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

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

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

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

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

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

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.

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)

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 *)‏

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.

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)‏

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

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

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.

Syntactic-Semantic Spectrum KR Knowledge Representation Syntactic Semantic Predicate calculus Statistical Methods Production Logic Conceptual Dependencies Scripts Frames Semantic Nets

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

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)‏

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

Alpha-Beta Pruning game theory Complexity: 3 Max S Min A C B 3 <= 2 12 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

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

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

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

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

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

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

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

Chess Ontology contd... Entity ontology Pawn Bishop King

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

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.

References [1] E. Rich and K. Knight, “Knowledge Representation,” in Artificial Intelligence, 2nd ed, McGraw Hill, 1991, pp. 103-303. [2] S. Russell and P. Norvig, “Game Theory,” in Artificial Intelligence: A modern approach , 2nd ed, Prentice Hall, 2003, pp. 189-199. [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] http://www.cse.iitb.ac.in/~pb/cs621-2008/cs621-lect1-and-2-intro- 2008-7-25. [5] http://www.wikipedia.org.