Mathematical machines and thinking elementary problems and definitions of artificial intelligence

Transcription

1 Mathematical machines and thinking elementary problems and definitions of artificial intelligence Przemysław Klęsk Department of Methods of Artificial Intelligence and Applied Mathematics

2 Contents 1 Examples of problems Searching game trees Searching graphs Optimization problems Strategy problems Pattern recognition problems Data mining problems Control, regulation problems Artificial life problems 2 Can machines think? Turing s views 3 Minsky s remarks on machines and intelligence 4 Conteporary research areas in AI

3 Contents 1 Examples of problems Searching game trees Searching graphs Optimization problems Strategy problems Pattern recognition problems Data mining problems Control, regulation problems Artificial life problems 2 Can machines think? Turing s views 3 Minsky s remarks on machines and intelligence 4 Conteporary research areas in AI

4 Games Examples of problems Searching game trees Commonly, two-person games are considered such us: chess, checkers, GO,..., where players have conflicting interests, and where rules of game are clearly defined. Problem of game tree search Given a game position (in particular an initial position), the task is to derive numeric scores for all possible moves of the player (whose turn it is to play now). A score should represent exact or probable pay off for the player if he chooses the move, usually assuming best counter-play by opponent. Przemysław Klęsk (KMSIiMS, ZUT) 4/52

5 Games Examples of problems Searching game trees Przemysław Klęsk (KMSIiMS, ZUT) 5/52

6 Contents 1 Examples of problems Searching game trees Searching graphs Optimization problems Strategy problems Pattern recognition problems Data mining problems Control, regulation problems Artificial life problems 2 Can machines think? Turing s views 3 Minsky s remarks on machines and intelligence 4 Conteporary research areas in AI

7 Examples of problems Searching graphs Puzzles, graphs, mazes (searching) Sudoku 1*5 *37 **8 *7* *** *** **8 1** *** **3 *7* **1 74* *1* *63 2** *4* 9** *** **5 1** *** *** *8* 4** 62* 5* Minimal sudoku ** ** ** 12 ** ** 4* *3, ** ** ** 12 ** ** 41 **, ** ** ** 12 ** *1 4* **,... Przemysław Klęsk (KMSIiMS, ZUT) 7/52

8 Examples of problems Searching graphs Puzzles, graphs, mazes (searching) n-queens problem On an n n board the goal is to set up n queens, in such a way they do not attack each other. Example solution for n=8 Przemysław Klęsk (KMSIiMS, ZUT) 8/52

9 Examples of problems Searching graphs Puzzles, graphs, mazes (searching) Sliding puzzle (n 2 1 puzzle) Mazes, movement of players (agents) in computer games Przemysław Klęsk (KMSIiMS, ZUT) 9/52

10 Examples of problems Searching graphs Puzzles, graphs, mazes (searching) Problem of graph search Given an initial node in a graph (or in a tree of states) the task is to find a path (if such exists) to the goal node. Additionally if specified, the path should be the shortest. Przemysław Klęsk (KMSIiMS, ZUT) 10/52

11 Contents 1 Examples of problems Searching game trees Searching graphs Optimization problems Strategy problems Pattern recognition problems Data mining problems Control, regulation problems Artificial life problems 2 Can machines think? Turing s views 3 Minsky s remarks on machines and intelligence 4 Conteporary research areas in AI

12 Examples of problems Optimization problems Discrete optimization problems Discrete knapsack problem Given a set of items A={(v 1, c 1 ), (v 2, c 2 ),...(v n, c n )} each described by two quantities: value v i and capacity (or cost) c i, the task is to find a subset A of A, s.t.: v i max oraz c i C, i i (v i,c i ) A (v i,c i ) A where C is the maximum capacity of knapsack (constraint). Przemysław Klęsk (KMSIiMS, ZUT) 12/52

13 Examples of problems Optimization problems Traveling Salesman Problem (TSP) On a map a set of n cities is given. Starting from a fixed origin city one should find the shortest path going through all the cities (visiting each at most once) and going back to the origin. Przemysław Klęsk (KMSIiMS, ZUT) 13/52

14 Jeep problem Examples of problems Optimization problems A jeep on a desert has n containers of fuel at disposal. Each container contains 1 unit of fuel. The fuel consumption is 1 : 1, i.e. 1 unit of fuel per 1 unit of distance. The goal of jeep is to maximize the distance D n it can travel into the desert, obeying the following rules. Jeep can fill up its tank with at most 1 unit of fuel and it must not take any additional fuel with it. Jeep can depart from the base and leave some fuel along the way, then it can go back to the base using the fuel remaining in its tank. At the base, jeep can fill up and depart again. When jeep reaches some fuel (left before) it can use it to fill up its tank. Przemysław Klęsk (KMSIiMS, ZUT) 14/52

15 Contents 1 Examples of problems Searching game trees Searching graphs Optimization problems Strategy problems Pattern recognition problems Data mining problems Control, regulation problems Artificial life problems 2 Can machines think? Turing s views 3 Minsky s remarks on machines and intelligence 4 Conteporary research areas in AI

16 Examples of problems Prisonner s dilemma Strategy problems The police have arrested two suspects. Each remains in an isolated room. The police do not have sufficient evidence, but tries to convince each of suspects to testify and to betray the co-suspect in exchange for a light sentence. Each suspect is confronted with the following table of penalties (sentences) in the game: B stays quiet B betrays A stays quiet A and i B senteced to 1 year A senteced to 5 years B free to go A betrays A free to go B sentenced to 5 years A and B sentenced to 4 years Przemysław Klęsk (KMSIiMS, ZUT) 16/52

17 Examples of problems Strategy problems Strategy problems Iterated prisonner s dilemma What strategy to use when a series of single prisoner s dilemma games (e.g. n games) is to be played in order to minimize to total sentence? After each game both players are told its result. Can the number of games be known in advance? Note that after n 1 are played through, the last n-th game reduces to an ordinary prisoner s dilemma. By induction the same happens with games n 1, n 2,.... Unfortunately, this argument and using the dominant strategy does not lead to minimization of total penalty. Przemysław Klęsk (KMSIiMS, ZUT) 17/52

18 Contents 1 Examples of problems Searching game trees Searching graphs Optimization problems Strategy problems Pattern recognition problems Data mining problems Control, regulation problems Artificial life problems 2 Can machines think? Turing s views 3 Minsky s remarks on machines and intelligence 4 Conteporary research areas in AI

19 Examples of problems Pattern recognition Pattern recognition problems Problem (in general) We are given a set of observations (examples from the past), where each observation is described by a certain number of variables. One variable is distinguished as the decision variable and has a finite set of values {1, 2,...,K} (classes). The goal is to build a classifier, i.e. to find a function, which assigns observations to classes with as few mistakes as possible. The classifier should approximate well the training data, but more importantly it should generalize well i.e. return correct answers to new observations unseen within the training data. Przemysław Klęsk (KMSIiMS, ZUT) 19/52

20 Examples of problems Pattern recognition problems Pattern recognition Examples anti-spam filter (regular mail vs. spam mail), automatic diagnosis (diseased/healthy, with risk of cancer/without risk, etc.), credit credibility specification (credible client/non-credible client), optical character recognition (OCR), object detection/recognition/tracking (faces, vehicles, road signs, military objects, etc.) in images or video sequences. Przemysław Klęsk (KMSIiMS, ZUT) 20/52

21 Examples of problems Pattern recognition problems Temporal pattern recognition Examples handwriting recognition (whole sequences, rather than individual characters), speech recognition, gestures recognition, musical score following, documents authorship recognition, DNA modeling. Przemysław Klęsk (KMSIiMS, ZUT) 21/52

22 Contents 1 Examples of problems Searching game trees Searching graphs Optimization problems Strategy problems Pattern recognition problems Data mining problems Control, regulation problems Artificial life problems 2 Can machines think? Turing s views 3 Minsky s remarks on machines and intelligence 4 Conteporary research areas in AI

