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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 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 mathematical logic, predicate logic is the generic term for symbolic formal systems like first-order logic, second-order logic, many-sorted logic or infinitary logic. This formal system is distinguished from other systems such as propositional logic in that its formulas contain variables which can be quantified .
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 ...
Lindström's theorem states that first-order logic is the strongest (subject to certain constraints) logic satisfying both compactness and completeness. A completeness theorem can be proved for modal logic or intuitionistic logic with respect to Kripke semantics.
In propositional calculus, a propositional function 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 is not defined or specified (thus being a free variable), which leaves the statement undetermined.
In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.