1. Dependency Lists Whenever you use PA in a proof,
you need to include dependency lists.

2. Dependency Lists Whenever you use PA in a proof,
you need to include dependency lists.
Here is why they are necessary:
1) M>B A
2) M PA
3) B ,2 >O

3. Dependency Lists Whenever you use PA in a proof,
you need to include dependency lists.
Here is why they are necessary:
1) M>B A
2) M PA
3) B ,2 >O
But the argument M>B | B is invalid!

4. We need a way to keep track of Provisional Assumptions.
Dependency Lists
Whenever you use PA in a proof,
you need to include dependency lists.
Here is why they are necessary:
1) M>B A
2) M PA
3) B ,2 >O
But the argument M>B | B is invalid!
Moral:
We need a way to keep track of Provisional Assumptions.

5. Moral: We need a way to keep track of Provisional Assumptions.
Dependency Lists
Whenever you use PA in a proof,
you need to include dependency lists.
Here is why they are necessary:
1) M>B A
2) M PA
3) B ,2 >O
But the argument M>B | B is invalid!
Moral: We need a way to keep track of Provisional Assumptions.

6. Dependency Lists 1) C>M 2) M>J 3) C 4) M 5) J 6) C>J A PA
1,3 >O
2,4 >O
3-5 >I

7. Assumptions depend on themselves
Dependency Lists 1 2 3
1) C>M
2) M>J
3) C
4) M
5) J
6) C>J A PA
1,3 >O
2,4 >O
3-5 >I
Assumptions depend on themselves

8. Dependency Lists 1 2 3 1,3 1) C>M 2) M>J 3) C 4) M 5) J
6) C>J A PA
1,3 >O
2,4 >O
3-5 >I
For >Out, &In, and &Out add together
the dependency lists for the lines used.

9. Dependency Lists 1 2 3 1,3 1,2,3 1) C>M 2) M>J 3) C 4) M 5) J
6) C>J A PA
1,3 >O
2,4 >O
3-5 >I
For >Out, &In, and &Out add together
the dependency lists for the lines used.

10. Dependency Lists 1 2 3 1,3 1,2,3 1,2 1) C>M 2) M>J 3) C 4) M
6) C>J A PA
1,3 >O
2,4 >O
3-5 >I
For >In, take the list for the consequent,
and remove the number for the PA.

11. Dependency Lists 1 2 3 1,3 1,2,3 1,2 1) C>M 2) M>J 3) C 4) M
6) C>J A PA
1,3 >O
2,4 >O
3-5 >I
For >In, take the list for the consequent,
and remove the number for the PA.
WHY DO YOU REMOVE THE PA NUMBER?

12. Dependency Lists 1 2 3 1,3 1,2,3 1,2 1) C>M 2) M>J 3) C 4) M
6) C>J A PA
1,3 >O
2,4 >O
3-5 >I
For >In, take the list for the consequent,
and remove the number for the PA.
WHY DO YOU REMOVE THE PA NUMBER?
A CONDITIONAL DOES NOT DEPEND
ON ITS ANTECEDENT.

13. For more click here Dependency Lists Why this “proof” does not work:
M>B A
M PA
1, B ,2 >O
No proof is complete if the dependency list contains the number of a PA!
For more click here