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Higher-order logic

In mathematics and logic, a higher-order logic (HOL) is a form of logic that is distinguished from first-order logic by additional quantifiers and, sometimes, stronger semantics. Higher-order logics with their standard semantics are more expressive, but their model-theoretic properties are less well-behaved than those of first-order logic.

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Overview

Quantification scope

Semantics

Properties

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Higher-order logic

Nodes45
Edges44
Triples84
Avg. degree1.96
Density0.044444
Components1

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Higher-order logic

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related to References · 46
Higher-order logic → An Introduction, Andrews, Automation, Bart, Benzmüller, Blackwell, Cambridge University Press, Case, Categorical Logic, Christoph, Classical Logic II, Computational Logic, Dale, Dov, Elsevier, Foundations, Foundations Without Foundationalism, Handbook, Higher Order Categorical Logic, Higher Order Logic
related to External links · 16
Higher-order logic → Andrews, Artificial Intelligence, Church's Type Theory, Dale, Dec, Encyclopedia, Enderton, Herbert, Higher-order, Logic, Mar, Miller, Peter, Philosophy, Second-order, Stanford Encyclopedia
related to Semantics · 10
Higher-order logic → For, HOL, However, In, Kurt Gödel, Löwenheim, The, The Löwenheim, There, Thus
related to Properties · 6
Higher-order logic → Church's, Gérard Huet, Higher-order, Jaakko Hintikka, Up, Using
see also · 3
Higher-order logic → First-order, Many-sorted, Zeroth-order
related to Quantification scope · 2
Higher-order logic → First-order, Higher-order
is a · 1
Higher-order logic → union of first

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Important terminology

logic higher-order semantics first-order hol type theory second-order isbn also standard simple types properties quantifiers proof model-theoretic individuals sets example

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Higher-order logicis aunion of first0.90text
Higher-order logicrelated to External linksAndrews0.60section
Higher-order logicrelated to External linksPeter0.60section
Higher-order logicrelated to External linksChurch's Type Theory0.60section
Higher-order logicrelated to External linksStanford Encyclopedia0.60section
Higher-order logicrelated to External linksPhilosophy0.60section
Higher-order logicrelated to External linksMiller0.60section
Higher-order logicrelated to External linksDale0.60section
Higher-order logicrelated to External linksLogic0.60section
Higher-order logicrelated to External linksHigher-order0.60section
Higher-order logicrelated to External linksEncyclopedia0.60section
Higher-order logicrelated to External linksArtificial Intelligence0.60section

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