Wedge Out (vOut)
BIG MISTAKE:
1. PvQ
2. P
1 vO
Wedge Out (vOut)
BIG MISTAKE:
1. PvQ
2. 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.
If CHEMO then the patient SUFFERS.
If RADIATION then the patient SUFFERS.
So the patient SUFFERS.
CvR
C>S
R>S
S
Wedge Out (vOut)
So What is Wedge Out?
Wedge Out is a THREE PREMISE RULE.
a.k.a (Simple Constructive) Dilemma
AvB
A>G
B>G
G
Wedge Out (vOut)
So What is Wedge Out?
Wedge Out is a THREE PREMISE RULE.
a.k.a (Simple Constructive) Dilemma
AvB
A>G
B>G
G
A v B
G
Wedge Out Strategy
How to use vOut.
1. AvM
A
AvB
A>G
B>G
G
A v B
G
MvA
GOAL
Wedge Out Strategy
How to use vOut.
1. AvM
AvB
A>G
B>G
G
A
A v B
When a disjunction
is available, use
the vOut strategy.
MvA
1,?,? vO
G
Wedge Out Strategy
How to use vOut.
1. AvM
AvB
A>G
B>G
G
A
A v B
Missing Conditionals
MvA
1,?,? vO
G
Wedge Out Strategy
How to use vOut.
1. AvM
AvB
A>G
B>G
G
A
A v B
Missing Conditionals
MvA
1,?,? vO
G
Wedge Out Strategy
How to use vOut.
1. AvM
AvB
A>G
B>G
G
A
A v B
A>(MvA)
GOAL
M>(MvA)
MvA
GOAL
1,?,? vO
G
Make the missing conditionals new goals.
Wedge Out Strategy
How to use vOut.
1. AvM
AvB
A>G
B>G
G
A
A v B
A>(MvA)
?-? >I
M>(MvA)
MvA
GOAL
1,?,? vO
G
Use the >In strategy to get the first goal.
Wedge Out Strategy
How to use vOut.
AvB
A>G
B>G
G
1. AvM
A
2. A
PA
MvA
GOAL
A>(MvA)
2-? >I
M>(MvA)
MvA
GOAL
1,?,? vO
How to get MvA?
A v B
G
Wedge Out Strategy
How to use vOut.
AvB
A>G
B>G
G
1.
2.
3.
4.
AvM
A
MvA
A>(MvA)
A
PA
2 vI
2-3 >I
M>(MvA)
MvA
GOAL
1,?,? vO
Just use vI!
A v B
G
Wedge Out Strategy
How to use vOut.
AvB
A>G
B>G
G
1.
2.
3.
4.
AvM
A
A
PA
MvA
2 vI
A>(MvA)
2-3 >I
M
PA
MvA
GOAL
M>(MvA)
?-? >I
MvA
1,?,? vO
A v B
G
Use the >I strategy to get the second goal.
Wedge Out Strategy
How to use vOut.
AvB
A>G
B>G
G
1.
2.
3.
4.
5.
6.
7.
8.
AvM
A
MvA
A>(MvA)
M
MvA
M>(MvA)
MvA
A
PA
2 vI
2-3 >I
PA
5 vI
5-6 >I
1,4,7 vO
A v B
G
... and finish the second subproof the same way.
A v B
Wedge Out Strategy
G
Summary of the vOut Strategy:
Whenever AvB is available,
and G is your goal ...
AvB
G
GOAL
Wedge Out Strategy
A v B
G
Summary 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.
For more click here
AvB
A>G GOAL
B>G GOAL
G
?,?,? vO