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The propositional calculus [a] is a branch of logic. [1] It is also called propositional logic, [2] statement logic, [1] sentential calculus, [3] sentential logic, [1] or sometimes zeroth-order logic. [4] [5] It deals with propositions [1] (which can be true or false) [6] and relations between propositions, [7] including the construction of ...
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 ...
In 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 ...
Automated theorem proving. Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. Automated reasoning over mathematical proof was a major impetus for the development of computer science .
O ( n ) {\displaystyle O (n)} (basic algorithm) In logic and computer science, the Davis–Putnam–Logemann–Loveland ( DPLL) algorithm is a complete, backtracking -based search algorithm for deciding the satisfiability of propositional logic formulae in conjunctive normal form, i.e. for solving the CNF-SAT problem.
In logic and computer science, the Davis–Putnam algorithm was developed by Martin Davis and Hilary Putnam for checking the validity of a first-order logic formula using a resolution -based decision procedure for propositional logic. Since the set of valid first-order formulas is recursively enumerable but not recursive, there exists no ...
A propositional proof system P p-simulates Q (written as P ≤ pQ) when there is a polynomial-time function F such that P ( F ( x )) = Q ( x) for every x. [1] That is, given a Q -proof x, we can find in polynomial time a P -proof of the same tautology. If P ≤ pQ and Q ≤ pP, the proof systems P and Q are p-equivalent.
In formal logic, Horn-satisfiability, or HORNSAT, is the problem of deciding whether a given set of propositional Horn clausesis satisfiable or not. Horn-satisfiability and Horn clauses are named after Alfred Horn. A Horn clause is a clausewith at most one positive literal, called the headof the clause, and any number of negative literals ...