1. CSE4/563: Knowledge Representation Recitation September 20, 2010
“In activities other than purely logical thought, our minds function much faster than any computer yet devised.”
--Daniel Crevier

2. HW1 Questions/Concerns?

3. Logical Entailment
A1,…, An ╞L B

4. Logical Entailment A1,…, An ╞L B Example:
A1 = Tom drives  Betty is the passenger
A2 = Tom drives
A1, A2 ╞ Betty is the passenger

5. Logical Entailment A1,…, An ╞L B ╞ B Example:
A1 = Tom drives  Betty is the passenger
A2 = Tom drives
A1, A2 ╞ Betty is the passenger
╞ B

6. Logical Entailment A1,…, An ╞L B ╞ B Example: Example: ╞ (P or ~P)
A1 = Tom drives  Betty is the passenger
A2 = Tom drives
A1, A2 ╞ Betty is the passenger
╞ B
Example: ╞ (P or ~P)

7. Well Formed Propositions
What is a WFP?

8. Well Formed Propositions
Every atomic proposition is a wfp.
If P is a wfp, then so is (~P).
If P and Q are wfps, then so are
(P ^ Q)
(P v Q)
(P => Q)
(P <=> Q)
4. Nothing else is a wfp.

9. Semantic Properties of WFPs
Satisfiable?
Contingent?
Valid?
Unsatisfiable?
Contradictory?

10. Model-Finding Refutation
TDB=>TD, TD=>BP, ~(TP^BP) ╞ ~(TDB ^ TP)

11. ‘How Dorothy Ended Up In Oz’ Domain
If there is a cyclone Dorothy should hide in the cellar. If Toto jumps from Dorothy’s arms and hides, she should find him. If Dorothy takes time to find Toto, or if she is too slow, she won’t make it to the cellar before the cyclone hits. Dorothy ends up in Oz if she doesn’t make it to the cellar in time. Assume: There is a cyclone and Toto jumps from Dorothy’s arms and hides. Prove: Dorothy ends up in Oz.