Resolution in Artificial intelligence

Resolution method is an inference rule which is used in both Propositional as well as First-order Predicate Logic This method is basically used for proving the satisfiability of a sentence In resolution method

Resolution in Propositional Logic

  • In propositional logic, resolution method is the only inference rule which gives a new clause when two or more clauses are coupled together
  • Using propositional resolution, it becomes easy to make a theorem prover sound and complete for all

The process followed to convert the propositional logic into resolution method contains the below steps:

  • Convert the given axiom into clausal form, i.e., disjunction form.
  • Apply and proof the given goal using negation rule
  • Use those literals which are needed to prove
  • Solve the clauses together and achieve the goal

Example of Propositional Resolution

Consider the following Knowledge Base:

  • The humidity is high or the sky is cloudy.
  • If the sky is cloudy, then it will rain.
  • If the humidity is high, then it is hot
  • It is not hot.

Goal: It will rain.

Use propositional logic and apply resolution method to prove that the goal is derivable from the given knowledge base

Solution: Let’s construct propositions of the given sentences one by one:

  • Let, P: Humidity is high
    • Q: Sky is cloudy.

It will be represented as P V Q.

  • Q: Sky is cloudy
    • Let, R: It will rain

It will be represented as bQ → R

  • P: Humidity is high
    • Let, S: It is hot

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