Answers.Body: <p>This has to do with the fact that you can define arithmetic inside the axiomatic system or not. In description logic you cannot speak about arithmetic sentences and in first order logic you do.</p>
  
  <p>if you look at the proof of incompleteness you will understand this in depth. This demonstration depends on an arithmetic coding of statements, and this representation is fundamental to obtain the conclusion.</p>
  
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Answers.Text: This seems like a good answer, but it would be a lot more useful if it cited references. Could you edit your answer to include relevant links?
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Answers.Text: Sorry its not clear to me yet... can you give examples?
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Body: <p>Description logic is a fragment of first order logic, but description logic is decidable and first order logic not decidable. Why is that? what is the role of variables in first order logic to make it undecidable?</p>
  
Tags: <logic>
Title: Why is description logic decidable but first order logic is not decidable?
UserDisplayName: shah
ThreadText: # Why is description logic decidable but first order logic is not decidable?
  
  (Asked by: username_0 on 2019-04-01)
  
  Description logic is a fragment of first order logic, but description logic is decidable and first order logic not decidable. Why is that? what is the role of variables in first order logic to make it undecidable?
  
  **Tags:** logic
  
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  ## 1 answers
  
  ### Answer by username_1 on 2019-04-01. Score: 1
  
  This has to do with the fact that you can define arithmetic inside the axiomatic system or not. In description logic you cannot speak about arithmetic sentences and in first order logic you do.
  
  if you look at the proof of incompleteness you will understand this in depth. This demonstration depends on an arithmetic coding of statements, and this representation is fundamental to obtain the conclusion.
  
  > **Comments:**
  > **username_2**: This seems like a good answer, but it would be a lot more useful if it cited references. Could you edit your answer to include relevant links?  
  > **username_0**: Sorry its not clear to me yet... can you give examples?  
  
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