CSE4/563: Knowledge Representation Recitation September 27, 2010

1. CSE4/563: Knowledge RepresentationRecitation September 27, 2010 “Imagination is more important than knowledge.” --Albert Einstein

2. HW2/Proj1 Questions/Concerns? http://www.cse.buffalo.edu/~shapiro/Courses/CSE563/2010/Homeworks/hw2.pdf http://www.cse.buffalo.edu/~shapiro/Courses/CSE563/2010/Projects/proj1.pdf

3. Logical Entailment Metatheorm Proof A1,…, An ╞L B <=> ╞LA1 ^ A2 ^ … ^ An => B

4. Logical Entailment Metatheorm Proof A1,…, An ╞L B <=> ╞LA1 ^ A2 ^ … ^ An => B => Assume A1,…, An ╞L B Therefore B is true whenever all Ai are true From this we can say ╞LA1,…, An => B

5. Logical Entailment Metatheorm Proof A1,…, An ╞L B <=> ╞LA1 ^ A2 ^ … ^ An => B => Assume A1,…, An ╞L B If this is uncomfortable for you, assume it’s not the case that ╞LA1,…, An => B. Then all A’s must be true and B is false. This contradicts the original assumption.

6. Logical Entailment Metatheorm Proof A1,…, An ╞L B <=> ╞LA1 ^ A2 ^ … ^ An => B <= Assume ╞LA1 ^ A2 ^ … ^ An => B We can agree then, that: A1,…, An ╞L A1 ^ A2 ^ … ^ An => B And: A1,…, An ╞L A1 ^ A2 ^ … ^ An By modus ponens: A1,…, An ╞L B

7. Properties of Logical Syntax • Soundness • ├ P implies ╞ P • “If you can prove it, it’s logically valid” • Consistency • Not both ├ P and ├ ~P • Completeness • ╞ P implies ├ P • “If it is valid, you can prove it”

8. ‘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.