Class Project

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 youre doing,
  and who youre 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/Wumpus.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 isnt
• Arithmetic examples
• x2 gt y is a sentence, x2 gt isnt

7
Two kinds of logics well 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, Id be late
• If I were a rule, I would bend
• I am a rule
• The knowledge base KB entails a means a is true
  in all worlds where KB is true
• e.g. if a I would bend
• KB a

9
Models and soundness

• A world m is a model of a sentence a if a is true
  in m
• a It is raining today
• a 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 a entailed by KB?
14
Enumeration is too computationally intense

• For n proposition symbols, enumeration takes 2n
  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
Common inference rules for propositional logic

• Modus Ponens (Implication-Elimination)
• And-EliminationAnd-Introduction
• Or Introduction

16
Common inference rules for propositional logic

• Double-Negation Elimination
• Unit Resolution
• Resolution

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. Dont 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

• KB contains

Stench Agent
Start Breeze
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 S1,1, S2,1, S1,2,
  S2,2, W1,1, W2,1, W1,2, W2,2, W3,1, W1,3, B1,1,
  B2,1, B1,2, B2,2
• ? 214 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 doesnt 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
• A1,1 ? A11,1 , A21,1 , A31,1, 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