23 Examples of problems Data mining problems Data mining Examples rules induction in shopping data, rules induction in behaviour of social media users (e.g. next click predicition), finding artciles based on user preferences, sport/market events prediction. Przemysław Klęsk (KMSIiMS, ZUT) 23/52

24 Contents 1 Examples of problems Searching game trees Searching graphs Optimization problems Strategy problems Pattern recognition problems Data mining problems Control, regulation problems Artificial life problems 2 Can machines think? Turing s views 3 Minsky s remarks on machines and intelligence 4 Conteporary research areas in AI

25 Examples of problems Control, regulation problems Control, regulation problems Examples Inverted pendulum, Rule-based house temperature controller, Automatic crane controller for ship unloading, Automatic medication feeder, Image stabilizer for digital video camera,. Przemysław Klęsk (KMSIiMS, ZUT) 25/52

26 Contents 1 Examples of problems Searching game trees Searching graphs Optimization problems Strategy problems Pattern recognition problems Data mining problems Control, regulation problems Artificial life problems 2 Can machines think? Turing s views 3 Minsky s remarks on machines and intelligence 4 Conteporary research areas in AI

27 Examples of problems Artificial life problems Artificial life Examples Cellular automata (ang. cellular automata) a, Conway s The Game of Life, Simulation of worlds with agents (living creatures) having defined certain: senses, hunger, movement, aggression, etc. b. a YouTube: an interesting Stephen Wolfram s lecture can be found. b Master thesis by: M. Suchorzewski, 2005, at WI s library Przemysław Klęsk (KMSIiMS, ZUT) 27/52

28 Cellular automata Examples of problems Artificial life problems Przemysław Klęsk (KMSIiMS, ZUT) 28/52

29 Examples of problems Artificial life problems Conway s Game of life 1 If full cell has 0 or 1 neighbours then it dies (loneliness). 2 If full cell has 4 or more neighbours then it dies (crowd). 3 If full cell has 2 or 3 neighbours then it remains full. 4 If empty cell has exactly 3 neighbors then it becomes full. Przemysław Klęsk (KMSIiMS, ZUT) 29/52

30 Contents 1 Examples of problems Searching game trees Searching graphs Optimization problems Strategy problems Pattern recognition problems Data mining problems Control, regulation problems Artificial life problems 2 Can machines think? Turing s views 3 Minsky s remarks on machines and intelligence 4 Conteporary research areas in AI

31 Can machines think? Turing s views Can machines think? 1 No, if thinking is defined as an activity related only to human beings. Then each such behaviour by machines can only be called similar to thinking. 2 No, if we assume that in the nature of thinking itself there is something mysterious, mystical. 3 Yes, if we assume that this problem ought to be solved by means of an experiment and observation, by comparing machine s behaviour to such human activities, for which the term thinking is typically applied. Przemysław Klęsk (KMSIiMS, ZUT) 31/52

32 Can machines think? Turing s views Paper: Computing machinery and intelligence (A.M. Turing, 1950) Turing proposes to consider a problem: Can machines think?. It requires to define: machine and to think. Definitions should be good enough to encapsulate the common understanding of these words. Difficulties: non-precise, ambiguous definitions, or statistical (if built by surveys 1 ). Turing replaces original problem by a less ambiguous one the imitation game. 1 Danger: answer to the posed problem would also be statistical. Przemysław Klęsk (KMSIiMS, ZUT) 32/52

33 Imitation game Can machines think? Turing s views A man A and a woman B are in a separate room with respect to a interrogator C. C poses questions and receives responses from players as from X and Y, and tries to decide wether X=Aand Y=B, or rather X=B and Y=A. The goal of A is to mislead C, so that C identifies him wrong. Questions are put via a terminal which excludes possibility of identification based on voice, smell, etc. Przemysław Klęsk (KMSIiMS, ZUT) 33/52

