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First-order logic—also called predicate logic, predicate calculus, quantificational logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables.
A predicate is a statement or mathematical assertion that contains variables, sometimes referred to as predicate variables, and may be true or false depending on those variables’ value or values. In propositional logic, atomic formulas are sometimes regarded as zero-place predicates. [1] In a sense, these are nullary (i.e. 0-arity) predicates.
In mathematical logic, a first-order predicate is a predicate that takes only individual(s) constants or variables as argument(s). [1] Compare second-order predicate and higher-order predicate . This is not to be confused with a one-place predicate or monad, which is a predicate that takes only one argument.
In mathematical logic, a sentence (or closed formula) [1] of a predicate logic is a Boolean-valued well-formed formula with no free variables.A sentence can be viewed as expressing a proposition, something that must be true or false.
In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some". It is usually denoted by the logical operator symbol ∃, which, when used together with a predicate variable, is called an existential quantifier (" ∃x" or "∃(x)" or ...
In logic, a symbol that represents a function from individuals or tuples of individuals to truth values, essentially a generalization of a predicate. [234] predicate functor logic A logical system that combines elements of predicate logic with the concept of functors, allowing for a more expressive representation of properties and relations ...
A Boolean-valued function (sometimes called a predicate or a proposition) is a function of the type f : X → B, where X is an arbitrary set and where B is a Boolean domain, i.e. a generic two-element set, (for example B = {0, 1}), whose elements are interpreted as logical values, for example, 0 = false and 1 = true, i.e., a single bit of information.
In predicate logic, generalization (also universal generalization, universal introduction, [1] [2] [3] GEN, UG) is a valid inference rule. ... Example of a proof