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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, so that rather than ...
First-order logic includes the same propositional connectives as propositional logic but differs from it because it articulates the internal structure of propositions. This happens through devices such as singular terms, which refer to particular objects, predicates , which refer to properties and relations, and quantifiers, which treat notions ...
There are three common ways of handling this in first-order logic: Use first-order logic with two types. Use ordinary first-order logic, but add a new unary predicate "Set", where "Set(t)" means informally "t is a set". Use ordinary first-order logic, and instead of adding a new predicate to the language, treat "Set(t)" as an abbreviation for ...
Gödel's completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first-order logic . The completeness theorem applies to any first-order theory: If T is such a theory, and φ is a sentence (in the same language) and every model of T is a model of ...
However, the relational language RML is an imperative programming language [31] whose core construct is a relational expression, which is similar to an expression in first-order predicate logic. Other relational programming languages are based on the relational calculus [ 32 ] or relational algebra.
First-order logic is a particular formal system of logic. Its syntax involves only finite expressions as well-formed formulas, while its semantics are characterized by the limitation of all quantifiers to a fixed domain of discourse. Early results from formal logic established limitations of first-order logic.
The propositional calculus[ a] is a branch of logic. [ 1] It is also called propositional logic, [ 2] statement logic, [ 1] sentential calculus, [ 3] sentential logic, [ 1] or sometimes zeroth-order logic. [ 4][ 5] It deals with propositions [ 1] (which can be true or false) [ 6] and relations between propositions, [ 7] including the ...
The term classical logic refers primarily to propositional logic and first-order logic. [4] It is the dominant logical system accepted and used by most theorists. But the philosophy of logic is also concerned with non-classical or alternative logics. [ 2 ]