# Are soundness and completeness necessary for decidability? [closed]

Is it necessary for a logical system to be both sound and complete in order to be decidable?

## closed as off-topic by Namaste, Shailesh, José Carlos Santos, choco_addicted, hardmathSep 12 '18 at 13:35

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Namaste, Shailesh, José Carlos Santos, choco_addicted, hardmath
If this question can be reworded to fit the rules in the help center, please edit the question.

• As many authors define these terms, an inconsistent system would be decidable. Perhaps you could cite the textbook or source from which you take the definitions? Adding context would improve your Question. – hardmath Sep 12 '18 at 13:34

This is clearly decidable: a formula is provable exactly if it is an axiom, which is easy to check. But it is not sound (because it proves $A\land\neg A$), and it is not complete (because $\neg A\lor\neg\neg A$ is not provable, yet it is valid -- remember that we're assuming the usual semantics).