NTA-NET (UGC-NET) Computer Science & Applications (87) Discrete Mathematics-Refutation, Resolution, Refinements to Resolution Study Material (Page 1 of 3)

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Resolution: Resolution Rule, What Steps Do We Follow for Resolution

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Resolution

It is a powerful rule of inference for Propositional Logic. Using Propositional Resolution, it is possible to build a theorem prover that is sound and complete for all of Propositional Logic. Further, the search space using propositional resolution is much smaller than for standard propositional logic.

  • More technically, Resolution is a rule of inference leading to a refutation theorem-proving technique for sentences in propositional logic and first-order logic. In other words, iteratively applying the resolution rule in a suitable way allows for telling whether a propositional formula is satisfiable and for proving that a formula is satisfiable.

Resolution Rule

In propositional l…

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Refutation: Who Uses this Mechanism

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Refutation

Just like the dictionary meaning, here too the word “refute” would mean to disprove. When the resolution process is used to prove inconsistency, it is called as refutation. The binary tree that we have shown above is also used showing refutation in resolution. The purpose of refutation, the binary tree must result in the empty clause. Such a depiction is called as a refutation tree.

The Refutation
  • In the “leaf node” , the presence of an empty clause means inconsistency, thus refutation
  • In fact,…

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