaning). Common symbols for denoting predicate variables include capital roman letters such as , and , or lower case roman letters, e.g., .[1] In first-order logic, they can be more properly called metalinguistic variables. In higher-order logic, predicate variables correspond to propositional variables which can stand for well-formed formulas of the same logic, and such variables can be quantified by means of (at least) second-order quantifiers.
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In mathematical logic, a predicatevariable is a predicate letter which functions as a "placeholder" for a relation (between terms), but which has not...
{\displaystyle \gamma } . Propositional variables with no object variables such as x and y attached to predicate letters such as Px and xRy, having instead...
domain. It asserts that a predicate within the scope of a universal quantifier is true of every value of a predicatevariable. It is usually denoted by...
by the logical operator symbol ∃, which, when used together with a predicatevariable, is called an existential quantifier ("∃x" or "∃(x)" or "(∃x)"). Existential...
symbol and x {\displaystyle x} is a variable. Monadic predicate calculus can be contrasted with polyadic predicate calculus, which allows relation symbols...
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...
corresponds to a predicatevariable; the contents of a table to a relation; key constraints, other constraints, and SQL queries correspond to predicates. However...
or predicatevariable in axiom schemas and P {\displaystyle P} or Q {\displaystyle Q} is used for particular such predicates. The word "predicate" is...
Q(John))} ". In this case, the existential quantifier is applied to the predicatevariable " Q {\displaystyle Q} ". The added expressive power is especially...
Predicate transformer semantics were introduced by Edsger Dijkstra in his seminal paper "Guarded commands, nondeterminacy and formal derivation of programs"...
defined as Predicate symbols F {\displaystyle F} , G {\displaystyle G} , etc. (with appropriate arities, which are left implicit) Singular variable symbols...
expressing computation based on function abstraction and application using variable binding and substitution. It is a universal model of computation that can...
mathematical logic and computer science, a variable may be said to be either free or bound. A free variable is a notation (symbol) that specifies places...
formal expression that denotes an atomic formula. For predicate logic, the atoms are predicate symbols together with their arguments, each argument being...
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...
be made to avoid variable capture). Others (maybe most) just call parameters passed to (or operated on by) an open predicatevariables, and when defining...
Laplacian of the indicator Dirac delta Extension (predicate logic) Free variables and bound variables Heaviside step function Identity function Iverson...
In logic, a metavariable (also metalinguistic variable or syntactical variable) is a symbol or symbol string which belongs to a metalanguage and stands...
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