34 Imitation game Can machines think? Turing s views Interrogator might ask: Will X please tell me the length of his or her hair?. Suppose X is actually A, then A s answer might therefore be:. My hair is shingled, and the longest strands are about nine inches long.. The goal of B is to help interrogator. Probably, the best strategy for her is simply to tell the truth. She might add I am the woman, don t listen to him!, but obviously A can do the same. Przemysław Klęsk (KMSIiMS, ZUT) 34/52

35 Can machines think? Turing s views Imitation game Turing s test What happens if A is replaced by a machine in the game? Will the interrogator be able to make correct identification as frequently as in the case of human players? Let the questions above replace the original problem: Can machines think? Przemysław Klęsk (KMSIiMS, ZUT) 35/52

36 Can machines think? Turing s views Imitation game, exemplary conversation Q: Please write me a sonnet on the subject of the Forth Bridge? A: Count me out on this one. I never could write poetry. Q: Add to A: (After a pause of 30 seconds) Q: Do you play chess? O: Yes. P: I have K at my K1, and no other pieces. You have only K at K6 and R at R1. It is your move. What do you play? O: (After a pause of 15 seconds) R-R8 mate. Przemysław Klęsk (KMSIiMS, ZUT) 36/52

37 Can machines think? Turing s views Imitation game, critique by Turing himself Plus: Strong separation between body and intellect. Artificial skin (if existed) does not make a machine dressed in it more humane. inus: Odds are are weighted too heavily against the machine. Think of an opposite game, where human tries to pretend to be a machine, and immediately is given away by slowness and inaccuracy in arithmetic. inus: May not machines carry out something which ought to be described as thinking but which is very different from what a man does? (Very strong objection.) Plus: Nevertheless, if a machine can be constructed to play the imitation game satisfactorily, we need not be troubled by the above objection Turing predicted that in 50 years computers shall have a memory of order 10 9 bits, and be able to mislead about 30% of interrogators. Przemysław Klęsk (KMSIiMS, ZUT) 37/52

38 Can machines think? Turing s views Contrary views to Turing s The Theological Objection Thinking is a function of man s immortal soul. God has given an immortal soul to every man and woman, but not to any other animal or to machines. Hence no animal or machine can think. In scientific sense noone should be bothered by this objection! In theological terms the following remarks can be given. The argument would be more convincing if animals were classed with men, for there is a greater difference between the typical animate and the inanimate than there is between man and the other animals. Any orthodox view becomes clearer if we consider how it might appear to a member of some other religious community. How do Christians regard the Moslem view that women have no souls? Why did Christians accept Copernican theory at last? The objection implies a serious restriction of the omnipotence of the Almighty. there are certain things that He cannot do such as making one equal to two, but should we not believe that He has freedom to confer a soul on an elephant if He sees fit? All these turn out to be dogmatical speculations... Przemysław Klęsk (KMSIiMS, ZUT) 38/52

39 Can machines think? Turing s views Contrary views to Turing s The Heads in the Sand Objection The consequences of machines thinking would be too dreadful. Let us hope and believe that they cannot do so. Also scientifically ridiculous. Connected to the theological objection. We like to believe that Man is in some subtle way superior to the rest of creation. It is best if he can be shown to be necessarily superior, for then there is no danger of him losing his commanding position. It is likely to be quite strong in intellectual people, since they value the power of thinking more highly than others, and are more inclined to base their belief in the superiority of Man on this power. Przemysław Klęsk (KMSIiMS, ZUT) 39/52

40 Can machines think? Turing s views Contrary views to Turing s The Mathematical Objection Basing on certain results from mathematical logic there exist limits to possibilities of discrete states machines. One of such results is Godel s theorem (1931): In any logical system, one can construct statements which cannot be assigned true or false value (cannot be proved or disproved within the system). a. a E.g.: The statement I am saying now is false. Questions which cannot be answered by one machine may be satisfactorily answered by another (in other formal system). Although limits of all machines has been proved, it is often claimed (without proof) that no such limits apply to human. Anytime a Godel-like question is posed to machine, the given answer must be wrong. This gives us an illusionary feeling of superiority. People do make mistakes in answering many more trivial questions. Those who hold to the mathematical argument would mostly be willing to accept the imitation game as a basis for discussion. Those who believe in the two previous objections would probably not be interested in any criteria. Przemysław Klęsk (KMSIiMS, ZUT) 40/52

