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Satisfiability

In mathematical logic, a formula is satisfiable if it is true under some assignment of values to its variables. For example, the formula x + 3 = y {\displaystyle x+3=y} is satisfiable because it is true when x = 3 {\displaystyle x=3} and y = 6 {\displaystyle y=6} , while the formula x + 1 = x {\displaystyle x+1=x} is not satisfiable over the integers.…

Products, Overview & Finite satisfiability

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Overview

Mathematical logicFormulaVariablesValiditySyntax
31 related topics

Finite satisfiability

Finite model propertyFinite model theoryConjunctionConstantsDecidable
7 related topics

Satisfiability in first-order logic

UndecidableCo-RE-completeSemidecidableDavid HilbertChurch–Turing theorem
5 related topics

Propositional satisfiability for classical logic

Classical propositional logicNP-completeComputational complexity theory
3 related topics

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Overview

Reduction of validity to satisfiability

Propositional satisfiability for classical logic

Satisfiability in first-order logic

Satisfiability in model theory

Finite satisfiability

Numerical constraints

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Satisfiability

Nodes60
Edges59
Triples40
Avg. degree1.97
Density0.033333
Components1

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Satisfiability

Top relations

related to Further reading · 14
Satisfiability → An Algorithmic Point, Biere, Business Media, Daniel Kroening, Decision Procedures, Handbook, Heule, IOS Press, ISBN, Maaren, Ofer Strichman, Springer Science, View, Walsh
related to Satisfiability in first-order logic · 13
Satisfiability → Church, David Hilbert, Entscheidungsproblem, FOL, For, Gödel's, If, More, RE-complete, So, The, This, Turing
related to Reduction of validity to satisfiability · 4
Satisfiability → For, In, NP, Put
related to Finite satisfiability · 3
Satisfiability → Finite, For, This
is a · 2
Satisfiability → NP-complete problem, semantic property because it relates to the meaning of the symbols
related to Propositional satisfiability for classical logic · 2
Satisfiability → In, NP-complete
see also · 1
Satisfiability → NP-complete

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Important terminology

formula satisfiable validity logic theory problem true decidable finite first-order one model whether displaystyle propositional example symbols variables theorem valid

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Satisfiabilityis asemantic property because it relates to the meaning of the symbols0.90text
Satisfiabilityis aNP-complete problem0.90text
Peano arithmetic are satisfiable because they are true in the natural numbersinstance oftheories of arithmetic0.80text
Satisfiabilityrelated to Finite satisfiabilityFor0.60section
Satisfiabilityrelated to Finite satisfiabilityThis0.60section
Satisfiabilityrelated to Finite satisfiabilityFinite0.60section
Satisfiabilityrelated to Further readingDaniel Kroening0.60section
Satisfiabilityrelated to Further readingOfer Strichman0.60section
Satisfiabilityrelated to Further readingDecision Procedures0.60section
Satisfiabilityrelated to Further readingAn Algorithmic Point0.60section
Satisfiabilityrelated to Further readingView0.60section
Satisfiabilityrelated to Further readingSpringer Science0.60section

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