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 | Constraint Name | Abbreviation
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 |  |  |  |  |  |  |  |

**

e e i |  |  |  |  |  |  |  |  |  |  |  | *! |  |
e i i |  |  |  |  |  |  |  |  |  |  |  | *! |  | *
e e e |  |  |  |  |  |  |  | *! | * |  |  |  |  |

/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 |  |  |  |  |  |  |  |  |  |  |  |  |  | *!*
i i i i |  | *! |  |  |  |  |  |  |  |  |  |  |  | **

/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 |  |  |  |  |  |  |  |

* |

i i |  |  |  |  |  |  |  | *! |  |  |  |  |  | *
i 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 i |  |  |  |  |  |  |  |

*

*

e e |  |  |  |  |  |  |  |  | *! | * |  |  |  |
E e |  |  |  |  |  |  | *! |  | * |  |  |  |  |
E i |  |  |  |  |  | *! |  |  |  |  |  |  |  |
i i |  |  |  | *! |  |  |  |  |  |  |  |  |  |
E E |  |  | *! |  |  |  |  |  |  |  |  |  |  |

/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 |  |  |  |  |  |  |  |

* |

e e |  |  |  |  |  |  |  |  |  | *! |  |  |  |
E 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 |  |  |  |  |  |  |  |

**

*

e e e |  |  |  |  |  |  |  |  | *! | ** |  |  |  |
E e i |  |  |  |  |  |  | *! |  |  | * |  | * |  |
E E i |  |  |  |  |  | *! |  |  |  |  |  |  |  |
i i i |  |  |  | *!* |  |  |  |  |  |  |  |  |  |
E E E |  |  | *! |  |  |  |  |  |  |  |  |  |  |

/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 |  |  |  |  |  |  |  |

* |

E E |  |  |  |  |  |  |  |  |  |  | *! |  |  |
e e |  |  |  |  |  |  |  |  |  | *! |  |  |  |

/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 |  |  |  |  |  |  |  |

**

*

*

e e e e |  |  |  |  |  |  |  | *! | * | ** |  |  |  |
E E e i |  |  |  |  |  |  | *! |  |  |  |  | * |  |
i i i i |  |  |  | *!* |  |  |  |  |  |  |  |  |  | *
E E E E |  |  | *! |  |  |  |  | * |  |  | * |  |  |
e e e i | *! |  |  |  |  |  |  |  |  | ** |  | * |  |

3. Status of Proposed Constraints: Necessary or Unnecessary

Constraint | Status
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 |

**

e e i | * |

/e e i/: | *e i | *Map(e i)
☞ i i i |

**

e i i | * | *

/i e/: | *i e | *Map(i e)
☞ e e |

*

i e | * |

/E i/: | *E i | *Map(E e) | *e i
☞ e i |

*

*

E i | * |  |

/E i/: | *Map(i E) | *Map(E e) | *e i
☞ e i |

*

*

E E | * |  |

/E i/: | *Map(i e) | *Map(E e) | *e i
☞ e i |  | *

*

e e | * | * |

/E i/: | *Map(E i) | *Map(E e) | *e i
☞ e i |

*

*

i i | * |  |

/E e/: | *E e | *Map(e E)
☞ E E |

*

E e | * |

/E e/: | *Map(E e) | *Map(e E)
☞ E E |

*

e e | * |

/E E i/: | *E e | *Map(E e) | *e i
☞ e e i |

**

*

E e i | * | * | *

/E E i/: | *E i | *Map(E e) | *e i
☞ e e i |

**

*

E E i | * |  |

/E E i/: | *Map(E i) | *Map(E e) | *e i
☞ e e i |

**

*

i i i | * * |  |

/E E i/: | *Map(i E) | *Map(E e) | *e i
☞ e e i |

**

*

E E E | * |  |

/E E i/: | *Map(i e) | *Map(E e) | *e i
☞ e e i |  | **

*

e e e | * | ** |

/e E/: | *Map(E e) | *e E
☞ e E |

*

e e | * |

/e E/: | *Map(e E) | *e E
☞ e E |

*

E E | * |

/E E e i/: | BeGood | *Map(E e) | *e i | *Map(e i)
☞ e e i i |

**

*

*

e e e i | * | ** | * |

/E E e i/: | *E e | *Map(E e) | *e i | *Map(e i)
☞ e e i i |

**

*

*

E E e i | * |  | * |

/E E e i/: | *Map(E i) | *Map(E e) | *e i | *Map(e i)
☞ e e i i |

**

*

*

i i i i | * * |  |  | *

6. Hasse Diagram

The following Hasse diagram (in output folder at KikuriaClassHasse.gif) summarizes the rankings obtained.