The process by which the soundness of an inference rule is established through truth tables can be extended to entire classes of inferences. There are certain patterns of inferences that occur over and over, and their soundness can be shown once and for all. Then the pattern can be captured in what is called an inference rule. Once this has been done, the rule can be used to make inferences without going through the tedious process of building truth tables.
We have already seen the notation to say that can be derived from by inference. An alternate notation emphasizes that this is not a sentence, but rather an inference rule:
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Here and match sentences.
Whenever something in the knowledge base matches the pattern above the line, the inference rule concludes the sentence below the line.
An inference rule is sound if the conclusion is true in all cases in which the premises are true.
Some example inference rules: