Soundness is a property of proof systems that requires no prover can make the verifier accept a wrong statement except with some small probability. The upper bound of this probability is referred to as the soundness error of a proof system.
Soundness is a property of proof systems that requires that no prover can make the verifier accept for a wrong statement except with some small probability. The upper bound of this probability is referred to as the soundness error of a proof system.
An interactive or non-interactive protocol is said to be sound for a language $\mathcal{L}$ if it is "hard" for a (malicious) prover $\textsf{P}$ to convince a verifier $\textsf{V}$ of a statement $I\not\in\mathcal{L}$. Depending on how "hard" it actually is for $\textsf{P}$ to cheat, we either get a (interactive or non-interactive) proof system (when $\textsf{P}$ is computationally unbounded) or an argument system (when $\textsf{P}$ is computationally bounded).
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In logic, more precisely in deductive reasoning, an argument is sound if it is both valid in form and its premises are true. Soundness also has a related meaning in mathematical logic, wherein logical systems are sound if and only if every formula that can be proved in the system is logically valid with respect to the semantics of the system.
