VIEWS: 7 PAGES: 82 CATEGORY: College POSTED ON: 3/11/2012
Artificial intelligence Academic lecture
Artificial Intelligence Knowledge Representation Problem Knowledge Representation In symbolic functionalism we represent intelligence via manipulation of our beliefs about the surrounding world and knowledge we know. Therefore we have to address two fundamental issues how to represent knowledge how to implement the process of reasoning State space is a space of possible courses of inference when combining actual beliefs about current world general knowledge rules of inference Knowledge bases Knowledge base = set of sentences in a formal language What is Knowledge? data – primitive verifiable facts, of any representation. Data reflects current world,often voluminous frequently changing. information – interpreted data knowledge – relation among sets of data (information), that is very often used for further information deduction. Knowledge is (unlike data) general. Knowledge contain information about behavior of abstract models of the world. Representation Set of syntactic and semantic conventions which make it possible to describe things Syntax specific symbols allowed and rules allowed Semantics how meaning is associated with symbol arrangements allowed by syntax Knowledge Representation Schemas Logic based representation – first order predicate logic, Prolog Procedural representation – rules, production system Network representation – semantic networks, conceptual graphs Structural representation – scripts, frames, objects Natural Language English appears to be expressive But natural language is a medium of communication, not a knowledge representation Much of the information and logic conveyed by language is dependent on context Information exchange is not well defined Not compositional (combining sentences may mean something different) It is ambiguous Conceptual Graphs each concept has got its type and an instance general concept – a concept with a wildcard instance dog:*X colour brown specific concept – a concept with a concrete instance dog:Emma colour brown animal there exsists a hierarchy of types subtype: concept w is specialisation of concept v if dog cat type(v)>type(w) or instance(w)::type(v) Types of Knowledge Objects both physical & concepts Events usually involve time maybe cause & effect relationships Performance how to do things META Knowledge knowledge about how to use knowledge Stages of Knowledge Use Acquisition structure of facts integration of old & new knowledge Retrieval (recall) roles of linking and chunking means of improving recall efficiency Mathematical Logic Propositional Logic – syntactical primitives: , , , , symbols, true, false rule of inference: de morgan rule, modus ponens, … semantic interpretation rains blows-wind sun-will-shine First Order Predicate Logic – enriched by variables, predicates, functions quantifiers , friends(father(david),father(andrew)) Y friends(Y, petr) X likes(X,ice_cream) X Y Z parent(X,Y) parent(X,Z) siblings(Y,Z) Propositional logic Propositional logic is the simplest logic The proposition symbols P1, P2 etc are sentences If S is a sentence, S is a sentence (negation) If S1 and S2 are sentences, S1 S2 is a sentence (conjunction) If S1 and S2 are sentences, S1 S2 is a sentence (disjunction) If S1 and S2 are sentences, S1 S2 is a sentence (implication) If S1 and S2 are sentences, S1 S2 is a sentence (biconditional) Truth tables for connectives Logical equivalence Two sentences are logically equivalent} iff true in same models: α ≡ ß iff α╞ β and β╞ α First-order logic Whereas propositional logic assumes the world contains facts, first-order logic (like natural language) assumes the world contains Objects: people, houses, numbers, colors, baseball games, wars, … Relations: red, round, prime, brother of, bigger than, part of, comes between, … Functions: father of, best friend, one more than, plus, … Syntax of FOL: Basic elements Constants KingJohn, 2, NUS,... Predicates Brother, >,... Functions Sqrt, LeftLegOf,... Variables x, y, a, b,... Connectives , , , , Equality = Quantifiers , Universal quantification <variables> <sentence> Everyone at NUS is smart: x At(x,NUS) Smart(x) x P is true in a model m iff P is true with x being each possible object in the model Roughly speaking, equivalent to the conjunction of instantiations of P At(KingJohn,NUS) Smart(KingJohn) At(Richard,NUS) Smart(Richard) At(NUS,NUS) Smart(NUS) ... Existential