1. Knowledge Representation & Game Theory
“Once acquired, knowledge must be organized for use”

2. Road map Motivation Introduction to KR Classification of KR
Introduction to Game Theory
Details of Game tree
Ontology for games
Game Ontology Project
Conclusion
References

3. Motivation KR Search Vision Planning Machine Learning
Knowledge Representation
Logic
Expert Systems
Robotics
NLP

4. Introduction to KR KR
An area in artificial intelligence that is concerned with how to use a symbol system to represent “a domain of discourse”
Once acquired, knowledge must be organized for use
Most artificial intelligence systems consist of:
Knowledge Base
Inference Mechanism

5. Classification KR Knowledge Representation Unstructured Structured
Primitive Oriented
Semantic Nets
Frames
Predicate calculus
Conceptual
Dependencies
Scripts

6. Predicate Calculus KR By Gottlob Frege Key points
Simplest type of representation
Fully logic based
Deduction, Abduction and Induction
Resolution and Refutation
Application: In rule-based systems

7. Semantic Nets KR By Richard H. Richens in 1956
“The meaning of a concept comes from the ways in which it is connected to the other concepts” KR
Game
G23
isa
5-3
score
Cubs
visiting-
team
home-team
Dodgers
Stronger_than
Links can define new entities, e.g. score link between G23 and 5-3 nodes.
Links can also relate two existing entities, e.g. Stronger_than link between Cubs and Dodgers.

8. Frames KR By Marvin Minsky in 1970 Evolution of Frame System
Definition- A collection of attributes and associated values that describe some entity in the world
Differs from semantic nets in a way that frames may involve procedural embedding in place of values of attributes. (which are called as fillers)

9. Frames example
EPL-Team
isa: Team
cardinality : 20
*team-size :
*manager :
Chelsea
instance : EPL-Team
team-size : 24
manager : L. P. Scholari
players : {deco, terry, …}
Striker
isa: EPL-Player
*total-goals:
*team :
*stamina :
Drogba
instance: Striker
total-goals : 15
team : Chelsea
stamina : 90% KR
This is an example of a part of a frame system involving four frames.
EPL-Team, Chelsea, Striker, Drogba are all frames.
EPL-Team has isa and cardinality as its class attributes.
EPL-Team has team-size and manager attributes which are inherited by its objects. (indicated by *)‏

10. Conceptual Dependency
I gave the man a book I  p
ATRANS o
book to R
man
from KR
Arrows indicate direction of dependency
Double arrow indicates two way link between actor and action
p indicates past tense.
ATRANS is a primitive act
o indicates object case relation.
R indicates recipient case relation.
By Roger Schank
Not word primitives, but conceptual primitives are represented.

11. Conceptual Dependency contd…KR
A typical set of primitive acts and their descriptions:
ATRANS: Transfer of abstract relationship (e.g. give)‏
PTRANS: Transfer of physical location of object (e.g. go)‏
PROPEL: Application of physical force to an object (e.g. push)‏
MOVE: Move of body part by its owner (e.g. kick)‏
GRASP: Grasping of an object by an actor (e.g. clutch)‏
INGEST: Ingestion of an object by an animal (e.g. eat)‏
MTRANS: Transfer of mental information (e.g. tell)‏
MBUILD: Building new information from old (e.g. decide)‏
SPEAK: Production of sound (e.g. say)‏
ATTEND: Focus of a sense organ toward a stimulus (e.g. listen)‏

12. Conceptual Dependency contd…
Advantages:
Fewer Inference Rules are needed than would be required if knowledge was not broken down into primitives: Rules are represented once for each primitive act rather than once for each verb that describes that act.
Many Inferences are already contained in the representation itself.
The initial structure that is built to represent the information contained in one sentence will have holes that need to be filled. These holes can serve as an attention focuser for the program that must understand ensuing sentences.
Disadvantages:
It requires that all knowledge be decomposed into fairly low-level primitives. So it gets inefficient in some situations.
It is only a theory of representation of events . There have been attempts to describe a set of primitives that can be used to describe other kinds of knowledge, but this has not been subjected to same amount of empirical investigation. KR

13. Scripts KR By Roger Schank and Robert P. Abelson
Entering a Restaurant:
S PTRANS S into restaurant
S ATTEND eyes to tables
S MBUILD where to sit
S MOVE S to sitting position
Ordering:
S MBUILD choice of F
S MTRANS signal to W
W PTRANS W to table
S MTRANS “I want F” to W
Eating:
C ATRANS F to W
W ATRANS F to S
S INGEST F
Exiting:
W ATRANS bill to S
S ATRANS money to W
S PTRANS S to out of restaurant KR
By Roger Schank and Robert P. Abelson
Represents Sequence of Events
Events are giant casual chain

14. Scripts contd… KR Advantages:
Ability to predict events that have not been explicitly observed.
John went out to a restaurant last night. He ordered steak. When he paid for it, he noticed that he was running out of money. He hurried home since it had started to rain.
Question: Did John eat dinner last night?????
>> Though not explicitly mentioned it can be inferred from the sequence of events in the representation.
It focuses attention on unusual events.
John went to a restaurant. He was shown to his table. He ordered a large steak. He waited there for a long time. He got mad and left.
>> The story represents an unexpected set of events. So once the typical set of events is interrupted the script can no longer be used to predict other events. So here we should not infer that John paid his bill but we can infer that he saw menu since reading the menu would have occurred before the interruption.
Though Scripts are less general structures than are frames, they can be very effective for representing the specific kinds of knowledge for which they were designed.

