1. Class Project Due at end of finals week Essentially anything you want, so long as its AI related and I approve Any programming language you want In pairs or individual

2. Class Project Examples: Implement a game player Implement supervised learning algorithms Use a series of learning methods to classify existing data....? Email me by Monday to tell me what you’re doing, and who you’re working with

3. Agents that Reason Logically Logical agents have a knowledge base, from which they draw conclusions about how to act TELL: provide new facts to the agent ASK: decide on appropriate action Can perceive agent at different levels: Knowledge level (logical): What the agent “knows” Implementation level: How the information is actually stored internally in the computer We will concentrate on the logical level

4. Sample: Wumpus World Show sample wumpus game goal is to shoot wumpus example of logical reasoning Textbook example http://baldur.mm.rpi.edu/otter/wumpus/W umpus.html http://baldur.mm.rpi.edu/otter/wumpus/W umpus.html goal is to find gold and avoid wumpus, and climb back out of cave

5. Some complex reasoning examples Start in (1,1) Breeze in (1,2) and (2,1) Probably a pit in (2,2) Smell in (1,1) – where can you go? Pick a direction – shoot Walk in that direction Know where wumpus is

6. The use of logic A logic is a formal language for representing information, and rules for drawing conclusions Syntax: what “sentences” are legal Semantics: what the sentences “mean” What is true in a particular world and what isn’t Arithmetic examples: x+2 >= y is a sentence, x+2 > isn’t

7. Two kinds of logics we’ll consider Propositional Logic (Chap 6) Represents facts First Order Logic (Chap 7) Represents facts, objects, and relations

8. Entailment At any given time, we have a knowledge base of information If I were a train, I’d be late If I were a rule, I would bend I am a rule The knowledge base KB entails  means  is true in all worlds where KB is true e.g. if  = “I would bend” KB 

9. Models and soundness A world m is a model of a sentence  if  is true in m  = It is raining today  = The wumpus is not in (2,2) Rules of inference allow us to derive new sentences entailed by a knowledge base Rules of inference must be sound: sentences inferred by a KB should be entailed by that KB What is a non-sound inference? Video

10. Propositional Logic: Syntax

11. Propositional Logic: Semantics

12. Inference by Enumeration

13. Enumeration Solution: is  entailed by KB?

14. Enumeration is too computationally intense For n proposition symbols, enumeration takes 2 n rows (exponential) Inference rules allow you to deduce new sentences from the KB Can use inference rules as operators in a standard search algorithm Think of testing if something as true as searching for it

15. Modus Ponens (Implication-Elimination) And-Elimination And-Introduction “Or Introduction” Common inference rules for propositional logic

16. Double-Negation Elimination Unit Resolution Resolution Common inference rules for propositional logic

17. A propositional logic agent in Wumpus World Agent does not perceive its own location (unlike sample game), but it can keep track of where it has been Percepts: Stench – wumpus is nearby Breeze – pit is nearby Glitter – gold is here Bump – agent has just bumped against a wall Scream – agent has heard another player die

18. Wumpus Agent Actions Forward, Turn Left, Turn Right Grab (gold) Shoot (shoots arrow forward until hits wumpus or wall) agent only has one arrow Climb (exit the cave)

19. Wumpus Agent Death Agent dies if it enters a pit or square with wumpus Goal: get gold and climb back out. Don’t die. 1000 points for climbing out of cave with gold 1 point penalty for each action taken 10,000 point penalty for death

20. Example of using logic in Wumpus World Stench Agent StartBreeze KB contains:

21. KB also contains knowledge of environment No stench  no wumpus nearby Stench  wumpus nearby

22. We can determine where wumpus is! Method 1: Truth table At least 14 symbols currently: S 1,1, S 2,1, S 1,2, S 2,2, W 1,1, W 2,1, W 1,2, W 2,2, W 3,1, W 1,3, B 1,1, B 2,1, B 1,2, B 2,2  2 14 rows, ouch!

23. We can determine where wumpus is! Method 2: Inference Modus Ponens And-Elimination

24. Inference continued... Modus Ponens and And-Elimination again: One more Modus Ponens:

25. Inference continued... Unit Resolution: Wumpus is in (1,3)!!! Shoot it. Shoot where?

26. Determining action based on knowledge Propositional logic cannot answer question “What action should I take?” It only answers “Should I take action X?”

27. Propositional logic doesn’t cut the mustard in this application Rule: “Shoot if the wumpus is in front of you” 16 x 4 = 64 rules for the 4x4 grid Agent needs to know where it was, to backtrack A 1,1  A 1 1,1, A 2 1,1, A 3 1,1, etc. superscript is time index 64 rules over 100 time units : 6400 rules  explodes wide open

28. First-order logic to the rescue Uses variables to represent generalities Can reduce those 6400 rules down to 1  on to Chapter 7