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logic, the systematic study of valid inference. A distinction is drawn between logical validity and truth. Validity merely refers to formal properties of the process of inference. Thus, a conclusion whose value is true may be drawn from an invalid argument, and one whose value is false, from a valid sequence. For example, the argument All professors are brilliant; Smith is a professor, therefore, Smith is brilliant is a valid inference, but the argument All professors are brilliant; Smith is brilliant; therefore, Smith is a professor is an invalid inference, even if Smith is a professor.
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