Satisfiability

Satisfiability is the property of a logical formula that is true under at least one interpretation of its symbols. A satisfying interpretation is called a model.

Interpretation (logic): An assignment of meanings or values to the symbols of a formal language. An interpretation supplies the conditions under which a formula can be evaluated as true or false.
Propositional logic: A formal system for reasoning about propositions combined by logical connectives. Propositional satisfiability asks whether a formula in this system can be true.
Boolean satisfiability problem: The decision problem of determining whether a propositional formula has a satisfying truth assignment. SAT is the computational form of propositional satisfiability.
Satisfiability problem: A decision problem asking whether a formal formula has a model. The general problem includes logics beyond Boolean satisfiability and can have different complexity.
Model theory: The study of formal languages, structures, and the relationships between them. Satisfiability is defined through structures that make sentences true.
Predicate logic: A formal logic with variables, predicates, quantifiers, and domains of objects. In predicate logic, satisfiability depends on both an interpretation and a domain.
2-satisfiability: The satisfiability problem for formulas whose clauses contain at most two literals. This restricted case is solvable in polynomial time, unlike general SAT unless P equals NP.
2-SAT: The decision problem of determining whether a Boolean formula with clauses of at most two literals is satisfiable. Unlike unrestricted SAT, 2-SAT has a polynomial-time decision algorithm.
Truth table: A table listing a compound proposition's truth value for every assignment of its variables. For finite propositional formulas, a truth table directly checks whether any assignment satisfies the formula.
Logical consequence: A relation in which a conclusion is true in every model of given premises. Satisfiability asks whether a model exists; consequence asks whether all premise models preserve a conclusion.

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