Soundness

(This article discusses the soundness notion of informal logic. For soundness in mathematical logic see the entry on the soundness theorem.)

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A logical argument is sound if and only if

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• the argument is valid
• all of its premises are true.

A proof procedure (e.g. natural deduction) for a logic is sound if it proves only valid formulas (also tautologies). Formally: a system is sound when if "X1...Xn ⊢ Y", then also "X1...Xn ⊨ Y"

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Soundness: Sound arguments ►



 

Mathematical logic: Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics....

Soundness theorem: Soundness theorems are among the most fundamental results in mathematical logic. They are relative to a particular semantic theory for a formal logical language and a formal deductive system for that language. Soundness theorems come in two main varieties: weak and strong soundness....

Natural deduction: In mathematical logic, natural deduction is the name given to a class of foundational approaches for two key concepts in logic, propositions and proofs. There is no universal agreement on the proper foundation of these concepts; natural deduction takes the approach of mimicking the mental picture of...