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INTELLIGENCE_ THIKING_ AND PERSO

VIEWS: 35 PAGES: 33

									LANGUAGE, THINKING AND
MEMORY


PROBLEM SOLVING AND GAME
PLAYING



                           1
RESEARCH ON PROBLEM
SOLVING
   Mainly on how “novices” solve puzzle
    book problems (see examples later).
   They are well defined, in that they have
    – A start state
    – A goal state
    – A set of operators for transforming one
      state into another
   Real life problems are often less clearly
    defined                                   2
SOME PUZZLES
   (1) Eight Puzzle: eight movable numbers in a 3 x 3 matrix.
    Move them so that they are set out as illustrated below (or in
    some other specified configuration).
       1    2    3
       8         4
       7    6    5
   (2) Missionaries and Cannibals: transport three missionaries
    and three cannibals across a river, using a boat that can carry
    only 2 people, and that needs at least one person to get it
    across the river. There must never be more cannibals than
    missionaries on either bank, or the missionaries will get eaten.


                                                                       3
SOME MORE PUZZLES
   (3) Jug Problems: Example - Three jugs, A, B, and C,
    can hold 8 litres, 5 l, and 3 l, respectively. A is
    initially full, B and C empty. Find a sequence of
    pourings that leaves 4 l in A and 4 l in B.
   (4) Tower of Hanoi: three vertical pegs with 2 (or
    more) discs of increasing size piled on one peg.
    Transfer all the discs to the third peg, moving only
    one disc at a time, and never placing a larger disc on
    top of a smaller one.


                                                         4
TOWER OF HANOI




                 5
SOME MORE PUZZLES

   (5) A patient has an inoperable tumour. The
    tumour can be destroyed by radiation.
    Although weak radiation will not harm normal
    flesh, radiation strong enough to destroy the
    tumour will. How would you treat the patient?
   (6) Estimate how much it cost the Prince
    Regent (later George IV of England) to build
    Brighton Pavilion (an ornate summer palace,
    built 1811).
                                                6
HEURISTIC vs ALGORITHMIC
METHODS FOR PROBLEM SOLVING
    Heuristic methods have a good chance
     of finding a solution quickly, but are not
     guaranteed to find one, even if one
     exists.
    Heuristics are contrasted with
     Algorithmic methods
    Algorothmic methods will always find a
     solution, if there is one, but may be very
     slow.                                      7
TYPE OF HEURISTIC
METHOD
   Weak Methods
    – rely on general principles, that are
      independent of the particular domain (or
      subject matter) of the problem
   Strong Methods
    – make use of information that is specific to a
      particular problem solving domain (e.g.
      mathematics or medical diagnosis)

                                                  8
PRODUCTIONS SYSTEMS

   Heuristic methods can be captured by
    sets of “if (condition) then (action)”
    rules.
    – E.g. diagnosis - if(fever and red blotchy
      spots) then (diagnose measles)
   Such rules are called productions.
   A set of productions is called a
    production system.
                                                  9
PRODUCTION SYSTEMS AS
PROBLEM SOLVERS
   To make a problem solver from a set of
    productions it is usually necessary to
    have a conflict resolution strategy for
    deciding which production to use when
    several can apply (because each has its
    conditions satisfied).
   A usual component of such a strategy is
    that the most specific production should
    be used.                                10
    UNIFIED THEORIES OF
    COGNITION
   Some theorists have suggested that production
    systems can be used not only to model
    problem solving but to model all of thinking and
    reasoning and, indeed all of cognition.
   In a sense, they take all of cognition to be
    problem solving.
   The two best known "unified theories of
    cognition" are:
    – ACT* John Anderson
    – SOAR Allen Newell                            11
STATE-ACTION REPRESENTATIONS
OF PROBLEMS
    Suggested by the initial definition of a
     problem in terms of start state, goal
     state and operators.
    Represent (in principle) all possible
     states the relevant part of the world can
     be in, and all sequences of states that
     can be produced from the start state by
     the operators
                                             12
STATE-ACTION
REPRESENTATION
OF THE
MISSIONARIES AND
CANNIBALS PROBLEM




              13
SOLUTION TO
MISSIONARIES
AND CANNIBALS
PROBLEM




            14
METHODS OF SEARCHING
STATE-ACTION TREES
   (a) Algorithmic
    –   Breadth first
    –   Depth first
    –   Branch and bound
    –   A*
   (a) Heuristic
    –   Hill climbing
    –   Best first search
    –   Forward chaining
    –   Backward chaining
    –   Means-end analysis
                             15
EMPIRICAL RESULTS ON
STATE-ACTION TREES
   “Think aloud” protocols show that
    problem solvers do think in terms of
    states and transitions between them.
   However, novices find it difficult to hold
    more than two levels of a state-action
    tree in mind at any one time (current
    state, and those reachable from it in one
    move)
                                            16
PROBLEM REDUCTION

   Divide a larger problem into smaller
    problems each of which must be solved
    to solve the larger problem
   Continue with the division until “trivial”
    problems are reached
   Note: a useful division of a problem may
    not be obvious, so problem solver may
    have to fall back on the method of
    thinking of states and actions.            17
PROBLEM REDUCTION
REPRESENTATION OF
THE TOWER OF HANOI




                 18
EMPIRICAL RESULTS ON
PROBLEM REDUCTION
   With the Tower of Hanoi, people who
    adopt a problem reduction approach do
    better than those who use a state-action
    approach




                                          19
AND/OR TREES
   State-Action trees set out systematically alternative
    ways of trying to solve a problem
   Problem reduction divides a problem into
    subproblems, all of which must be solved
   A complex problem may be solved by a combination
    of problem reduction and state-action methods
   The two can be combined by representing problem
    spaces using AND/OR trees.
   In such a tree an OR branch leads to alternative
    possibilities (state-action), whereas and AND branch
    leads to subproblems all of which must be solved
                                                          20
    (problem reduction)
ANALOGICAL PROBLEM
SOLVING
   Favourite problem: inoperable tumour
   Analogy - general attacking a castle
    along mined roads. Whole army
    marching down any one road will
    detonate mines
   Gick and Holyoak - people are not very
    good at spontaneous use of analogies,
    but they will use them if prompted or if
    given several analogies                  21
ANALOGICAL PROBLEM
SOLVING (cont.)
   Use of analogy requires mapping of structure
    from the source domain to the target domain.
   The primary mapping is of relations between
    objects in the domain, not the objects
    themselves
   Gentner proposes a principle of systematicity
    for deciding which relations to map -
    interlinked sets of relations are preferred,
    isolated relation are ignored
                                                22
ANALOGICAL PROBLEM
SOLVING (cont.)
   The mapping of structure from one domain to
    another can be misleading
   Gentner and Gentner (1983) - analogies for
    understanding electricity
   (a) water in pipes - good for understanding
    how batteries work together
   (b) crowds going through turnstiles - good for
    understanding combinations of resistors

                                                 23
RESEARCH ON GAME
PLAYING
   Mainly on how experts play games such as chess,
    draughts (checkers), poker, go
   There are millions of possible games (or more)
    – So, very large state-action trees that cannot be held in
      memory
   Well defined (by rules of the game) as are puzzle
    book problems
   Emphasis on expertise and use of long-term memory,
    unlike work on problem solving


                                                                 24
GAME PLAYING AS
PROBLEM SOLVING
   Overall problem is usually taken to be
    how to win current game
    – Though could think, for example, of how to
      improve one’s game
       • (Samuel’s checker player)
   Local problem is what move to make at
    current point in the game

                                               25
STATE-ACTION ANALYSIS
OF CHESS
   Straightforward, but must remember that players take
    turns, and that what is good for one is bad for the
    other (chess, for example, is a “zero-sum game”).
   If using such a representation to select a move, a
    player can rarely look ahead to a winning position.
    So, as in hill climbing, he or she must try to force
    what appears to be the most favourable local
    development of the game.
   And, as in hill climbing, the player must be able to
    evaluate reachable positions (using a so-called static
    evaluation function).

                                                        26
STATE-ACTION ANALYSIS
OF CHESS - STATIC EVALUATION
   Factors relevant to evaluation of position at
    end of lookahead include:
    – number and type of the pieces that each player
      has
    – which pieces have relative freedom of movement
    – which pieces are vulnerable
    – which parts of the board are controlled
    – where the pawns are located.
   NOTE USE OF CHESS-SPECIFIC
    KNOWLEDGE - “strong heuristic method”
                                                       27
STATE-ACTION REPRESENTATION OF
TWO-PERSON GAMES - MINIMAXING
    Minimaxing means minimising the
     maximum loss that the other player can
     inflict on you
    Based on the assumption that the other
     player will, in making things good for
     him- or herself, make things as bad as
     possible for you

                                          28
STATE-ACTION REPRESENTATION OF
TWO-PERSON GAMES - MINIMAXING
         Current position          S1
         Program to move                            Backed-up value
                                   -2               Program can select best value
   Possible positions
   after next move           S2           S3
   Opponent to move                                    Backed-up values
                             -2           -5
                                                       Opponent will select
                                                       Least favourable value
  Possible positions
  after opponent’s      S4        S5 S6        S7
  Next move
                                                           Static evaluations
                        -2        2 -5         7
                                                           (for program)
                                                           at end of lookahead



                                                                              29
HUMAN AND MACHINE
CH ESS
   In machine chess (CRAY BLITZ; DEEP
    THOUGHT) the evaluated positions may be
    “selected” by brute force (because program
    can evaluate a very large number of
    positions).
   But, in human chess very many fewer
    positions can be considered, and they are
    selected using “domain specific” knowledge.
    i.e. EXPERTISE (“strong methods” again)
                                                  30
THE NATURE OF (HUMAN)
EXPERTISE IN CHESS
   Chess masters and grandmasters typically think through a
    relatively small number of developments of the game.
   They assume a rational opponent, and try to force play to the
    development that seems most favourable.
   Choices of move are assessed not in terms of the position they
    create immediately, but in terms of the position that they will
    eventually lead to (at a so-called “quiet position”).
   Most moves are not followed up. They are assumed to be less
    valued that those that are.




                                                                  31
DE GROOT - “THOUGHT AND
CHOICE IN CHESS”
   (Dutch thesis - 1946; English book - 1965)
   Main Findings
    – Human chess players consider only a few developments of
      the game at each move (Not surprising,given our knowledge
      about limitations on short-term memory).
    – Excellent players (at the grandmaster level) do not follow up
      any more moves than good tournament players.
    – They follow up better moves (as rated by other players), and
      they assess moves more quickly.
    – Better players reconstruct (from memory) briefly presented
      board positions more accurately than less good players.

                                                                 32
CHASE AND SIMON (1973)
   Chase and Simon (1973) showed that this finding
    only held for real chess positions (not random board
    positions with the same number of pieces).
   Chase and Simon suggested that a grandmaster
    might have 50,000 “chunks” of chess-related
    information in long-term memory.
   Explains why chess masters study previous games
    and why it takes 10 years to become a grandmaster
    (THE 10-YEAR RULE FOR THE ACQUISITION OF
    EXPERTISE IN A COMPLEX SKILL - Ericsson)

                                                           33

								
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