15. Syntactic-Semantic SpectrumKR
Knowledge Representation
Syntactic
Semantic
Predicate calculus
Statistical Methods
Production Logic
Conceptual
Dependencies
Scripts
Frames
Semantic Nets

16. Game Theory game theory
Mostly involves mathematics, logic and algorithm
Zero-sum and Non-zero-sum games:
The game in which win of one player can always be on the expense of loss of other players is called a zero-sum game.
Key Terms:
Game Tree
Utility Function
game theory

17. Minimax Algorithm game theory
The minimax value of the node is the utility (for max) of being in the corresponding state, assuming that both players play optimally from there to the end of game.
game theory 2 3 12 8 15 5 4 6
Max
Min A B C S
With, b = no. legal moves at each point, m = max. depth of the tree
Time Complexity: O(b^m)‏
Space Complexity: O(bm)‏

18. Minimax Algorithm contd…
function Minimax-Decision (state) returns an action
inputs: state, current state in game
returns the a in Actions (state) maximizing Min-Value (Result (a, state))‏
game theory
function Max-Value (state) returns a utility value
if Terminal-Test (state) then return Utility (state)‏
v  -∞
for a, s in Successors (state) do v  Max (v, Min-Value (s))‏
return v
function Min-Value (state) returns a utility value
if Terminal-Test (state) then return Utility (state)‏
v  ∞
for a, s in Successors (state) do v  Min (v, Max-Value (s))‏
return v

19. Alpha-Beta Pruning game theory Complexity: 3 Max S Min A C B 3 <= 212 8 2 15 5 2
α - value of best (highest value) choice, found so far at any choice point along the path of Max
β - value of best (lowest value) choice found so far at any choice point along the path of Min
Complexity:
O(b^(d/2)) with best first order
O(b^(3d/4)) with random order

20. Alpha-Beta Pruning contd…
function Alpha-Beta-Search (state) returns an action
inputs: state, current state in game
v  Max-Value(state,− ∞,+ ∞)‏
returns the action in Successors(state) with value v
game theory
function Max-Value (state,α,β) returns a utility value
if Terminal-Test (state) then return Utility (state)‏
v  − ∞
for a, s in Successors (state) do
v  Max (v, Min-Value (s,α,β))‏
if v ≥ β then return v
β  Min(β,v)‏
return v
function Min-Value (state,α,β) returns a utility value
if Terminal-Test (state) then return Utility (state)‏
v  + ∞
for a, s in Successors (state) do
v  Min (v, Max-Value (s,α,β))‏
if v ≤ α then return v
β  Min(β,v)‏
return v

21. Game Ontology ontology Ontology – specification of concepts
Why ontology for Games?
Ontology deals with questions concerning what entities exist or can be said to exist, and how such entities can be grouped, related within a hierarchy, and subdivided according to similarities and differences.
Prototype theory – Background of Game Ontology
We categorize on perceiving.
Ontology is not developed from the top (more abstract) or the bottom (concrete and specific).Rather, our ontology grows in a middle-out fashion- the obvious (most readily observable) categories tend to exist in the middle of the ontology. As we refine and revisit them, we discover both more abstract and more specific concepts.
ontology

22. Game Ontology Project By Zegal, Mateas, Clara, Hochhalter and Lichti in 2005
Interface
Cardinality of gameworld
Presentation hardware
Presentation software
Rules
gameplay rules
gameworld rules
rule synergies
Goals
Entities
Entity manipulation
Abilities (verbs)‏
Attributes (adjectives )‏
ontology

23. Game Ontology Project contd…
An example of Ontology entry – “ To Own “

24. Game Ontology example ontology Interface Rules Goals Entity
Entity manipulation
Cardinality of
game world
Presentation
Hardware
Presentation
Software
2-dimensional

25. Example : Chess Ontology
Rules
ontology
Gameworld rules
Gameplay rules
Rule synergies
No move is possible
out side the 8*8 board
No castling is
allowed after check
Bishop can move only diagonally
A pawn converts to queen when
reaches the end of board, alive
Entity of player x is killed when any
entity of player y comes in the same block
If king is checked , a move which doesn’t
remove the check can not be made

26. Chess Ontology contd... ontology Goals Short term goals
Long term goals
Avoid the check
Kill the front pawn
Check and Mate

27. Chess Ontology contd...
Entity
ontology
Pawn
Bishop
King

28. Chess Ontology contd... ontology Entity Manipulation Kill the bishop
of the opponent
Move the pawn
Move the pawn
one step ahead
Move the pawn
two steps ahead

29. Conclusion
KR is the most basic branch of AI which directly feeds to the other branches of it.
Every area of AI involves a good representation of knowledge for efficient processing. So for solving any task of data processing, importance of organization of data is more than the data itself.
Even in the domain of Games, although most of the part involves mathematics and algorithms, but when it comes to analyze a large set of games in general, development of Ontology is a must.
This field of research is not going to get saturated, since as we design a good representation of Knowledge for a problem, the possibility of coming up with a better representation can never be denied.

30. References
[1] E. Rich and K. Knight, “Knowledge Representation,” in Artificial Intelligence, 2nd ed, McGraw Hill, 1991, pp
[2] S. Russell and P. Norvig, “Game Theory,” in Artificial Intelligence: A modern approach , 2nd ed, Prentice Hall, 2003, pp
[3] Zagal, Michael Mateas, Clara Fernandez-Vara, Brian Hochhalter and Nolan Litchi, Towards an Ontological Language for Game Analysis, presentd at DiGRA 2005 Conference: Changing Views--Worlds in Play, 2005.
[4]
[5]