Results of Applying Recursive Constraint Demotion to TurkishWithIyor.txt


4-04-2019, 9:17 a.m.

OTSoft 2.5, release date 1/17/2017


1. Result

A ranking was found that generates the correct outputs.

   Stratum #1
      Max(rd)                                   Max(rd)
   Stratum #2
      Agree back                                Agr bk
      RoLo                                      RoLo
   Stratum #3
      Agree round                               Agr rd
   Stratum #4
      No left(round)                            No L(rd)
   Stratum #5
      Dep(+rd)                                  Dep(+rd)

2. Tableaux


/[ o ] /: 
       Max(rd)|RoLo¦Agr bk|Agr rd|No L(rd)|Dep(+rd)
>[ o ]        | 1  ¦      |      |        |        
 [ a ]   1!   |    ¦      |      |        |        


/[ o ] A/: 
         Max(rd)|RoLo¦Agr bk|Agr rd|No L(rd)|Dep(+rd)
>[ o ] a        | 1  ¦      |  1   |        |        
 [ o ] e        | 1  ¦  1!  |  1   |        |        
 [ o ] o        | 2! ¦      |      |        |        


/[ o ] I/: 
          Max(rd)|RoLo¦Agr bk|Agr rd|No L(rd)|Dep(+rd)
>[ o ] u         | 1  ¦      |      |        |        
 [ o ] i-        | 1  ¦      |  1!  |        |        
 [ o ] i         | 1  ¦  1!  |  1   |        |        


/[ o ] I yor/: 
              Max(rd)|RoLo¦Agr bk|Agr rd|No L(rd)|Dep(+rd)
>[ o ] u yor         | 2  ¦      |      |   1    |   1    
 [ o ] i- yor        | 2  ¦      |  2!  |        |        


/[ a ] I yor/: 
              Max(rd)|RoLo¦Agr bk|Agr rd|No L(rd)|Dep(+rd)
>[ a ] i- yor        | 1  ¦      |  1   |        |        
 [a ] u yor          | 1  ¦      |  1   |   1!   |   1    


/[ e ] I yor/: 
             Max(rd)|RoLo¦Agr bk|Agr rd|No L(rd)|Dep(+rd)
>[ e ] i yor        | 1  ¦  1   |  1   |        |        
 [ e ] u yor        | 1  ¦  1   |  1   |   1!   |   1    
 [ e ] U yor        | 1  ¦  1   |  1   |   1!   |   1    
 [ e ] i yer   1!   |    ¦      |      |        |        


/[ u ] I a/: 
            Max(rd)|RoLo¦Agr bk|Agr rd|No L(rd)|Dep(+rd)
>[ u ] u a         |    ¦      |  1   |        |   1    
 [ u ] i- a        |    ¦      |  1   |   1!   |        


3. Status of Proposed Constraints:  Necessary or Unnecessary

   Agr bk    Necessary
   Agr rd    Necessary
   RoLo      Necessary
   Max(rd)   Necessary
   No L(rd)  Necessary
   Dep(+rd)  Not necessary (but included to show Faithfulness violations
                of a winning candidate)


4. Ranking Arguments, based on the Fusional Reduction Algorithm

This run sought to obtain the Skeletal Basis, intended to keep each final ranking argument as pithy as possible.

Original set of ERCs

Index  ERC     Reason                                        
1      eeeLWe  for /[ o ] /, [ o ] >> [ a ]                  
2      eLeWee  for /[ o ] A/, [ o ] a >> [ o ] o             
3      eWLeeL  for /[ o ] I yor/, [ o ] u yor >> [ o ] i- yor
4      LLeLWe  for /[ e ] I yor/, [ e ] i yor >> [ e ] i yer 
5      eeLeeW  for /[ u ] I a/, [ u ] u a >> [ u ] i- a      

Recursive ranking search

Recursive search has now reached this location in the search tree:  1


   Fusion of this ERC set is:  LLLLWL

   The following ERCs form the total information-loss residue:

      eLeWee
      eWLeeL
      eeLeeW

   Fusion of total residue:  eLLWeL


   Skeletal basis of the fusion:  LeeLWe

   LeeLWe includes at least one L and thus is not entailed by eLLWeL.

   Thus it may be retained in the Skeletal Basis of ERCs.

Recursive search has now reached this location in the search tree:  1, 5

Current set of ERCs is based on constraint #5, Max(rd)

Working with the following ERC set:

      eLeWee
      eWLeeL
      eeLeeW

   Fusion of this ERC set is:  eLLWeL

   The following ERCs form the total information-loss residue:

      eWLeeL
      eeLeeW

   Fusion of total residue:  eWLeeL


   Skeletal basis of the fusion:  eLeWee

   eLeWee includes at least one L and thus is not entailed by eWLeeL.

   Thus it may be retained in the Skeletal Basis of ERCs.

Recursive search has now reached this location in the search tree:  1, 5, 4

Current set of ERCs is based on constraint #4, RoLo

Working with the following ERC set:

      eWLeeL
      eeLeeW

   Fusion of this ERC set is:  eWLeeL

   The following ERCs form the total information-loss residue:

      eeLeeW

   Fusion of total residue:  eeLeeW


   Skeletal basis of the fusion:  eWeeeL

   eWeeeL includes at least one L and thus is not entailed by eeLeeW.

   Thus it may be retained in the Skeletal Basis of ERCs.

Recursive search has now reached this location in the search tree:  1, 5, 4, 2

Current set of ERCs is based on constraint #2, Agr rd

Working with the following ERC set:

      eeLeeW

   Fusion of this ERC set is:  eeLeeW

   The following ERCs form the total information-loss residue:



   eeLeeW has a null residue 
and thus may be retained in the Skeletal Basis of ERCs.



5. Ranking argumentation:  Final result

The following set of ERCs forms the Skeletal Basis for the ERC set as a whole, 
and thus encapsulates the available ranking information.

      LeeLWe
      eLeWee
      eWeeeL
      eeLeeW

The final rankings obtained are as follows:

      Max(rd) >> { Agr bk, RoLo }
      RoLo >> Agr rd
      Agr rd >> No L(rd)
      No L(rd) >> Dep(+rd)


6. 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.


/[ o ] /: 
       Max(rd)|RoLo
>[ o ]        | 1  
 [ a ]   1    |    


/[ o ] A/: 
         RoLo|Agr rd
>[ o ] a  1  |  1   
 [ o ] o  2  |      


/[ o ] I yor/: 
              RoLo|Agr rd|No L(rd)|Dep(+rd)
>[ o ] u yor   2  |      |   1    |   1    
 [ o ] i- yor  2  |  2   |        |        


/[ e ] I yor/: 
             Max(rd)|RoLo¦Agr bk|Agr rd
>[ e ] i yor        | 1  ¦  1   |  1   
 [ e ] i yer   1    |    ¦      |      


/[ u ] I a/: 
            Agr rd|No L(rd)|Dep(+rd)
>[ u ] u a    1   |        |   1    
 [ u ] i- a   1   |   1    |        

