4-09-2019, 9:01 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	Ident(rd)	Id rd
Stratum #2	*RoLo	*RoLo
	Agree back	Agr bk
Stratum #3	Agree round	Agr rd
Stratum #4	Ident before spec	Ident before spec

2. Tableaux

/[ o ] /:	Id rd	*RoLo	Agr bk	Agr rd	Ident before spec
☞   [ o ]		*
[ a ]	*!

/[ o ] A/:	Id rd	*RoLo	Agr bk	Agr rd	Ident before spec
☞   [ o ] a		*		*
[ o ] e		*	*!	*
[ o ] o		**!

/[ o ] I/:	Id rd	*RoLo	Agr bk	Agr rd	Ident before spec
☞   [ o ] u		*
[ o ] i-		*		*!
[ o ] i		*	*!	*

/[ o ] I yor/:	Id rd	*RoLo	Agr bk	Agr rd	Ident before spec
☞   [ o ] u yor		**			*
[ o ] i- yor		**		*!*

/[ a] I yor/:	Id rd	*RoLo	Agr bk	Agr rd	Ident before spec
☞   [ a ] i- yor		*		*
[ a ] u yor		*		*	*!
[ a ] i- yar	*!

/[ e] I yor/:	Id rd	*RoLo	Agr bk	Agr rd	Ident before spec
☞   [ e ] i yor		*	*	*
[ e ] u yor		*	*	*	*!
[ e ] U yor		*	*	*	*!
[ e ] i yer	*!

/[ u ] I - a/:	Id rd	*RoLo	Agr bk	Agr rd	Ident before spec
☞   [ u ] u a				*
[ u ] i- a				*	*!
[ u ] u o	*!	*

3. Status of Proposed Constraints: Necessary or Unnecessary

Constraint	Status
*RoLo	Necessary
Ident(rd)	Necessary
Agree back	Necessary
Agree round	Necessary
Ident before spec	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	LWeee	for /[ o ] /, [ o ] >> [ a ]
2	WeeLe	for /[ o ] A/, [ o ] a >> [ o ] o
3	eeeWL	for /[ o ] I yor/, [ o ] u yor >> [ o ] i- yor
4	LWeLe	for /[ a] I yor/, [ a ] i- yor >> [ a ] i- yar
5	LWLLe	for /[ e] I yor/, [ e ] i yor >> [ e ] i yer
6	WWeLe	for /[ u ] I - a/, [ u ] u a >> [ u ] u o

Recursive ranking search

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

Fusion of this ERC set is: LWLLL

The following ERCs form the total information-loss residue:

WeeLe

eeeWL

Fusion of total residue: WeeLL

Skeletal basis of the fusion: LWLee

LWLee 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

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

Working with the following ERC set:

WeeLe

eeeWL

Fusion of this ERC set is: WeeLL

The following ERCs form the total information-loss residue:

eeeWL

Fusion of total residue: eeeWL

Skeletal basis of the fusion: WeeLe

WeeLe includes at least one L and thus is not entailed by eeeWL.

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

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

Current set of ERCs is based on constraint #1, *RoLo

Working with the following ERC set:

eeeWL

Fusion of this ERC set is: eeeWL

The following ERCs form the total information-loss residue:

eeeWL 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.

LWLee	Must dominate these constraints
WeeLe
eeeWL

The final rankings obtained are as follows:

Id rd >> { *RoLo, Agr bk }	Must dominate these constraints
*RoLo >> Agr rd
Agr rd >> Ident before spec

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 ] /:	Id rd	*RoLo
☞   [ o ]		*
[ a ]	*

/[ o ] A/:	*RoLo	Agr rd
☞   [ o ] a	*	*
[ o ] o	**

/[ o ] I yor/:	*RoLo	Agr rd	Ident before spec
☞   [ o ] u yor	**		*
[ o ] i- yor	**	* *

/[ a] I yor/:	Id rd	*RoLo	Agr rd
☞   [ a ] i- yor		*	*
[ a ] i- yar	*

/[ e] I yor/:	Id rd	*RoLo	Agr bk	Agr rd
☞   [ e ] i yor		*	*	*
[ e ] i yer	*