quantification <variables> <sentence> Someone at NUS is smart: x At(x,NUS) Smart(x)$ x P is true in a model m iff P is true with x being some possible object in the model Roughly speaking, equivalent to the disjunction of instantiations of P At(KingJohn,NUS) Smart(KingJohn) At(Richard,NUS) Smart(Richard) At(NUS,NUS) Smart(NUS) ... Properties of quantifiers x y is the same as y x x y is the same as y x x y is not the same as y x x y Loves(x,y) “There is a person who loves everyone in the world” y x Loves(x,y) “Everyone in the world is loved by at least one person” Quantifier duality: each can be expressed using the other x Likes(x,IceCream)x Likes(x,IceCream) x Likes(x,Broccoli) x Likes(x,Broccoli) Using FOL Brothers are siblings x,y Brother(x,y) Sibling(x,y) One's mother is one's female parent m,c Mother(c) = m (Female(m) Parent(m,c)) “Sibling” is symmetric x,y Sibling(x,y) Sibling(y,x) A first cousin is a child of a parent’s sibling x,y FirstCousin(x,y) p,ps Parent(p,x) Sibling(ps,p) Parent(ps,y) Generalized Modus Ponens Example knowledge base The law says that it is a crime for an American to sell weapons to hostile nations. The country Nono, an enemy of America, has some missiles, and all of its missiles were sold to it by Colonel West, who is American. Prove that Col. West is a criminal Example knowledge base ... it is a crime for an American to sell weapons to hostile nations: American(x) Weapon(y) Sells(x,y,z) Hostile(z) Criminal(x) Nono … has some missiles, i.e., x Owns(Nono,x) Missile(x): Owns(Nono,M1) and Missile(M1) … all of its missiles were sold to it by Colonel West Missile(x) Owns(Nono,x) Sells(West,x,Nono) Missiles are weapons: Missile(x) Weapon(x) An enemy of America counts as "hostile“: Enemy(x,America) Hostile(x) West, who is American … American(West) The country Nono, an enemy of America … Enemy(Nono,America) Resolution proof: definite clauses Consider L be the first-order language with the following primitives: S(X,L) -- Person X speaks language L. C(X,Y) -- Persons X and Y can communicate. I(W,X,Y) -- Person W can serve as an interpreter between persons X and Y. J, P,E, F --- Constants: Joe, Pierre, English, and French respectively. a) Express the following statements in L: i. Joe speaks English. ii Pierre speaks French. iii. If X and Y both speak L, then X and Y can communicate. iv. If W can communicate both with X and with Y, then W can serve as an interpreter between X and Y. v. For any two languages L and M, there is someone who speaks both L and M. vi. There is someone who can interpret between Joe and Pierre. Show how (vi) can be proven from (i)---(v) using backward- chaining resolution. Reasoning Retrospective Reasoning Why/how explanations are limited in their power because only focus on local reasoning Counterfactual Reasoning “why not” capabilities Hypothetical Reasoning “what if” capabilities Rule Based Reasoning The advantages of rule-based approach: The ability to use Good performance Good explanation The disadvantage are Cannot handle missing information Knowledge tends to be very task dependent Rule-Based Systems Also known as “production systems” or “expert systems” Rule-based systems are one of the most successful AI paradigms Used for synthesis (construction) type systems Also used for analysis (diagnostic or classification) type systems Other Reasoning There exist some other approaches as: Case-Based Reasoning Model-Based Reasoning Hybrid Reasoning Rule-based + case-based Rule-based + model-based Model-based + case-based Forward Chaining Remember this from propositional logic? Start with atomic sentences in KB Apply Modus Ponens add new sentences to KB discontinue when no new sentences Hopefully find the sentence you are looking for in the generated sentences Forward chaining Idea: fire any rule whose premises are satisfied in the KB, add its conclusion to the KB, until query is found Forward chaining example Forward chaining example Forward chaining example Forward chaining example Forward chaining example Forward chaining example Forward chaining example Forward chaining example Backward chaining example Backward chaining example Backward chaining example Backward chaining example Backward chaining example Backward chaining example Backward chaining example Backward chaining example Backward chaining example Backward chaining example Reduction