程序代写代做代考 Logic Supplementary Slides

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 AB and

Show BA

 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

PW

PQ

E Show P

Then apply E

WP, PW

QP, PQ

E Show ¬P

Then apply E

WP, P  W

QP, PQ

E —-

P  W

P  Q

E —-

¬W  P RAA —-

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Desperate?

No Idea which inference Rule to Use?

Try RAA.