Results of Applying Recursive Constraint Demotion to KikuriaClass.txt


5-30-2019, 3:14 p.m.

OTSoft 2.5, release date 1/17/2017


1. Result

A ranking was found that generates the correct outputs.

   Stratum #1
      BeGood                                    BeGood
      Id low                                    Id low
      *Map(i E)                                 *Map(i E)
      *Map(E i)                                 *Map(E i)
      *i e                                      *i e
      *E i                                      *E i
      *E e                                      *E e
      Final(hi)                                 Final(hi)
   Stratum #2
      *Map(i e)                                 *Map(i e)
      *Map(E e)                                 *Map(E e)
   Stratum #3
      *Map(e E)                                 *Map(e E)
      *e i                                      *e i
   Stratum #4
      *Map(e i)                                 *Map(e i)
      *e E                                      *e E

2. Tableaux


/e e i/: 
       BeGood¦Id low¦*Map(i E)¦*Map(E i)¦*i e¦*E i¦*E e¦Final(hi)|*Map(i e)¦*Map(E e)|*Map(e E)¦*e i|*e E¦*Map(e i)
>i i i       ¦      ¦         ¦         ¦    ¦    ¦    ¦         |         ¦         |         ¦    |    ¦   2     
 e e i       ¦      ¦         ¦         ¦    ¦    ¦    ¦         |         ¦         |         ¦ 1! |    ¦         
 e i i       ¦      ¦         ¦         ¦    ¦    ¦    ¦         |         ¦         |         ¦ 1! |    ¦   1     
 e e e       ¦      ¦         ¦         ¦    ¦    ¦    ¦   1!    |   1     ¦         |         ¦    |    ¦         


/e e a i/: 
         BeGood¦Id low¦*Map(i E)¦*Map(E i)¦*i e¦*E i¦*E e¦Final(hi)|*Map(i e)¦*Map(E e)|*Map(e E)¦*e i|*e E¦*Map(e i)
>e e a i       ¦      ¦         ¦         ¦    ¦    ¦    ¦         |         ¦         |         ¦    |    ¦         
 i i a i       ¦      ¦         ¦         ¦    ¦    ¦    ¦         |         ¦         |         ¦    |    ¦   2!    
 i i i i       ¦  1!  ¦         ¦         ¦    ¦    ¦    ¦         |         ¦         |         ¦    |    ¦   2     


/i e/: 
     BeGood¦Id low¦*Map(i E)¦*Map(E i)¦*i e¦*E i¦*E e¦Final(hi)|*Map(i e)¦*Map(E e)|*Map(e E)¦*e i|*e E¦*Map(e i)
>e e       ¦      ¦         ¦         ¦    ¦    ¦    ¦         |   1     ¦         |         ¦    |    ¦         
 i i       ¦      ¦         ¦         ¦    ¦    ¦    ¦   1!    |         ¦         |         ¦    |    ¦   1     
 i e       ¦      ¦         ¦         ¦ 1! ¦    ¦    ¦         |         ¦         |         ¦    |    ¦         


/E i/: 
     BeGood¦Id low¦*Map(i E)¦*Map(E i)¦*i e¦*E i¦*E e¦Final(hi)|*Map(i e)¦*Map(E e)|*Map(e E)¦*e i|*e E¦*Map(e i)
>e i       ¦      ¦         ¦         ¦    ¦    ¦    ¦         |         ¦   1     |         ¦ 1  |    ¦         
 e e       ¦      ¦         ¦         ¦    ¦    ¦    ¦         |   1!    ¦   1     |         ¦    |    ¦         
 E e       ¦      ¦         ¦         ¦    ¦    ¦ 1! ¦         |   1     ¦         |         ¦    |    ¦         
 E i       ¦      ¦         ¦         ¦    ¦ 1! ¦    ¦         |         ¦         |         ¦    |    ¦         
 i i       ¦      ¦         ¦   1!    ¦    ¦    ¦    ¦         |         ¦         |         ¦    |    ¦         
 E E       ¦      ¦   1!    ¦         ¦    ¦    ¦    ¦         |         ¦         |         ¦    |    ¦         


