Results of Applying Recursive Constraint Demotion to Tangale.txt


4-01-2019, 11:52 a.m.

OTSoft 2.5, release date 1/17/2017


1. Result

A ranking was found that generates the correct outputs.

   Stratum #1
      *A                                        *A
      Id-OO(ATR)                                Id-OO(ATR)
   Stratum #2
      Agree                                     Agree
   Stratum #3
      Id-IO(ATR)                                Id-IO(ATR)
      Id(IO)-ATR Initial                        Id(IO)-ATR Initial

2. Tableaux


/i ] I/: 
       *A¦Id-OO(ATR)|Agree|Id-IO(ATR)¦Id(IO)-ATR Initial
>i ] i   ¦          |     |    1     ¦                  
 i ] I   ¦          | 1!  |          ¦                  
 I ] I   ¦    1!    | 1   |          ¦        1         


/a ] i/: 
       *A¦Id-OO(ATR)|Agree|Id-IO(ATR)¦Id(IO)-ATR Initial
>a ] I   ¦          |     |    1     ¦                  
 a ] i   ¦          | 1!  |          ¦                  
 A ] i 1!¦    1     |     |    1     ¦        1         


/i ] a/: 
       *A¦Id-OO(ATR)|Agree|Id-IO(ATR)¦Id(IO)-ATR Initial
>i ] a   ¦          | 1   |          ¦                  
 I ] a   ¦    1!    |     |    1     ¦                  
 i ] A 1!¦          |     |    1     ¦                  


/i ] a ] i/: 
           *A¦Id-OO(ATR)|Agree|Id-IO(ATR)¦Id(IO)-ATR Initial
>i ] a ] I   ¦          | 1   |    1     ¦                  
 i ] a ] i   ¦          | 2!  |          ¦                  
 I ] a ] I   ¦    1!    |     |    2     ¦        1         
 i ] A ] i 1!¦          |     |    1     ¦                  


/i a/: 
     *A¦Id-OO(ATR)|Agree|Id-IO(ATR)¦Id(IO)-ATR Initial
>I a   ¦          |     |    1     ¦        1         
 i a   ¦          | 1!  |          ¦                  
 i A 1!¦          |     |    1     ¦                  


/i I/: 
     *A¦Id-OO(ATR)|Agree|Id-IO(ATR)¦Id(IO)-ATR Initial
>i i   ¦          |     |    1     ¦                  
 I I   ¦          |     |    1     ¦        1!        
 i I   ¦          | 1!  |          ¦                  


3. Status of Proposed Constraints:  Necessary or Unnecessary

   Agree               Necessary
   *A                  Necessary
   Id-OO(ATR)          Necessary
   Id(IO)-ATR Initial  Necessary
   Id-IO(ATR)          Not necessary


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      WeeLe  for /i ] I/, i ] i >> i ] I, a ] I >> a ] i, i ] a ] I >> i ] a ] i, i i >> i I
2      WeWLW  for /i ] I/, i ] i >> I ] I                                                    
3      LWeWe  for /i ] a/, i ] a >> i ] A                                                    
4      LeWWe  for /i ] a/, i ] a >> I ] a                                                    
5      LeWWW  for /i ] a ] i/, i ] a ] I >> I ] a ] I                                        
6      LWeee  for /i ] a ] i/, i ] a ] I >> i ] A ] i                                        
7      WeeLL  for /i a/, I a >> i a                                                          
8      eWeeL  for /i a/, I a >> i A                                                          

Recursive ranking search

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


   Fusion of this ERC set is:  LWWLL

   The following ERCs form the total information-loss residue:

      WeeLe
      WeWLW
      LWeWe
      LeWWe
      LeWWW
      LWeee
      WeeLL
      eWeeL

   Fusion of total residue:  LWWLL


   Skeletal basis of the fusion:  eWWee

   eWWee has no L's, so it cannot be retained in the Skeletal Basis.

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

Current set of ERCs is based on constraint #2, *A

Working with the following ERC set:

      WeeLe
      WeWLW
      LeWWe
      LeWWW
      WeeLL

   Fusion of this ERC set is:  LeWLL

   The following ERCs form the total information-loss residue:

      WeeLe
      WeeLL

   Fusion of total residue:  WeeLL


   Skeletal basis of the fusion:  LeWee

   LeWee includes at least one L and thus is not entailed by WeeLL.

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

Recursive search has now reached this location in the search tree:  1, 2, 3

Current set of ERCs is based on constraint #3, Id-OO(ATR)

Working with the following ERC set:

      WeeLe
      WeeLL

   Fusion of this ERC set is:  WeeLL

   The following ERCs form the total information-loss residue:



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

Recursive search has now reached this location in the search tree:  1, 3

Current set of ERCs is based on constraint #3, Id-OO(ATR)

Working with the following ERC set:

      WeeLe
      LWeWe
      LWeee
      WeeLL
      eWeeL

   Fusion of this ERC set is:  LWeLL

   The following ERCs form the total information-loss residue:

      WeeLe
      WeeLL

   Fusion of total residue:  WeeLL


   Skeletal basis of the fusion:  LWeee

   LWeee includes at least one L and thus is not entailed by WeeLL.

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

   ([1, 3, 2] not novel so not checked)



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.

      LeWee
      WeeLL
      LWeee

The final rankings obtained are as follows:

      Id-OO(ATR) >> Agree
      Agree >> { Id-IO(ATR), Id(IO)-ATR Initial }
      *A >> Agree


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.


/i ] I/: 
       Agree|Id-IO(ATR)
>i ] i      |    1     
 i ] I  1   |          


/a ] i/: 
       Agree|Id-IO(ATR)
>a ] I      |    1     
 a ] i  1   |          


/i ] a ] i/: 
           Agree|Id-IO(ATR)
>i ] a ] I  1   |    1     
 i ] a ] i  2   |          


/i ] a ] i/: 
           *A|Agree|Id-IO(ATR)
>i ] a ] I   | 1   |    1     
 i ] A ] i 1 |     |    1     


/i a/: 
     Agree|Id-IO(ATR)¦Id(IO)-ATR Initial
>I a      |    1     ¦        1         
 i a  1   |          ¦                  


/i a/: 
     *A|Id-IO(ATR)¦Id(IO)-ATR Initial
>I a   |    1     ¦        1         
 i A 1 |    1     ¦                  


/i I/: 
     Agree|Id-IO(ATR)
>i i      |    1     
 i I  1   |          