41 Can machines think? Turing s views Contrary views to Turing s The Argument from Consciousness Prof. Jefferson (1949): (... )Not until a machine can write a sonnet or compose a concerto because of thoughts and emotions felt, and not by the chance fall of symbols, could we agree that machine equals brain-that is, not only write it but know that it had written it. No mechanism could feel (and not merely artificially signal, an easy contrivance) pleasure at its successes, grief when its valves fuse, be warmed by flattery, be made miserable by its mistakes, be charmed by sex, be angry or depressed when it cannot get what it want. According to the most extreme form of this view the only way by which one could be sure that machine thinks is to be the machine and to feel oneself thinking. One could then describe these feelings to the world, but of course no one would be justified in taking any notice. Likewise according to this view the only way to know that a man thinks is to be that particular man. It is in fact the solipsist point of view. It may be the most logical view to hold but it makes communication of ideas difficult. A is liable to believe A thinks but B does not whilst B believes B thinks but A does not ; instead of arguing over it is usual to have the polite convention that everyone thinks. Prof. Jefferson would probably be willing to accept the imitation game as a test rather than an extreme argument above. Przemysław Klęsk (KMSIiMS, ZUT) 41/52

42 Can machines think? Turing s views Contrary views to Turing s Arguments from Various Disabilities The form: I grant you that you can make machines do all the things you have mentioned but you will never be able to make one to do X.. Numerous features X are suggested: Be kind, resourceful, beautiful, friendly, have initiative, have a sense of humour, tell right from wrong, make mistakes, fall in love, enjoy strawberries and cream, make some one fall in love with it, learn from experience, use words properly, be the subject of its own thought, have as much diversity of behaviour as a man, do something really new. No support is usually offered for these statements and comes from a false induction. A man has seen thousands of machines in his lifetime. From what he sees he draws a number of general conclusions. Machines are ugly, each is designed for a very limited purpose, when required for a different purpose they are useless. Many of these limitations are associated with the very small storage capacity (memory) of most machines. Other are a disguised version of objection from consciousness. The impossibility of making mistakes is clearly false. A machine playing the imitation game must make mistakes (planned and random) in order to be misidentified. Przemysław Klęsk (KMSIiMS, ZUT) 42/52

43 Can machines think? Turing s views Contrary views to Turing s Lady Lovelace s Objection Lady Lovelace (1842): (... )The Analytical Engine has no pretensions to originate anything. It can do whatever we know how to order it to perform(... ). Additional meaning of this objection is that a designer of an intelligent system must be capable to predict all the consequences of such system. The machine cannot surprise us. Assertion that machines can only do what they are designed to is clearly right. But it is not the reason for drawing false conclusions out of it. Human can create, compose, learn because a biological program he is equipped with has functions like: adaption, ability to change itself (the program) e.g. as a result of observational interaction with the environment. It is clearly false, that a designer is able to predict all the consequences of a programme, even the most remote ones (e.g. after billions of operations) by means of a device under his skull. Examples: artificial life, Conway s game of life, chaos theory programmes, chess programmes surprising the grand masters designing them. Przemysław Klęsk (KMSIiMS, ZUT) 43/52

44 Can machines think? Turing s views Contrary views to Turing s The Argument from Extrasensory Perception If one acknowledges (statistically confirmed) existence of telepathy, then one may consider the following scenario: let us play the imitation game having as players a machine and a human having strong telepathy skills. Interrogator could then ask e.g. what color is the card I am holding?. And a human would answer right more frequently than machine. According to Turing it is a strong argument. Telepathy, in general, produces difficulties in many scientific approaches. One solution is to strengthen the imitation game by a restriction which makes room telepathy-proof (in a similar sense as sound-proof rooms). This is compliant with Turing s postulate about strong body-mind separation in the experiment. Przemysław Klęsk (KMSIiMS, ZUT) 44/52

