Interactive Formula Resolution For Free

A resolution technique The steps are as follows. All sentences in the knowledge base and the negation of the sentence to be proved (the conjecture) are conjunctively connected. The resulting sentence is transformed into a conjunctive normal form with the conjuncts viewed as elements in a set, S, of clauses.

The resolution inference rule takes two premises in the form of clauses (A ? x) and (B ? ¬x) and gives the clause (A ? B) as a conclusion. The two premises are said to be resolved and the variable x is said to be resolved away. Resolving the two clauses x and x gives the empty clause.

The resolution principle, due to Robinson (1965), is a method of theorem proving that proceeds by constructing refutation proofs, i.e., proofs by contradiction. This method has been exploited in many automatic theorem provers. The resolution principle applies to first-order logic formulas in Skolemized form.

The resolution rule is applied to all possible pairs of clauses that contain complementary literals. After each application of the resolution rule, the resulting sentence is simplified by removing repeated literals. If the clause contains complementary literals, it is discarded (as a tautology).

In resolution method, we use Proof by Refutation technique to prove the given statement. The key idea for the resolution method is to use the knowledge base and negated goal to obtain null clause (which indicates contradiction). Resolution method is also called Proof by Refutation.

The resolution inference rule takes two premises in the form of clauses (A ? x) and (B ? ¬x) and gives the clause (A ? B) as a conclusion. The two premises are said to be resolved and the variable x is said to be resolved away. Resolving the two clauses x and x gives the empty clause.

The Resolution Principle : Given a set S of clauses, a (resolution) deduction of C from S is a finite sequence C1, C2, ... , Ck of clauses such that each Ci either is a clause in S or a resolvent of clauses preceding C and Ck = C.