\ti\ftResults of Applying Recursive Constraint Demotion to Tangale.txt

\hrRankings for Tangale.txt	4-01-2019	\pn

\cn4-01-2019, 11:52 a.m.

\cnOTSoft 2.5
\cnRelease date 1/17/2017


\h1Result
A ranking was found that generates the correct outputs.
\ks
\ts3
\ntStratum	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
\te\ke

\h1Tableaux
\ts6\ks
/i ] I/	*A\dl	Id-OO(ATR)	Agree	Id-IO(ATR)\dl	Id(IO)-ATR Initial
\wsF\we i ] i				*\sh	\sh
i ] I			*!	\sh	\sh
I ] I		*!	*\sh	\sh	*\sh
\te\ke
\ts6\ks
/a ] i/	*A\dl	Id-OO(ATR)	Agree	Id-IO(ATR)\dl	Id(IO)-ATR Initial
\wsF\we a ] I				*\sh	\sh
a ] i			*!	\sh	\sh
A ] i	*!	*\sh	\sh	*\sh	*\sh
\te\ke
\ts6\ks
/i ] a/	*A\dl	Id-OO(ATR)	Agree	Id-IO(ATR)\dl	Id(IO)-ATR Initial
\wsF\we i ] a			*\sh	\sh	\sh
I ] a		*!	\sh	*\sh	\sh
i ] A	*!	\sh	\sh	*\sh	\sh
\te\ke
\ts6\ks
/i ] a ] i/	*A\dl	Id-OO(ATR)	Agree	Id-IO(ATR)\dl	Id(IO)-ATR Initial
\wsF\we i ] a ] I			*	*\sh	\sh
i ] a ] i			**!	\sh	\sh
I ] a ] I		*!	\sh	**\sh	*\sh
i ] A ] i	*!	\sh	\sh	*\sh	\sh
\te\ke
\ts6\ks
/i a/	*A\dl	Id-OO(ATR)	Agree	Id-IO(ATR)\dl	Id(IO)-ATR Initial
\wsF\we I a				*\sh	*\sh
i a			*!	\sh	\sh
i A	*!	\sh	\sh	*\sh	\sh
\te\ke
\ts6\ks
/i I/	*A\dl	Id-OO(ATR)	Agree	Id-IO(ATR)\dl	Id(IO)-ATR Initial
\wsF\we i i				*	
I I				*	*!
i I			*!	\sh	\sh
\te\ke

\h1Status of Proposed Constraints:  Necessary or Unnecessary
\ts2
\ntConstraint	Status
Agree	Necessary
*A	Necessary
Id-OO(ATR)	Necessary
Id(IO)-ATR Initial	Necessary
Id-IO(ATR)	Not necessary
\te
\ks

\h1Ranking 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.
\ke
Original set of ERCs
\ks
\ts3
\ntIndex	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
\te\ke
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)

\h1Ranking 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

\h1Mini-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.
\ts3\ks
/i ] I/	Agree	Id-IO(ATR)
\wsF\we i ] i		*
i ] I	* 	
\te\ke
\ts3\ks
/a ] i/	Agree	Id-IO(ATR)
\wsF\we a ] I		*
a ] i	* 	
\te\ke
\ts3\ks
/i ] a ] i/	Agree	Id-IO(ATR)
\wsF\we i ] a ] I	*	*
i ] a ] i	** 	
\te\ke
\ts4\ks
/i ] a ] i/	*A	Agree	Id-IO(ATR)
\wsF\we i ] a ] I		*	*
i ] A ] i	* 		*
\te\ke
\ts4\ks
/i a/	Agree	Id-IO(ATR)\dl	Id(IO)-ATR Initial
\wsF\we I a		*	*
i a	* 		
\te\ke
\ts4\ks
/i a/	*A	Id-IO(ATR)\dl	Id(IO)-ATR Initial
\wsF\we I a		*	*
i A	* 	*	
\te\ke
\ts3\ks
/i I/	Agree	Id-IO(ATR)
\wsF\we i i		*
i I	* 	
\te\ke