/E e/: 
     BeGood¦Id low¦*Map(i E)¦*Map(E i)¦*i e¦*E i¦*E e¦Final(hi)|*Map(i e)¦*Map(E e)|*Map(e E)¦*e i|*e E¦*Map(e i)
>E E       ¦      ¦         ¦         ¦    ¦    ¦    ¦         |         ¦         |   1     ¦    |    ¦         
 e e       ¦      ¦         ¦         ¦    ¦    ¦    ¦         |         ¦   1!    |         ¦    |    ¦         
 E e       ¦      ¦         ¦         ¦    ¦    ¦ 1! ¦         |         ¦         |         ¦    |    ¦         


/E E i/: 
       BeGood¦Id low¦*Map(i E)¦*Map(E i)¦*i e¦*E i¦*E e¦Final(hi)|*Map(i e)¦*Map(E e)|*Map(e E)¦*e i|*e E¦*Map(e i)
>e e i       ¦      ¦         ¦         ¦    ¦    ¦    ¦         |         ¦   2     |         ¦ 1  |    ¦         
 e e e       ¦      ¦         ¦         ¦    ¦    ¦    ¦         |   1!    ¦   2     |         ¦    |    ¦         
 E e i       ¦      ¦         ¦         ¦    ¦    ¦ 1! ¦         |         ¦   1     |         ¦ 1  |    ¦         
 E E i       ¦      ¦         ¦         ¦    ¦ 1! ¦    ¦         |         ¦         |         ¦    |    ¦         
 i i i       ¦      ¦         ¦   2!    ¦    ¦    ¦    ¦         |         ¦         |         ¦    |    ¦         
 E E E       ¦      ¦   1!    ¦         ¦    ¦    ¦    ¦         |         ¦         |         ¦    |    ¦         


/e E/: 
     BeGood¦Id low¦*Map(i E)¦*Map(E i)¦*i e¦*E i¦*E e¦Final(hi)|*Map(i e)¦*Map(E e)|*Map(e E)¦*e i|*e E¦*Map(e i)
>e E       ¦      ¦         ¦         ¦    ¦    ¦    ¦         |         ¦         |         ¦    | 1  ¦         
 E E       ¦      ¦         ¦         ¦    ¦    ¦    ¦         |         ¦         |   1!    ¦    |    ¦         
 e e       ¦      ¦         ¦         ¦    ¦    ¦    ¦         |         ¦   1!    |         ¦    |    ¦         


/E E e i/: 
         BeGood¦Id low¦*Map(i E)¦*Map(E i)¦*i e¦*E i¦*E e¦Final(hi)|*Map(i e)¦*Map(E e)|*Map(e E)¦*e i|*e E¦*Map(e i)
>e e i i       ¦      ¦         ¦         ¦    ¦    ¦    ¦         |         ¦   2     |         ¦ 1  |    ¦   1     
 e e e e       ¦      ¦         ¦         ¦    ¦    ¦    ¦   1!    |   1     ¦   2     |         ¦    |    ¦         
 E E e i       ¦      ¦         ¦         ¦    ¦    ¦ 1! ¦         |         ¦         |         ¦ 1  |    ¦         
 i i i i       ¦      ¦         ¦   2!    ¦    ¦    ¦    ¦         |         ¦         |         ¦    |    ¦   1     
 E E E E       ¦      ¦   1!    ¦         ¦    ¦    ¦    ¦   1     |         ¦         |   1     ¦    |    ¦         
 e e e i   1!  ¦      ¦         ¦         ¦    ¦    ¦    ¦         |         ¦   2     |         ¦ 1  |    ¦         


3. Status of Proposed Constraints:  Necessary or Unnecessary

   BeGood     Necessary
   *Map(i e)  Necessary
   *Map(i E)  Necessary
   *Map(e E)  Necessary
   *Map(e i)  Necessary
   *Map(E i)  Necessary
   *Map(E e)  Necessary
   *e i       Necessary
   *i e       Necessary
   *E i       Necessary
   *E e       Necessary
   Final(hi)  Necessary
   Id low     Not necessary
   *e E       Not necessary

A check has determined that the grammar will still work even if the 
constraints marked above as unnecessary are removed en masse.


