Logic Supplementary Slides
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Logic Supplementary Slides
Fariba Sadri
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Some Hints on Constructing Proofs
Suppose we want to prove
S |- W
S set of wffs, W a wff.
• Look at the structure of W – table on slide
3.
• Look where W occurs in S – table on slide
4. Here W is sub-formula of Q.
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Principle
connective
of W
W is of the
form
Inference
rule to
consider
Subgoals
A B I
Assume A Show B
A B I
Show A and Show B
A B I
Show AB and
Show BA
A B I or
RAA
Show A or Show B
Assume (A B)
Show inconsistency
A RAA
Assume A
Show inconsistency
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In S we have Inference rule
to consider
Subgoals
PW
PQ
E Show P
Then apply E
WP, PW
QP, PQ
E Show ¬P
Then apply E
WP, P W
QP, PQ
E —-
P W
P Q
E —-
¬W P RAA —-
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Desperate?
No Idea which inference Rule to Use?
Try RAA.