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Hilbert system

In logic, more specifically proof theory, a Hilbert system, sometimes called Hilbert calculus, Hilbert-style system, Hilbert-style proof system, Hilbert-style deductive system or Hilbert–Ackermann system, is a type of formal proof system attributed to Gottlob Frege and David Hilbert. These deductive systems are most often studied for first-order logic…

Propositional logic, Overview & Predicate logic (example system)

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Overview

Formal deductions

Propositional logic

Predicate logic (example system)

Conservative extensions

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Map overview Semantic statistics

Hilbert system

Nodes64
Edges63
Triples39
Avg. degree1.97
Density0.03125
Components1

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Hilbert system

Top relations

related to Frege's Begriffsschrift · 11
Hilbert system → Ancient Greek, Axiomatic, BC, Begriffsschrift, But, Euclid's Elements, Frege's, Geometry, Gottlob Frege's, Hilbert, Proposition
related to Formal deductions · 8
Hilbert system → For, Gamma, Hilbert, In, Suppose, The, These, Thus
related to Propositional logic · 6
Hilbert system → Frege, Hilbert, One, P2, Schematic, The
related to Conservative extensions · 5
Hilbert system → Given, Hilbert, It, These, When
related to Predicate logic (example system) · 5
Hilbert system → Hilbert, Later, The, There, We
see also · 2
Hilbert system → Hilbert, List
is a · 1
Hilbert system → axiomatic system

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Important terminology

hilbert axioms system systems logic rules axiom proof displaystyle rule inference schemas logical propositional substitution use modus ponens set used

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Hilbert systemis aaxiomatic system0.90text
this that ranges over formulae is called a 'schematic variable'.With a second rule of uniform substitutioninstance ofA variable0.80text
Hilbert systemrelated to Conservative extensionsIt0.60section
Hilbert systemrelated to Conservative extensionsHilbert0.60section
Hilbert systemrelated to Conservative extensionsGiven0.60section
Hilbert systemrelated to Conservative extensionsThese0.60section
Hilbert systemrelated to Conservative extensionsWhen0.60section
Hilbert systemrelated to Formal deductionsIn0.60section
Hilbert systemrelated to Formal deductionsHilbert0.60section
Hilbert systemrelated to Formal deductionsThese0.60section
Hilbert systemrelated to Formal deductionsSuppose0.60section
Hilbert systemrelated to Formal deductionsGamma0.60section

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