5. Resolution
The chapter explores the resolution inference rule, a vital concept in logic used extensively in programming, particularly in AI applications like PROLOG. It defines how pairs of clauses with common literals can be resolved to form new conclusions, along with the introduction of proof by resolution refutation as a method for validating arguments. The content also delves into resolving sets of clauses and discusses the significance of unsatisfiability in the context of resolution.
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What we have learnt
- The resolution rule allows for canceling out common literals in clauses to derive conclusions.
- The resolvent of a set of clauses helps identify unsatisfiability, which is critical in logical proofs.
- Proof by resolution refutation can determine the validity of arguments by checking the unsatisfiability of premises when combined with the negation of the conclusion.
Key Concepts
- -- Resolution Rule
- A logical rule that allows the cancellation of a common literal present in both a positive and negative form across two clauses to derive a new clause.
- -- Resolvent
- The resulting clause derived from resolving two clauses using the resolution rule.
- -- Proof by Resolution Refutation
- A method for proving the validity of an argument by demonstrating that the conjunction of premises and the negation of the conclusion is unsatisfiable.
- -- Unsatisfiability
- A condition where no truth assignment exists that makes all clauses true, indicating that the set of clauses is inconsistent.
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