Difference between revisions of "Criteria:Soundness"
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(Created page with "The term “soundness” comes from formal, mathematical logic. In that setting, there is a proof system and a model. The proof system is a set of rules with which one can pro...") |
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The term “soundness” comes from formal, mathematical logic. In that setting, there is a proof system and a model. The proof system is a set of rules with which one can prove properties (aka statements) about the model, which is some kind of mathematical structure, such as sets over some domain. A proof system L is sound if statements it can prove are indeed true in the model. L is complete if it can prove any true statement about the model. Most interesting proof systems cannot be both sound and complete: Either there will be some true statements that L cannot prove, or else L may “prove” some false statements along with all the true ones. | The term “soundness” comes from formal, mathematical logic. In that setting, there is a proof system and a model. The proof system is a set of rules with which one can prove properties (aka statements) about the model, which is some kind of mathematical structure, such as sets over some domain. A proof system L is sound if statements it can prove are indeed true in the model. L is complete if it can prove any true statement about the model. Most interesting proof systems cannot be both sound and complete: Either there will be some true statements that L cannot prove, or else L may “prove” some false statements along with all the true ones. | ||
== Soundness on Dictionary == | |||
Latest revision as of 04:46, 19 July 2021
The term “soundness” comes from formal, mathematical logic. In that setting, there is a proof system and a model. The proof system is a set of rules with which one can prove properties (aka statements) about the model, which is some kind of mathematical structure, such as sets over some domain. A proof system L is sound if statements it can prove are indeed true in the model. L is complete if it can prove any true statement about the model. Most interesting proof systems cannot be both sound and complete: Either there will be some true statements that L cannot prove, or else L may “prove” some false statements along with all the true ones.