Soundness

In logic, soundness can refer to either a property of arguments or a property of formal deductive systems.

An argument is sound if (and only if) it is both valid in form and has no false premises.

A formal system is sound if (and only if) every well-formed formula that can be proven in the system is logically valid with respect to the logical semantics of the system.

These two properties are different but closely related. The former is more relevant for introductory deductive reasoning contexts and the latter arises in metalogic and mathematical logic.

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