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Rules of Inference

  • The basis for proof systems is the use of correct rules of inference that can be applied directly to sentences to derive conclusions that are guaranteed to be correct under all interpretations

    • Since the interpretations are not enumerated, time and space can often be saved

  • A rule of inference is a pattern of reasoning consisting of:

    • One set of sentence schemata, called premises , and

    • A second set of sentence schemata, called conclusions

  • A rule of inference is sound if and only if, for every instance, the premises logically entail the conclusions

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