Answers.Body: <p>According to the tree:</p>
  <ol>
  <li>&quot;x TPP c&quot; implies &quot;x IntInt c&quot; and &quot;x BndBnd c&quot; and &quot;x BndInt c&quot; and &quot;not x IntBnd c&quot;.</li>
  <li>&quot;c DC b&quot; implies &quot;not c IntInt b&quot; and &quot;not c BndBnd b&quot;.</li>
  </ol>
  <p>From &quot;x IntInt c&quot; and &quot;not x IntBnd c&quot; we can say &quot;not x IntExt c&quot;. This relation together to &quot;not c IntInt b&quot; proves that &quot;not x IntInt b&quot;.</p>
  <p>In similar way, we can infer &quot;not x BndBnd b&quot;.</p>
  <p>Following tree for &quot;not x IntInt b&quot; and &quot;not x BndBnd b&quot; we conclude &quot;x DC c&quot;.</p>
  <p>In other words, you need to use the composition of the relations &quot;IntInt&quot;, &quot;IntBnd&quot;, ... . Look for &quot;9-intersection model&quot;, &quot;4-intersection model&quot; and/or &quot;3-intersection model&quot;.</p>
  
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Answers.Text: @ pasaba por aqui thank you for the above.. I found the 9-int and 4-int models here https://web.mst.edu/~chaman/home/pubs/2011CAINE_HawaiiHonolulu.pdf in page 2. But still it is not clear how you used the 9-int matrix to conclude on the above.. Could you elaboarte a bit more ? For instance how to use the matrix to prove that "From "x IntInt c" and "not x IntBnd c" we can say "not x IntExt c" " or that " "not x IntExt c" along with "not c IntInt b" proves that "not x IntInt b" "
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Answers.UserDisplayName: pasaba por aqui
Body: <p>I am trying to use RCC8 algebra relations and axioms in order to tackle the following problem :</p>
  <p>We consider the below configuration and square <span class="math-container">$x$</span> such that &quot;<span class="math-container">$x$</span> NTPP <span class="math-container">$a$</span>&quot; and &quot;<span class="math-container">$x$</span> TPP <span class="math-container">$c$</span>&quot;</p>
  <p><a href="https://i.sstatic.net/vPnqF.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/vPnqF.png" alt="enter image description here" /></a></p>
  <p>and we must prove that :</p>
  <ul>
  <li>a) <span class="math-container">$x$</span> DC <span class="math-container">$b$</span></li>
  <li>b) For <span class="math-container">$y$</span> such that &quot;<span class="math-container">$y$</span> EC <span class="math-container">$a$</span>&quot;, prove that it is not possible to have &quot;<span class="math-container">$y$</span> EC <span class="math-container">$x$</span>&quot;</li>
  </ul>
  <p>using the tree</p>
  <p><a href="https://i.sstatic.net/bZHSu.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/bZHSu.png" alt="enter image description here" /></a></p>
  <p>My difficulty is that I do not know how to &quot;formally&quot; prove the above statements using the tree.</p>
  <p>For instance, regarding question (a), since &quot;<span class="math-container">$x$</span> TPP <span class="math-container">$c$</span>&quot; and &quot;<span class="math-container">$c$</span> DC <span class="math-container">$b$</span>&quot;, by the composition table we have that &quot;<span class="math-container">$x$</span> DC <span class="math-container">$b$</span>&quot;. But, this argument does not use &quot;Interior&quot; and &quot;Boundary&quot; statements as the tree suggests. Could you please assist with this ?</p>
  
Tags: <knowledge-representation><reasoning><semantics>
Title: Reasoning about 2d spatial square configuration
UserDisplayName: nick
ThreadText: # Reasoning about 2d spatial square configuration
  
  (Asked by: username_0 on 2022-02-06)
  
  I am trying to use RCC8 algebra relations and axioms in order to tackle the following problem :
  
  We consider the below configuration and square $x$ such that "$x$ NTPP $a$" and "$x$ TPP $c$"
  
  [![enter image description here](https://i.sstatic.net/vPnqF.png)](https://i.sstatic.net/vPnqF.png)
  
  and we must prove that :
  
  * a) $x$ DC $b$
  * b) For $y$ such that "$y$ EC $a$", prove that it is not possible to have "$y$ EC $x$"
  
  using the tree
  
  [![enter image description here](https://i.sstatic.net/bZHSu.png)](https://i.sstatic.net/bZHSu.png)
  
  My difficulty is that I do not know how to "formally" prove the above statements using the tree.
  
  For instance, regarding question (a), since "$x$ TPP $c$" and "$c$ DC $b$", by the composition table we have that "$x$ DC $b$". But, this argument does not use "Interior" and "Boundary" statements as the tree suggests. Could you please assist with this ?
  
  **Tags:** knowledge-representation, reasoning, semantics
  
  ---
  
  ## 1 answers
  
  ### Answer by username_1 on 2022-02-06. Score: 2 | Accepted answer
  
  According to the tree:
  
  1. "x TPP c" implies "x IntInt c" and "x BndBnd c" and "x BndInt c" and "not x IntBnd c".
  2. "c DC b" implies "not c IntInt b" and "not c BndBnd b".
  
  From "x IntInt c" and "not x IntBnd c" we can say "not x IntExt c". This relation together to "not c IntInt b" proves that "not x IntInt b".
  
  In similar way, we can infer "not x BndBnd b".
  
  Following tree for "not x IntInt b" and "not x BndBnd b" we conclude "x DC c".
  
  In other words, you need to use the composition of the relations "IntInt", "IntBnd", ... . Look for "9-intersection model", "4-intersection model" and/or "3-intersection model".
  
  > **Comments:**
  > **username_0**: @ pasaba por aqui thank you for the above.. I found the 9-int and 4-int models here https://web.mst.edu/~chaman/home/pubs/2011CAINE_HawaiiHonolulu.pdf in page 2. But still it is not clear how you used the 9-int matrix to conclude on the above.. Could you elaboarte a bit more ? For instance how to use the matrix to prove that "From "x IntInt c" and "not x IntBnd c" we can say "not x IntExt c" " or that " "not x IntExt c" along with "not c IntInt b" proves that "not x IntInt b" "  
  
  ---
  
  