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First-order logic

In mathematics, philosophy, linguistics, and computer science, first-order logic (FOL), also called predicate logic, predicate calculus, or quantificational logic, is a type of formal system. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables. Rather than propositions such as "all…

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Overview

Introduction

Syntax

Semantics

Deductive systems

Equality and its axioms

Metalogical properties

Limitations

Restrictions, extensions, and variations

Automated theorem proving and formal methods

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First-order logic

Nodes215
Edges214
Triples321
Avg. degree1.99
Density0.009302
Components1

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First-order logic

Top relations

related to References · 101
First-order logic → Ackermann, ACM Transactions, Alfred, American Mathematical Society, Amsterdam, An Introduction, Available, Avigad, Barwise, Berlin, Blackwell, Bocheński, Business Media, California, Chelsea, Chicago, Chicago Press, Classical Logic, Computational Logic, Concise Introduction
related to External links · 25
First-order logic → Cambridge Mathematical Tripos, Classical Logic, Computation, Covers, EMS Press, Encyclopedia, Introduction, John Fremlin, Karl, Logic, Magnus, Mathematics, Metamath, Philosophy, Podnieks, Predicate, Principia Mathematica, Set Theory, Shapiro, Stanford Encyclopedia
related to Completeness and undecidability · 14
First-order logic → Alan Turing, Alonzo Church, David Hilbert, Entscheidungsproblem, Gödel's, However, If, Kurt Gödel, Naively, Their, This, Thus, Unlike, Wilhelm Ackermann
related to Restricted languages · 12
First-order logic → Because, First-order, For, In, It, NAND, NOR, Peirce, Sheffer, Similarly, Since, This
related to Algebraizations · 11
First-order logic → Alfred Tarski, An, Cylindric, Lindenbaum, Paul Halmos, Polyadic, Predicate, Tarski, There, This, Willard Quine
related to First-order logic without equality · 10
First-order logic → An, If, In, Leibniz's, Löwenheim, Skolem, That, The, This, When
related to Decidable fragments · 9
First-order logic → Decidable, Examples, Other, Pratt-Hartmann, Schönfinkel, See, The Bernays, There, These
related to Lindström's theorem · 9
First-order logic → Chapter XIII, Ebbinghaus, Flum, He, Lindström, Lindström's, Löwenheim, Per Lindström, Skolem
related to Löwenheim–Skolem theorem · 9
First-order logic → For, Löwenheim, One, Since, Skolem, Skolem's, That, The Löwenheim, When
related to Additional quantifiers · 8
First-order logic → Additional, Also, Bounded, First-order, George Boolos, Qx, Sometimes, This

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Important terminology

logic first-order displaystyle formula symbols formulas interpretation theory one symbol predicate set true example logical equality may variables variable domain

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
First-order logicis aextension of propositional logic.A theory about a topic0.90text
First-order logicis astandard for the formalization of mathematics into axioms0.90text
second-order logic.Historically speakinginstance ofcan be obtained in stronger logics0.80text
the foundations of first-order logic were developed independently by Gottlob Fregeinstance ofcan be obtained in stronger logics0.80text
Charles Sanders Peirce in the 1880sinstance ofcan be obtained in stronger logics0.80text
pinstance ofby variables0.80text
qinstance ofby variables0.80text
Philinstance ofa non-logical predicate symbol0.80text
the Sheffer strokeinstance ofthese two constants can only be expressed using quantifiers.Additional logical connectives0.80text
Dpqinstance ofthese two constants can only be expressed using quantifiers.Additional logical connectives0.80text
Pinstance ofThese are often denoted by uppercase letters0.80text
Qinstance ofThese are often denoted by uppercase letters0.80text

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