Body: <p>I have to translate the following English sentences into First-Order Logic without using quantifiers:</p>
  <ol>
  <li>Everyone on flight 815 has a story.</li>
  <li>No one knows what is inside the hatch.</li>
  <li>Someone on the island isn't on the flight manifest.</li>
  </ol>
  <p>I have tried it, but can't translate without using ∀ and ∃:</p>
  <ol>
  <li><span class="math-container">$\forall x, \; \text{flight815}(x) \rightarrow \text{story}(x)$</span></li>
  <li><span class="math-container">$\forall x \neg(\text{knows}(x) \rightarrow \text{inside hatch}(x))$</span> // not sure about this OR <span class="math-container">$\neg \exists x, \; \text{knows}(x, \text{inside hatch})$</span></li>
  <li><span class="math-container">$\exists x, \; \text{island}(x) \land \neg(\text{flight manifest}(x))$</span></li>
  </ol>
  <p>Is it possible to do it? If not, why?</p>
  <p>Refer to chapter 8 of Artificial Intelligence: A Modern Approach (3rd edition). Stuart Russell and Peter Norvig, Prentice Hall (2010)</p>
  
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2017-02-24T04:55:04.343Z
Comments.Text: It's not possible to do it since the sentences which you gave are complex sentences. Words like "Everyone", "All", "Somebody", "At least", etc. are supported only by FOL and not by simple propositional logic!
Comments.UserDisplayName: kiner_shah
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2017-02-25T13:31:45.310Z
Comments.Text: @kiner_shah Thank so so much. Do you think I have translated it correctly to FOL. I am confused about the second sentence.
Comments.UserDisplayName: New_Coder
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2017-02-26T05:29:09.220Z
Comments.Text: @New_Coder, I am not sure about the second FOL sentence. Try forming the sentence: "Everybody knows what's inside the hatch" (It could be something like "for all x, if knows(x) then there exists y such that y is inside the hatch") and then figuring out how to modify the FOL to fit your second sentence.
Comments.UserDisplayName: kiner_shah
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2017-02-26T14:24:38.103Z
Comments.Text: @kiner_shah Is this looks better for 2nd sentence: ∀x ⌐(knows(x) → ∃y inside hatch(y))
  I have also changed the 1st sentence: ∀x fight815(x) → ∃y story(y)
  What do you think now?
  
  There's an example I found at:
  http://www.uobabylon.edu.iq/eprints/publication_5_29514_1380.pdf
  No student loves Bill: ¬ ∃ x ( Student(x) ∧ Loves(x, Bill) )
Comments.UserDisplayName: New_Coder
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2017-02-27T08:58:47.317Z
Comments.Text: `1. ∀x, onFlight815(x) -> hasStory(x)
  2. ~(∃x,y knows(x,y) ^ insideHatch(y))` What about this?
Comments.UserDisplayName: kiner_shah
Tags: <logic><knowledge-representation>
Title: How do I translate these English sentences into first-order logic without quantifiers?
UserDisplayName: New_Coder
ThreadText: # How do I translate these English sentences into first-order logic without quantifiers?
  
  (Asked by: username_0 on 2017-02-22)
  
  I have to translate the following English sentences into First-Order Logic without using quantifiers:
  
  1. Everyone on flight 815 has a story.
  2. No one knows what is inside the hatch.
  3. Someone on the island isn't on the flight manifest.
  
  I have tried it, but can't translate without using ∀ and ∃:
  
  1. $\forall x, \; \text{flight815}(x) \rightarrow \text{story}(x)$
  2. $\forall x \neg(\text{knows}(x) \rightarrow \text{inside hatch}(x))$ // not sure about this OR $\neg \exists x, \; \text{knows}(x, \text{inside hatch})$
  3. $\exists x, \; \text{island}(x) \land \neg(\text{flight manifest}(x))$
  
  Is it possible to do it? If not, why?
  
  Refer to chapter 8 of Artificial Intelligence: A Modern Approach (3rd edition). Stuart Russell and Peter Norvig, Prentice Hall (2010)
  
  **Tags:** logic, knowledge-representation
  > **Comments:**
  > **username_1**: It's not possible to do it since the sentences which you gave are complex sentences. Words like "Everyone", "All", "Somebody", "At least", etc. are supported only by FOL and not by simple propositional logic!  
  > **username_0**: @kiner_shah Thank so so much. Do you think I have translated it correctly to FOL. I am confused about the second sentence.  
  > **username_1**: @New_Coder, I am not sure about the second FOL sentence. Try forming the sentence: "Everybody knows what's inside the hatch" (It could be something like "for all x, if knows(x) then there exists y such that y is inside the hatch") and then figuring out how to modify the FOL to fit your second sentence.  
  > **username_0**: @kiner_shah Is this looks better for 2nd sentence: ∀x ⌐(knows(x) → ∃y inside hatch(y)) I have also changed the 1st sentence: ∀x fight815(x) → ∃y story(y) What do you think now?  There's an example I found at: http://www.uobabylon.edu.iq/eprints/publication_5_29514_1380.pdf No student loves Bill: ¬ ∃ x ( Student(x) ∧ Loves(x, Bill) )  
  > **username_1**: `1. ∀x, onFlight815(x) -> hasStory(x) 2. ~(∃x,y knows(x,y) ^ insideHatch(y))` What about this?  
  
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