to propositional inference Suppose the KB contains just the following: x King(x) Greedy(x) Evil(x) King(John) Greedy(John) Brother(Richard,John) Instantiating the universal sentence in all possible ways, we have: King(John) Greedy(John) Evil(John) King(Richard) Greedy(Richard) Evil(Richard) King(John) Greedy(John) Brother(Richard,John) The new KB is propositionalized: proposition symbols are King(John), Greedy(John), Evil(John), King(Richard), etc. Example proof: Did Curiosity kill the cat? Jack owns a dog. Every dog owner is an animal lover. No animal lover kills an animal. Either Jack or Curiosity killed the cat, who is named Tuna. Did Curiosity kill the cat? The axioms can be represented as follows: A. (x) Dog(x) ^ Owns(Jack,x) B. (x) ((y) Dog(y) ^ Owns(x, y)) => AnimalLover(x) C. (x) AnimalLover(x) => (y) Animal(y) => ~Kills(x,y) D. Kills(Jack,Tuna) Kills(Curiosity,Tuna) E. Cat(Tuna) F. (x) Cat(x) => Animal(x) Example: Did Curiosity kill the cat? 1. Dog(spike) 2. Owns(Jack,spike) 3. ~Dog(y) v ~Owns(x, y) v AnimalLover(x) 4. ~AnimalLover(x1) v ~Animal(y1) v ~Kills(x1,y1) 5. Kills(Jack,Tuna) v Kills(Curiosity,Tuna) 6. Cat(Tuna) 7. ~Cat(x2) v Animal(x2) Example: Did Curiosity kill the cat? 1. Dog(spike) 2. Owns(Jack,spike) 3. ~Dog(y) v ~Owns(x, y) v AnimalLover(x) 4. ~AnimalLover(x1) v ~Animal(y1) v ~Kills(x1,y1) 5. Kills(Jack,Tuna) v Kills(Curiosity,Tuna) 6. Cat(Tuna) 7. ~Cat(x2) v Animal(x2) 8. ~Kills(Curiosity,Tuna) negated goal 9. Kills(Jack,Tuna) 5,8 10. ~AnimalLover(Jack) V ~Animal(Tuna) 9,4 x1/Jack,y1/Tuna 11. ~Dog(y) v ~Owns(Jack,y) V ~Animal(Tuna) 10,3 x/Jack 12. ~Owns(Jack,spike) v ~Animal(Tuna) 11,1 13. ~Animal(Tuna) 12,2 14. ~Cat(Tuna) 13,7 x2/Tuna 15. False 14,6 Expert System Uses domain specific knowledge to provide expert quality performance in a problem domain It is practical program that use heuristic strategies developed by humans to solve specific class of problems Expert System Functionality replace human expert decision making when not available assist human expert when integrating various decisions provides an ES user with an appropriate hypothesis methodology for knowledge storage and reuse border field to Knowledge Based Systems, Knowledge Management knowledge intensive × connectionist expert system – software systems simulating expert-like decision making while keeping knowledge separate from the reasoning mechanism Expert System User Interface Knowledge editor Question&Answer User General Knowledge Inference Engine Natural Language Case-specific data Graphical interface Explanation Generic System Components Global Database content of working memory (WM) Production Rules knowledge-base for the system Inference Engine rule interpreter and control subsystem Rule-Based System knowledge in the form of if condition then effect (production) rules reasoning algorithm: (i) FR detect(WM) (ii) R select(FR) (iii)WM apply R (iv) goto (i) conflicts in FR: first, last recently used, minimal WM change, priorities incomplete WM – querying ES (art of logical and sensible querying) examples – CLIPS (OPS/5), Prolog Inference Engine It applies the knowledge to the solution of actual problem It is an interpreter for the knowledge base It performs the recognize-act control cycle Weaknesses of Expert Systems Require a lot of detailed knowledge Restrict knowledge domain Not all domain knowledge fits rule format Expert consensus must exist Knowledge acquisition is time consuming Truth maintenance is hard to maintain Forgetting bad facts is hard Expert Systems in Practice MYCIN example of medical expert system old well known reference great use of Stanford Certainty Algebra problems with legal liability and knowledge acquisition Prospector geological system knowledge encoded in semantic networks Bayesian model of uncertainty handling saved much money Expert Systems in Practice XCON/R1 classical rule-based system configuration DEC computer systems commercial application, well used, followed by XSEL, XSITE failed operating after 1700 rules in the knowledge base FelExpert rule-based, baysian model, taxonomised, used in a number of applications ICON configuration expert system uses proof planning structure of methods Uncertainty Let action At = leave for airport t minutes before flight Will At get me there on time? Problems: partial observability (road state, other drivers' plans, etc.) noisy sensors (traffic reports) uncertainty in action