Answers.Body: <p>A <strong>closed expression</strong> (or <strong>closed formula</strong>) refers to a formula that has no free variables <a href="https://page.mi.fu-berlin.de/raut/logic3/announce.pdf#page=79" rel="nofollow noreferrer">[1]</a>. This is also called <strong>sentence</strong>.</p>
  <p>In a logic system, you have a set of axioms, which are sentences, and rules which state how to derive a sentence from this <a href="https://page.mi.fu-berlin.de/raut/logic3/announce.pdf#page=55" rel="nofollow noreferrer">[2]</a>. If a sentence can be derived from the axioms, this means that the axioms <a href="https://cs.calvin.edu/courses/cs/344/kvlinden/resources/AIMA-3rd-edition.pdf#page=259" rel="nofollow noreferrer">entail</a> this sentence. If a sentence is not derivable, it is not entailed by the axioms.</p>
  
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Answers.CreationDate: 2017-01-30T12:52:25.903Z
Answers.LastActivityDate: 2021-12-10T22:38:44.607Z
Answers.LastEditDate: 2021-12-10T22:38:44.607Z
Answers.UserDisplayName: marli
Body: <p>I was reading about logic systems and the following phrase appeared.</p>
  <blockquote>
  <p>any <strong>closed expression</strong> that is not derivable inside the same system</p>
  </blockquote>
  <p>What is a &quot;closed expression&quot; in this context? What does &quot;closed expression that is not derivable&quot; mean?</p>
  
Tags: <terminology><logic>
Title: What is a "closed expression" in the context of logic?
UserDisplayName: Ale
ThreadText: # What is a "closed expression" in the context of logic?
  
  (Asked by: username_0 on 2016-11-01)
  
  I was reading about logic systems and the following phrase appeared.
  
  > any **closed expression** that is not derivable inside the same system
  
  What is a "closed expression" in this context? What does "closed expression that is not derivable" mean?
  
  **Tags:** terminology, logic
  
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  ## 1 answers
  
  ### Answer by username_1 on 2017-01-30. Score: 5 | Accepted answer
  
  A **closed expression** (or **closed formula**) refers to a formula that has no free variables [[1]](https://page.mi.fu-berlin.de/raut/logic3/announce.pdf#page=79). This is also called **sentence**.
  
  In a logic system, you have a set of axioms, which are sentences, and rules which state how to derive a sentence from this [[2]](https://page.mi.fu-berlin.de/raut/logic3/announce.pdf#page=55). If a sentence can be derived from the axioms, this means that the axioms [entail](https://cs.calvin.edu/courses/cs/344/kvlinden/resources/AIMA-3rd-edition.pdf#page=259) this sentence. If a sentence is not derivable, it is not entailed by the axioms.
  
  
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