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 | Constraint Name | Abbreviation
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 |  |

* |

i ] I |  |  | *! |  |
I ] I |  | *! | * |  | *

/a ] i/: | *A | Id-OO(ATR) | Agree | Id-IO(ATR) | Id(IO)-ATR Initial
☞ a ] I |  |

* |

a ] i |  |  | *! |  |
A ] i | *! | * |  | * | *

/i ] a/: | *A | Id-OO(ATR) | Agree | Id-IO(ATR) | Id(IO)-ATR Initial
☞ i ] a |  |

*

I ] a |  | *! |  | * |
i ] A | *! |  |  | * |

/i ] a ] i/: | *A | Id-OO(ATR) | Agree | Id-IO(ATR) | Id(IO)-ATR Initial
☞ i ] a ] I |  |

*

* |

i ] a ] i |  |  | **! |  |
I ] a ] I |  | *! |  | ** | *
i ] A ] i | *! |  |  | * |

/i a/: | *A | Id-OO(ATR) | Agree | Id-IO(ATR) | Id(IO)-ATR Initial
☞ I a |  |

* |

*

i a |  |  | *! |  |
i A | *! |  |  | * |

/i I/: | *A | Id-OO(ATR) | Agree | Id-IO(ATR) | Id(IO)-ATR Initial
☞ i i |  |

* |

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

3. Status of Proposed Constraints: Necessary or Unnecessary

Constraint | Status
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 | Must dominate these constraints
WeeLL |
LWeee |

The final rankings obtained are as follows:

Id-OO(ATR) >> Agree | Must dominate these constraints
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 |

*

i ] I | * |

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

*

a ] i | * |

/i ] a ] i/: | Agree | Id-IO(ATR)
☞ i ] a ] I | *

*

i ] a ] i | ** |

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

*

*

i ] A ] i | * |  | *

/i a/: | Agree | Id-IO(ATR) | Id(IO)-ATR Initial
☞ I a |

* |

*

i a | * |  |

/i a/: | *A | Id-IO(ATR) | Id(IO)-ATR Initial
☞ I a |

* |

*

i A | * | * |

/i I/: | Agree | Id-IO(ATR)
☞ i i |

*

i I | * |