| 11. | We fix some axiomatization of the predicate calculus : logical axioms and rules of inference.
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| 12. | The concepts described in articles in this category may be also expressed as rules of inference.
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| 13. | First-order logic requires at least one additional rule of inference in order to obtain completeness.
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| 14. | Axioms are usually regarded as starting points for applying rules of inference and generating a set of conclusions.
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| 15. | In other formal proof systems, the deduction theorem is sometimes taken as a primitive rule of inference.
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| 16. | Mathematics deals with precise formal definitions and rules of inference and the theorems that can be so derived.
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| 17. | As of March 5, there are several such cases in the : Category : Rules of inference.
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| 18. | For example, one common rule of inference is the "'rule of substitution " '.
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| 19. | A theorem is a statement that can be derived from those axioms by application of these rules of inference.
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| 20. | This rule is equivalent to the rule of inference known as modus ponens, except it is going backwards.
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