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 | Constraint Name | Abbreviation |
| 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 ] |
|
* |
|
|
|
|
| [ a ] |
*! |
|
|
|
|
|
| /[ o ] A/: |
Max(rd) |
RoLo |
Agr bk |
Agr rd |
No L(rd) |
Dep(+rd) |
| ☞ [ o ] a |
|
* |
|
* |
|
|
| [ o ] e |
|
* |
*! |
* |
|
|
| [ o ] o |
|
**! |
|
|
|
|
| /[ o ] I/: |
Max(rd) |
RoLo |
Agr bk |
Agr rd |
No L(rd) |
Dep(+rd) |
| ☞ [ o ] u |
|
* |
|
|
|
|
| [ o ] i- |
|
* |
|
*! |
|
|
| [ o ] i |
|
* |
*! |
* |
|
|
| /[ o ] I yor/: |
Max(rd) |
RoLo |
Agr bk |
Agr rd |
No L(rd) |
Dep(+rd) |
| ☞ [ o ] u yor |
|
** |
|
|
* |
* |
| [ o ] i- yor |
|
** |
|
*!* |
|
|
| /[ a ] I yor/: |
Max(rd) |
RoLo |
Agr bk |
Agr rd |
No L(rd) |
Dep(+rd) |
| ☞ [ a ] i- yor |
|
* |
|
* |
|
|
| [a ] u yor |
|
* |
|
* |
*! |
* |
| /[ e ] I yor/: |
Max(rd) |
RoLo |
Agr bk |
Agr rd |
No L(rd) |
Dep(+rd) |
| ☞ [ e ] i yor |
|
* |
* |
* |
|
|
| [ e ] u yor |
|
* |
* |
* |
*! |
* |
| [ e ] U yor |
|
* |
* |
* |
*! |
* |
| [ e ] i yer |
*! |
|
|
|
|
|
| /[ u ] I a/: |
Max(rd) |
RoLo |
Agr bk |
Agr rd |
No L(rd) |
Dep(+rd) |
| ☞ [ u ] u a |
|
|
|
* |
|
* |
| [ u ] i- a |
|
|
|
* |
*! |
|
3. Status of Proposed Constraints: Necessary or Unnecessary
| Constraint | Status |
| Agree back | Necessary |
| Agree round | Necessary |
| RoLo | Necessary |
| Max(rd) | Necessary |
| No left(round) | 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 | Must dominate these constraints |
| eLeWee | |
| eWeeeL | |
| eeLeeW |
The final rankings obtained are as follows:
| Max(rd) >> { Agr bk, RoLo } | Must dominate these constraints |
| 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 ] |
|
* |
| [ a ] |
* |
|
| /[ o ] A/: |
RoLo |
Agr rd |
| ☞ [ o ] a |
* |
* |
| [ o ] o |
** |
|
| /[ o ] I yor/: |
RoLo |
Agr rd |
No L(rd) |
Dep(+rd) |
| ☞ [ o ] u yor |
** |
|
* |
* |
| [ o ] i- yor |
** |
* * |
|
|
| /[ e ] I yor/: |
Max(rd) |
RoLo |
Agr bk |
Agr rd |
| ☞ [ e ] i yor |
|
* |
* |
* |
| [ e ] i yer |
* |
|
|
|
| /[ u ] I a/: |
Agr rd |
No L(rd) |
Dep(+rd) |
| ☞ [ u ] u a |
* |
|
* |
| [ u ] i- a |
* |
* |
|