Resolution (logic)In mathematical logic and automated theorem proving, resolution is a rule of inference leading to a refutation complete theorem-proving technique for sentences in propositional logic and first-order logic. For propositional logic, systematically applying the resolution rule acts as a decision procedure for formula unsatisfiability, solving the (complement of the) Boolean satisfiability problem. For first-order logic, resolution can be used as the basis for a semi-algorithm for the unsatisfiability problem of first-order logic, providing a more practical method than one following from Gödel's completeness theorem.
Clause (logic)In logic, a clause is a propositional formula formed from a finite collection of literals (atoms or their negations) and logical connectives. A clause is true either whenever at least one of the literals that form it is true (a disjunctive clause, the most common use of the term), or when all of the literals that form it are true (a conjunctive clause, a less common use of the term). That is, it is a finite disjunction or conjunction of literals, depending on the context.
DatalogDatalog is a declarative logic programming language. While it is syntactically a subset of Prolog, Datalog generally uses a bottom-up rather than top-down evaluation model. This difference yields significantly different behavior and properties from Prolog. It is often used as a query language for deductive databases. Datalog has been applied to problems in data integration, networking, program analysis, and more. A Datalog program consists of facts, which are statements that are held to be true, and rules, which say how to deduce new facts from known facts.
Boolean satisfiability problemIn logic and computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated SATISFIABILITY, SAT or B-SAT) is the problem of determining if there exists an interpretation that satisfies a given Boolean formula. In other words, it asks whether the variables of a given Boolean formula can be consistently replaced by the values TRUE or FALSE in such a way that the formula evaluates to TRUE. If this is the case, the formula is called satisfiable.
