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Resolution - Principle

  • Resolution is a refutation system .

    • To prove a statement we attempt to refute its negation

  • Basic idea: Given a consistent set of axioms KB and goal sentence Q , we want to show that KB Q

    • This means that every interpretation I that satisfies KB also satisfies Q

    • Any interpretation I only satisfies either Q or ¬ Q, but not both

    • Therefore, if in fact KB Q holds , an interpretation that satisfies KB , satisfies Q and does not satisfy ¬ Q

        Hence KB { ¬ Q } is unsatisfiable, i.e., it is false under all interpretations

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