Wedge Out (vOut)
BIG MISTAKE:
1. PvQ2. P 1 vO
Wedge Out (vOut)
BIG MISTAKE:
1. PvQ2. P 1 vO
This is NOT vOut, and besides...the reasoning is INVALID!
Wedge Out (vOut)
So What is Wedge Out?
Wedge Out is a THREE PREMISE RULE.a.k.a (Simple Constructive) Dilemma
Wedge Out (vOut)
So What is Wedge Out?
Wedge Out is a THREE PREMISE RULE.a.k.a (Simple Constructive) Dilemma
An illustration of a Dilemma:
We have to use CHEMO or RADIATION. CvRIf CHEMO then the patient SUFFERS. C>SIf RADIATION then the patient SUFFERS. R>SSo the patient SUFFERS. S
Wedge Out (vOut)
So What is Wedge Out?
Wedge Out is a THREE PREMISE RULE.a.k.a (Simple Constructive) Dilemma
A v BA>GB>GG
Wedge Out (vOut)
So What is Wedge Out?
Wedge Out is a THREE PREMISE RULE.a.k.a (Simple Constructive) Dilemma
A v BA>GB>GG
A v B
G
Wedge Out Strategy
How to use vOut.
A v BA>GB>GG
1. AvM A
MvA GOAL
A v B
G
Wedge Out Strategy
How to use vOut.
A v BA>GB>GG
A v B
G
1. AvM A
MvA 1,?,? vO
When a disjunctionis available, use
the vOut strategy.
Wedge Out Strategy
How to use vOut.
A v BA>GB>GG
A v B
G
1. AvM A
MvA 1,?,? vO
Missing Conditionals
Wedge Out Strategy
How to use vOut.
A v BA>GB>GG
A v B
G
1. AvM A
MvA 1,?,? vO
Missing Conditionals
Wedge Out Strategy
How to use vOut.
A v BA>GB>GG
A v B
G
1. AvM A
A>(MvA) GOAL
M>(MvA) GOAL MvA 1,?,? vO
Make the missing conditionals new goals.
Wedge Out Strategy
How to use vOut.
A v BA>GB>GG
A v B
G
1. AvM A
A>(MvA) ?-? >I
M>(MvA) GOAL MvA 1,?,? vO
Use the >In strategy to get the first goal.
Wedge Out Strategy
How to use vOut.
A v BA>GB>GG
A v B
G
1. AvM A2. A PA MvA GOAL A>(MvA) 2-? >I
M>(MvA) GOAL MvA 1,?,? vO
How to get MvA?
Wedge Out Strategy
How to use vOut.
A v BA>GB>GG
A v B
G
1. AvM A2. A PA3. MvA 2 vI4. A>(MvA) 2-3 >I
M>(MvA) GOAL MvA 1,?,? vO
Just use vI!
Wedge Out Strategy
How to use vOut.
A v BA>GB>GG
A v B
G
1. AvM A2. A PA3. MvA 2 vI4. A>(MvA) 2-3 >I M PA MvA GOAL M>(MvA) ?-? >I MvA 1,?,? vO
Use the >I strategy to get the second goal.
Wedge Out Strategy
How to use vOut.
A v BA>GB>GG
A v B
G
1. AvM A2. A PA3. MvA 2 vI4. A>(MvA) 2-3 >I5. M PA6. MvA 5 vI7. M>(MvA) 5-6 >I8. MvA 1,4,7 vO
... and finish the second subproof the same way.
Wedge Out StrategySummary of the vOut Strategy:
Whenever AvB is available,and G is your goal ...
A v B
G GOAL
A v B
G
Wedge Out StrategySummary of the vOut Strategy:
Whenever AvB is available,and G is your goal ...
calculate the missing conditionals(namely A>G and B>G)and make them new goals.
When these conditionals are proven,your old goal will follow by vOut.
A v B
A>G GOAL
B>G GOALG ?,?,? vO
A v B
G
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