1. CSE391-2005LOGIC1 Propositional Logic An “adventure game” example Thinking?

2. CSE391-2005LOGIC2 PSSS The Physical Symbol System Hypothesis: A physical symbol system has the necessary and sufficient means for general intelligent action. Where a symbol is a designating pattern that can be combined with others to form another designating pattern.

3. CSE391-2005LOGIC3 Knowledge Representation Key is problem formulation – –What happens when an n-dimensional array is insufficient? Need a language that is –Expressive and concise –Unambiguous and independent of context –Has an inference procedure for new sentences

4. CSE391-2005LOGIC4 Inference Rules And Elimination  1   2, ...   n  1 And Introduction  1,...,  n  1   2, ...   n

5. CSE391-2005LOGIC5 Inference Rules (cont’d) Or Introduction  i  1   2, ...   i  …   n Double Negation Elimination  

6. CSE391-2005LOGIC6 Inference Rules (cont’d) Modus Ponens (Implication Elimination) ,   (Chaining) ,    

7. CSE391-2005LOGIC7 Inference Rules (cont’d) Unit Resolution: ,   (cf.Modus Ponens) Resolution: ,    is true or false. If  is true,  is true. If  is false,  is true.

8. CSE391-2005LOGIC8 The Lion World Percepts: [Stench, Breeze, Glitter, Bump, Scream] Operators: [Right 90, Left 90, Forward, Grab, Shoot,Climb]

9. CSE391-2005LOGIC9 The Lion World (1,1) [none,none,none,none,none] A ok

10. CSE391-2005LOGIC10 The Lion World (1,1) [none,none,none,none,none] (2,1) [none,breeze,none,none,none] ok B P? A

11. CSE391-2005LOGIC11 The Lion World (1,1) [none,none,none,none,none] (2,1) [none,breeze,none,none,none] ok B P? A (1,2) [stench,none,none,none,none] L? ok

12. CSE391-2005LOGIC12 The Lion World (1,1) [none,none,none,none,none] (2,1) [none,breeze,none,none,none] (1,2) [stench,none,none,none,none] ok B P? A (2,3)[Stench,none,Glitter,none,none] L? (2,2) [none,none,none,none,none] ok

13. CSE391-2005LOGIC13 The Lion World The Knowledge Base ¬ S 1,1, ¬ B 1,1 P 3,1, B 4,1 ¬ S 2,1, B 2,1 ¬ S 3,2, B 3,2 S 1,2, ¬ B 1,2 ¬ S 2,2, ¬ B 2,2 ¬ S 3,3, ¬ B 3,3 Gl 1,4,¬ S 1,4, ¬ B 1,4 ¬ S 2,4, ¬ B 2,4, G 2.4 B 3,4, Gl 3,4 ¬ S 1,3, ¬ B 1,3, L 1,3 B 4,3 S 2.3, ¬ B 2.3, Gl 2.3 P 4,4

14. CSE391-2005LOGIC14 Lion World Implications R1 : ¬ S 1,1 → ¬ L 1,2 /\ ¬ L 2,1 R2 : ¬ S 2,1 → ¬ L 1,1 /\ ¬ L 2,2 /\ ¬ L 3,1 R3 : ¬ S 1,2 → ¬ L 1,1 /\ ¬ L 2,2 /\ ¬ L 1,3 R4 : S 1,2 → L 1,1 \/ L 2,2 \/ L 1,3

15. CSE391-2005LOGIC15 Lion World Implications transformed into Conjunctive Normal Form (R1-R3) R1 : ¬ S 1,1 → ¬ L 1,2 /\ ¬ L 2,1 R1 : ¬ ¬ S 1,1 \/ ( ¬ L 1,2 /\ ¬ L 2,1 ) R1 : S 1,1 \/ (¬ L 1,2 /\ ¬ L 2,1 ) R1: (S 1,1 \/ ¬ L 1,2 )/\ (S 1,1 \/ ¬ L 2,1 ) R1: (S 1,1 \/ ¬ L 1,2 ), (S 1,1 \/ ¬ L 2,1 )

16. CSE391-2005LOGIC16 Lion World Implications transformed into Conjunctive Normal Form – R4 R4 : S 1,2 → L 1,1 \/ L 2,2 \/ L 1,3 R4 : ¬ S 1,2 \/ (L 1,1 \/ L 2,2 \/ L 1,3 ) R4: ¬ S 1,2 \/ L 1,1 \/ L 2,2 \/ L 1,3

17. CSE391-2005LOGIC17 The Lion World (1,1) [none,none,none,none,none] A ok

18. CSE391-2005LOGIC18 ¬ S 1,1, S 1,1 \/ ¬L 1,2 Unit Resolution ¬ L 1,2 ¬ S 1,1, S 1,1 \/ ¬L 2,1 Unit Resolution ¬ L 2,1 Finding the Lion

19. CSE391-2005LOGIC19 The Lion World ok B P? A (1,2) [stench,none,none,none,none] L?

20. CSE391-2005LOGIC20 S 1,2, ¬ S 1,2 \/ L 1,1 \/ L 2,2 \/ L 1,3 L 1,1 \/ L 2,2 \/ L 1,3 Unit Resolution L 1,1 \/ L 2,2 \/ L 1,3,¬ L 1,1 L 2,2 \/ L 1,3 Unit Resolution Finding the Lion

21. CSE391-2005LOGIC21 Finding the Lion L 2,2 \/ L 1,3,¬ L 2,2 L 1,3 Unit Resolution How do we know ¬ L 2,2 ?

22. CSE391-2005LOGIC22 Avoiding the Lion Don’t go forward if the lion is in front – A 1,2 /\ North A /\ L 1,3  ¬Forward 64 rules (16 squares x 4 orientations)

23. CSE391-2005LOGIC23 Avoiding the Lion in the next move After the Agent moves, A 1,2 is no longer true, now A 2,3 is true. A 2,3 /\ West A /\ L 1,3  ¬Forward

24. CSE391-2005LOGIC24 Limitations of Propositional Logic Can’t express generalities Need new propositions for each time stamp