outcomes (flat tire, etc.) “A25 will get me there on time if there's no accident on the bridge and it doesn't rain and my tires remain intact etc etc.” Making decisions under uncertainty Suppose I believe the following: P(A25 gets me there on time | …) = 0.04 P(A90 gets me there on time | …) = 0.70 P(A120 gets me there on time | …) = 0.95 P(A1440 gets me there on time | …) = 0.9999 Which action to choose? Depends on my preferences for missing flight vs. time spent waiting, etc. Utility theory is used to represent and infer preferences Uncertainty in Expert Systems from correct premises and correct sound rules correct conclusions but sometimes we have to manage uncertain information, encode uncertain pieces of knowledge, model parallel firing of inference rules, tackle ambiguity There is a number of various models of uncertain reasoning: Bayesian Reasoning – classical statistical approach Dempster-Shafer Theory of Evidence Stanford Certainty Algebra – MYCIN Bayesian Reasoning P(a b) P(a) P(b) ……. given that a and b are independent P(a b) P(a | b) P(b) ……. given that a depends on b - prior probability (unconditional) … p(hypothesis) - posterior probability (conditional)… p(hypothesis|evidence) P(e|h) P(h e) P(h) P(e | h) P(e) P(h) P(h | e) P(e | h) P(e) P(e) P(h) P(e | h) P(h | e) P(hj ) P(e | hj ) j prospector, dice examples What is Fuzzy logic Fuzzy logic is a superset of conventional logic (Boolean) It was created by Dr. Lotfi Zadeh in 1960s for the purpose of modeling the inherent in natural language In fuzzy logic, it is possible to have partial truth values • Fuzzy logic driven picture generator • Massive Engine • Battle scenes from Lord of the Rings Reasoning With Uncertainty Term Certainty Factor Definitely not -1.0 Almost certainly not -0.8 Probably not -0.6 Maybe not -0.4 Unknown -0.2 to +0.2 Maybe +0.4 Probably +0.6 Almost certainly +0.8 Definitely +1.0 Fuzzy Sets categorization of elements xi into a set S described through a membership function (s) : x [0,1] associates each element xi with a degree of membership in S: 0 means no, 1 means full membership values in between indicate how strongly an element is affiliated with the set Reasoning With Uncertainty Conventional set theory 38.7°C 38°C 40.1°C 41.4°C Fuzzy set theory 42°C 39.3°C “Strong Fever” 38.7°C 37.2°C 38°C 40.1°C 41.4°C 42°C 39.3°C “Strong Fever” 37.2°C Degree’s of truth The word “fuzzy” can be defined as “imprecisely defined, confused, vague” Humans represent and manage natural language terms (data) which are vague. Almost all answers to questions raised in everyday life are within some proximity of the absolute truth Sets Fuzzyfuzzy Sets with boundaries A = Set of tall people Crisp set A Fuzzy set A 1.0 1.0 .9 .5 Membership function 5’10’’ Heights 5’10’’ 6’2’’ Heights Possibility vs.. Probability possibility refers to allowed values probability expresses expected occurrences of events Example: rolling dice X is an integer in U = {2,3,4,5,6,7,8,9,19,11,12} probabilities p(X = 7) = 2*3/36 = 1/6 7 = 1+6 = 2+5 = 3+4 possibilities Poss{X = 7} = 1 the same for all numbers in U Fuzzy Sets Formal definition: A fuzzy set A in X is expressed as a set of ordered pairs: A {( x, A ( x ))| x X } Membership Universe or Fuzzy set function universe of discourse (MF) A fuzzy set is totally characterized by a membership function (MF). Set-Theoretic Operations A B A B Subset: A X A A ( x ) 1 A ( x ) Complement: C A B c ( x ) max( A ( x ), B ( x )) A ( x ) B ( x ) Union: C A B c ( x ) min( A ( x ), B ( x )) A ( x ) B ( x ) Intersection: Rough Sets Rough set theory was developed by Zdzislaw Pawlak in the early 1980’s. The main goal of the rough set analysis is induction of approximations of concepts. It can be used for feature selection, feature extraction, data reduction, decision rule generation, and pattern extraction (templates, association rules) etc. identifies partial or total dependencies in data, eliminates redundant data, gives approach to null values, missing data, dynamic data and others. Logics in general Language Ontological Epistemological Commitment Commitment Propositional logic facts true/false/unknown First-order logic facts, objects, true/false/unknown relations Temporal logic facts, objects, true/false/unknown relations, times Probability theory facts degree of belief Fuzzy logic facts+degree of truth known interval value facts+degree of truth known interval value