4. Ranking Arguments, based on the Fusional Reduction Algorithm

This run sought to obtain the Most Informative Basis, intended to minimize the set of final ranking arguments.



The final rankings obtained are as follows:

      Final(hi) >> { *Map(i e), *Map(e i), *e i }
      *Map(i e) >> { *Map(e i), *e i }
      *e i >> *Map(e i)
      *Map(e E) >> *e E
      *Map(E e) >> { *Map(e E), *e E }
      *E e >> { *Map(e E), *Map(e i), *Map(E e), *e E }
      *E i >> { *Map(e E), *Map(e i), *Map(E e), *e i, *e E }
      *i e >> { *Map(i e), *Map(e i), *e i }
      *Map(E i) >> { *Map(e E), *Map(e i), *Map(E e), *e i, *e E }
      *Map(i E) >> { *Map(e E), *Map(e i), *Map(E e), *e i, *e E }
      BeGood >> *Map(e i)


5. Mini-Tableaux

The following small tableaux may be useful in presenting ranking arguments. 
They include all winner-rival comparisons in which there is just one 
winner-preferring constraint and at least one loser-preferring constraint.  
Constraints not violated by either candidate are omitted.


/e e i/: 
       *e i|*Map(e i)
>i i i     |   2     
 e e i  1  |         


/e e i/: 
       *e i|*Map(e i)
>i i i     |   2     
 e i i  1  |   1     


/i e/: 
     *i e|*Map(i e)
>e e     |   1     
 i e  1  |         


/E i/: 
     *E i|*Map(E e)|*e i
>e i     |   1     | 1  
 E i  1  |         |    


/E i/: 
     *Map(i E)|*Map(E e)|*e i
>e i          |   1     | 1  
 E E    1     |         |    


/E i/: 
     *Map(i e)¦*Map(E e)|*e i
>e i          ¦   1     | 1  
 e e    1     ¦   1     |    


/E i/: 
     *Map(E i)|*Map(E e)|*e i
>e i          |   1     | 1  
 i i    1     |         |    


/E e/: 
     *E e|*Map(e E)
>E E     |   1     
 E e  1  |         


/E e/: 
     *Map(E e)|*Map(e E)
>E E          |   1     
 e e    1     |         


/E E i/: 
       *E e|*Map(E e)|*e i
>e e i     |   2     | 1  
 E e i  1  |   1     | 1  


/E E i/: 
       *E i|*Map(E e)|*e i
>e e i     |   2     | 1  
 E E i  1  |         |    


/E E i/: 
       *Map(E i)|*Map(E e)|*e i
>e e i          |   2     | 1  
 i i i    2     |         |    


/E E i/: 
       *Map(i E)|*Map(E e)|*e i
>e e i          |   2     | 1  
 E E E    1     |         |    


/E E i/: 
       *Map(i e)¦*Map(E e)|*e i
>e e i          ¦   2     | 1  
 e e e    1     ¦   2     |    


/e E/: 
     *Map(E e)|*e E
>e E          | 1  
 e e    1     |    


/e E/: 
     *Map(e E)|*e E
>e E          | 1  
 E E    1     |    


/E E e i/: 
         BeGood|*Map(E e)|*e i|*Map(e i)
>e e i i       |   2     | 1  |   1     
 e e e i   1   |   2     | 1  |         


/E E e i/: 
         *E e|*Map(E e)|*e i|*Map(e i)
>e e i i     |   2     | 1  |   1     
 E E e i  1  |         | 1  |         


/E E e i/: 
         *Map(E i)|*Map(E e)|*e i|*Map(e i)
>e e i i          |   2     | 1  |   1     
 i i i i    2     |         |    |   1     