45 Can machines think? Turing s views Turing s chess test Version one A human plays a chess game against an unknown opponent, and has to decide wether it is a man or a machine. Version two A human looks at a finished chess game played by to opponents and has to identify each of them as: human or machine. Garri Kasparov passes Turing s chess test in version two with success ratio of over 80%. Przemysław Klęsk (KMSIiMS, ZUT) 45/52

46 Contents 1 Examples of problems Searching game trees Searching graphs Optimization problems Strategy problems Pattern recognition problems Data mining problems Control, regulation problems Artificial life problems 2 Can machines think? Turing s views 3 Minsky s remarks on machines and intelligence 4 Conteporary research areas in AI

47 Minsky s remarks on machines and intelligence Minsky s remarks The paper Steps Towards Artificial Intelligence (Minsky, 1961). Minsky agrees with Turing s views. There exist no unified and generally acceptable theory of intelligence. 5 main areas can be named within AI: search, image recognition, learning, planning and induction. Przemysław Klęsk (KMSIiMS, ZUT) 47/52

48 Minsky s remarks on machines and intelligence Minsky s remarks On search problems If for given problem we know the way to check the correctness of a candidate solution, then we are always able to browse through multiple candidate solutions. From a certain point of view all search problems may seem trivial. E.g. think of chess game tree. It is for sure finite! Each terminal node (leaf) is either a win for white or black or a draw. By propagating it upwards (min-max procedur) the initial node is also assigned with one of these three values. In this sense chess is similarly non-interesting as tic-tac-toe. Przemysław Klęsk (KMSIiMS, ZUT) 48/52

49 Minsky s remarks on machines and intelligence Minsky s remarks On search problems Usually, it is not difficult to program an exhaustive search procedure, but for every complex problem it is too inefficient to be practically applied. What good comes from the fact that we have a programme which will not finish the computation within our lifetime or even our civilization lifetime? Samuel (1959) estimates: checkers approx states, chess approx states. Let us assign generously 1µs for each tree node to be analyzed by computer and let us estimate the number of centuries needed to analyze the whole game tree for checkers: } {{ } numer ofµs in 1 century = 10 17= Przemysław Klęsk (KMSIiMS, ZUT) 49/52

50 Minsky s remarks on machines and intelligence Minsky s remarks On search problems Therefore, technological improvements of computers does not lead to solution of all problems. Wise algorithms are more needed, that would be directed to searching more promising states in first order and discarding less promising ones. Every technique (or a heuristic) which can potentially reduce the search is valuable. Przemysław Klęsk (KMSIiMS, ZUT) 50/52

51 Minsky s remarks on machines and intelligence Minsky s remarks We should believe, that sooner or later we shall be able to create complex programmes, equipped with combinations of heuristics, recurrences, image processing techniques, etc. One should not try to see true intelligence in them. It is rather a matter of esthetics than science. Every machine capable of ideal 100% introspection (self-awareness) must conclude it is only a machine. Introduction of a body/mind duality on the grounds of psychology, sociology etc. is actually only implied by the fact that our currently known mechanical model of the brain is not complete. At the low mechanical level (or digital-like level) all we have is simple rules: if... then... it is hard to be excited by this. Similarly in mathematics, as soon as the proof for a theorem becomes understood, the contents of the theorem seems trivial. Przemysław Klęsk (KMSIiMS, ZUT) 51/52

52 Conteporary research areas in AI Conteporary research areas in AI Graph and game tree search algorithms Artificial neural networks Genetic and evolutionary algorithms Fuzzy logic and control Expert systems Data mining Ant-colony algorithms Reinforcement learning Artificial life Statistical Learning Theory (SLT) Przemysław Klęsk (KMSIiMS, ZUT) 52/52