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Tautological consequence

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Logical and tautological CONSEQUENCE ⟨05,03⟩

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LPL You Try It 10.2: Tautological Consequence

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What is a Logical Consequence?

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Language, Proof and Logic - 4.2.2 - Logical and Tautological Equivalence

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Language, Proof and Logic - 2.1.1 - A Definition of Logical Consequence

In propositional logic, tautological consequence is a strict form of logical consequence in which the tautologousness of a proposition is preserved from one line of a proof to the next. Not all logical consequences are tautological consequences. A proposition is said to be a tautological consequence of one or more other propositions in a proof with respect to some logical system if one is validly able to introduce the proposition onto a line of the proof within the rules of the system and in all cases when each of those one or more other propositions are true, the proposition also is true.
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