FOL meaning in Maths ?

Answer:

What is First Order Logic mean?

First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—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 propositions such as "Socrates is a man", one can have expressions in the form "there exists x such that x is Socrates and x is a man", where "there exists" is a quantifier, while x is a variable. This distinguishes it from propositional logic, which does not use quantifiers or relations; in this sense, propositional logic is the foundation of first-order logic.

A theory about a topic is usually a first-order logic together with a specified domain of discourse (over which the quantified variables range), finitely many functions from that domain to itself, finitely many predicates defined on that domain, and a set of axioms believed to hold about them. Sometimes, "theory" is understood in a more formal sense, which is just a set of sentences in first-order logic.

The adjective "first-order" distinguishes first-order logic from higher-order logic, in which there are predicates having predicates or functions as arguments, or in which predicate quantifiers or function quantifiers or both are permitted.: 56 In first-order theories, predicates are often associated with sets. In interpreted higher-order theories, predicates may be interpreted as sets of sets.

There are many deductive systems for first-order logic which are both sound (i.e., all provable statements are true in all models) and complete (i.e. all statements which are true in all models are provable). Although the logical consequence relation is only semidecidable, much progress has been made in automated theorem proving in first-order logic. First-order logic also satisfies several metalogical theorems that make it amenable to analysis in proof theory, such as the Löwenheim–Skolem theorem and the compactness theorem.

First-order logic is the standard for the formalization of mathematics into axioms, and is studied in the foundations of mathematics.Peano arithmetic and Zermelo–Fraenkel set theory are axiomatizations of number theory and set theory, respectively, into first-order logic.No first-order theory, however, has the strength to uniquely describe a structure with an infinite domain, such as the natural numbers or the real line. Axiom systems that do fully describe these two structures (that is, categorical axiom systems) can be obtained in stronger logics such as second-order logic.

The foundations of first-order logic were developed independently by Gottlob Frege and Charles Sanders Peirce. For a history of first-order logic and how it came to dominate formal logic, see José Ferreirós (2001).

reference

Full Form	Category
First Order Language	Academic & Science
Forms Overlay Language	Academic & Science
Free On Loan	Business
Free On Lorry	Business
Functional Operations Leader	Business
Friend Of The Library	Community
Foundations Of Leadership	Community
Form Object Library	Computing
Free On Line	Computing
Flash of Light (World of Warcraft)	Computing
Folder Protocol	Cryptocurrency
1st Reader Folder of Saved Messages	File Type
Flying Optic Linear	General
Friends Of Levys	General
Fact Of Life	General
Friends Of Laphroaig	General
Fear Of Loss	General
Fan Of LEGO	General
Find Occupation Later	General
Fog Lamps	General
Formula One Licensing	General
Fairbanks Offroad Lions	General
Forum Otomotif Lampung	General
Front Outside Left	General
Forester l	General
Friends Of Lulu	General
Fond Of Leather	General
Front of Liberation	General
Friends of Liberia	General
Form and Overlay Language	General
Flash of Light	General
Full Over Lap	General
Flavor of Love	General
Fear Of Litigation	Governmental
F*** Our Lives	Internet
First Or Last	Internet
First Order Logic	Maths
Fibre Optic Laryngoscopy	Medical
Forward Operating Location	Military and Defence
Fiber Optic Link	Networking