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I have always tried to understand the difference between all the above, but I always ended up being confused. The field I am referring to is cryptography in particular, but I guess this question is valid for all of computer science.

Is there a proper way to understand and differentiate them all?

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In my notes so far:

  • Completeness: all the true statements are provable
  • Soundness: all the false statements are not provable (or no false statement is provable, or every statement that’s proven is true)
  • Validity: all the statements are true (a system is valid iff it is sound and complete (?))
  • Consistency: (?)
  • Integrity: (?)
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    $\begingroup$ This looks like about five different questions to me. The site usually works better if you ask one question per post. In any case, where have you looked? Have you looked in textbooks or lecture notes that cover the topic? Soundness and completeness should be defined in anything that covers the topic. Where have you seen consistency or integrity? Personally, I've never seen those used as a property of a proof system. I suggest you ask about each property in a separate question; tell us what research you've done; and give some context where you saw the term used. $\endgroup$ – D.W. Apr 20 '17 at 17:18

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