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Also known as: Logical Satisfiability, Model Satisfiability
A property indicating whether there exists an interpretation or model that makes a formula or set of statements true.
DESCRIPTION
Satisfiability asks if some interpretation satisfies given statements. In propositional logic, the SAT problem is NP-complete and foundational to many solvers. In description logics, class satisfiability ensures concepts are non-contradictory. SAT solvers and OWL reasoners compute satisfiability to support verification and inference. Understanding satisfiability underpins consistency checks, entailment, and formal modeling practices.
ALTERNATIVE DEFINITIONS
Wikipedia
In logic, satisfiability is the property of a logical formula that there exists an interpretation that makes the formula true.
Concise general definition across logical systems.
Stanford Encyclopedia of Philosophy
A formula is satisfiable if there is at least one assignment of truth values to its variables that makes it true.
Focuses on propositional logic truth assignments.
RELATED TERMS
Consistency Checking Entailment SAT Solver CNF Propositional Logic Description Logic Reasoner
COMPETING TERMS
Validity Unsatisfiability
KNOWLEDGE AREAS
Mathematics AI Semantic & Knowledge Modeling Data Science
TARGET AUDIENCE
AI Engineer Data Scientist MLOps Engineer Data Modeler Data Architect
EXTERNAL SOURCES
- Wikipedia - Satisfiability
- SAT Competition - Benchmarking of SAT solvers
- MiniSat - MiniSat solver information
- W3C - OWL 2 overview mentioning class satisfiability
TOP QUESTIONS
What is satisfiability in logic?
It means there exists a model or interpretation that makes a formula or set of statements true.
Category: Definition
Why does satisfiability matter in AI?
It underlies verification, constraint solving, and reasoning; unsatisfiable models indicate contradictions that must be resolved.
Category: Relevancy
How is satisfiability checked?
SAT solvers handle propositional formulas; OWL reasoners check concept satisfiability in ontologies.
Category: How-to
What is a hot topic around Satisfiability?
Scalable SAT solving for combinatorial optimization and formal verification remains an active research and engineering area.
Category: Topic
What’s the relation between satisfiability and consistency?
In many logics, global consistency implies each component is satisfiable; unsatisfiability indicates inherent contradictions.
Category: Definition
What are common mistakes in satisfiability reasoning?
Misencoding constraints, ignoring implicit assumptions, and failing to interpret solver outputs correctly.
Category: Mistakes
What risks occur when models are unsatisfiable?
Systems may fail, produce no valid solutions, or mislead users with contradictory results.
Category: Risks
What competes with satisfiability as a property?
Validity concerns formulas true in all interpretations, while satisfiability only requires one model.
Category: Alternatives
Where to learn more about satisfiability?
Explore SAT Competition resources, MiniSat documentation, and foundational logic texts in SEP.
Category: Learning