Knowledge and search

1
Knowledge and search

• Points
• Properties of knowledge
• Completeness
• Objectivity
• Certainty
• Formalizability
• The role of search
• A small case study

2
Properties of knowledgecompleteness

• "Knowledge is always incomplete"true or false?
• What do we need to know when we
• play a game?
• make a holiday plan?
• recognize a picture?

3
... completeness (2)

• Even in a very restricted real-life domain there
  may be unexpected situations. Find examples of
  such situations in
• buying groceries,
• fixing a car.
• Knowledge contained in an AI software system for
  some application is necessarily much less
  complete than what we know about this
  application true or false?

4
Properties of knowledgeobjectivity

• Knowledge may be objective or subjective we have
  to make a distinction between facts and beliefs.
  Beliefs are associated with agents.
• Jack is planning a gift for his mother. He
  believes that she dislikes classical music. Will
  he buy a Mozart CD for her?
• Is there anything subjective in the game of
  chess?
• Is there anything objective in art appreciation?

5
Properties of knowledgecertainty

• Knowledge may be certain or uncertain. Diagnostic
  expert systems are a good example faults and
  repair advice do not always logically follow from
  observations or symptoms.
• What (if anything) can we conclude with certainty
  from
• a sick person's short breath?
• a car engine noise?
• a position in a chess game?
• Probability plays an essential role here -- more
  to come, later.

6
Properties of knowledgeformalizability

• Knowledge may or may not be easily formalized --
  written down in some symbolic language (recall
  the physical-symbol systems).
• People often operate in an approximate manner and
  allow themselves a margin of error.
• Perhaps the same should be possible for
  intelligent systems, except that systems only
  have explicit knowledge that has been put into
  them.

7
... formalizability (2)

• People rely on experience systems must have
  experience formalized as well.
• Which of the following can be formalized
  (represented!) with little effort
• the rules of ice hockey?
• the relationship between moods and colours?
• the decision-making of a loan officer in a
  bank?
• a surgical procedure?

8
The role of search

• Intelligent behaviour requires knowledge.
• There is a hypothesis is that intelligent action
  can be reduced to search.
• While intelligence is certainly more than search,
  the hypothesis is attractive search is well
  understood, easily mechanized, manageable, and so
  on.
• Formally represented knowledge can also be easily
  used in search.

9
The role of search (2)

• Search means systematic traversal of a space of
  possible solutions of a problem.
• A search space is usually a graph (often as
  simple as a tree).
• A node represents a partial solution.
• An edge represents a step in the construction of
  a solution.

10
The role of search (3)

• The purpose of search may be
• to find a path in the graph from a start node
  to a goal node (that is, from an initial to a
  final situation),
• to find a goal node.
• Examples in textbooks are often puzzles and games
  -- not surprisingly, because these problems are
  the easiest to present as search. The challenge
  is to try it with other kinds of problems.

11
The role of search (4)

• Examples of such problems
• Analyze an English sentence.
• Debug a Pascal procedure.
• Program a robot.

12
A small case study

• A farmer has a wolf, a goat and a cabbage. He
  wants to cross the river from the south bank to
  the north bank.
• There is a boat that can only carry the farmer
  and at most one of his possessions.
• The wolf left alone with the goat will eat it.
• The goat left alone with the cabbage will eat it.
• How can the farmer cross the river and lose none
  of the three?

13
... case study (2)

• This is a classical example of a planning
  problem. We must find a sequence of actions that
  will take the farmer across the river. At each
  moment, the whole situation is in one of its
  possible states.
• A state describes the position of the farmer, his
  three possessions and the boat with respect to
  the north and south bank of the river.
• An action is one crossing of the river, north or
  south. As a result of such an action, the farmer,
  the boat and possibly one of the three objects
  transfer from one bank to the other. There are
  constraints on actions, as no action should leave
  to an unsafe state.

14
... case study (3)

• In the initial situation, everything is on the
  south bank. In the desired final situation the
  farmer and his three possessions are on the north
  bank.
• We will represent a situation as a four-tuple of
  locations of the farmer, the wolf, the goat and
  the cabbage. We do not need to represent the
  position of the boat, because in is always
  located on the same bank as the farmer. For
  example, in the situation
• situation(s, n, s, n)
• the farmer and the goat are on the south bank,
  and the other two on the north bank. Is this
  situation safe?

15
... case study (4)

• We represent the initial situation
  as situation(s,s,s,s)and the final situation
  as situation(n,n,n,n)
• Four actions are possible in each situation. The
  farmer transfers himself to the opposite bank he
  also transfers nothing, or the wolf, or the goat,
  or the cabbage.
• We will represent these actions as Prolog terms
• moved( nothing )
• moved( wolf )
• moved( goat )
• moved( cabbage )

16
... case study (5)

• A situation is safe if it is safe both for the
  goat and the cabbage. The goat is safe if the
  farmer is on the same bank of the river, or when
  the wolf is not. The cabbage is safe if the
  farmer is on the same bank, or when the goat is
  not.
• We can express in Prolog everything we know about
  this problem. First, the main predicate
• successfulMoves( Mvs ) - movesLeadingTo(
  Mvs, situation( n, n, n, n ) ).
• Mvs is a list of representations of actions.

17
... case study (6)

• No actions are necessary to stay in the initial
  situation
• movesLeadingTo( , situation( s, s,
  s, s ) ).
• Otherwise, let Mvs1 be a list of legal actions
  leading to situation S1. Perform one more action
  and add it to Mvs1
• movesLeadingTo( Mvs, S ) - movesLeadingTo(
  Mvs1, S1 ), transforms( Mv, S1, S ),
  append( Mvs1, Mv, Mvs ), safe( S ).

18
... case study (7)

• North is opposite south
• opposite( n, s ).opposite( s, n ).
• The four possible actions
• transforms( moved( nothing ),
  situation( X, Z1, Z2, Z3 ),
  situation( Y, Z1, Z2, Z3 ) ) - opposite( X,
  Y ).
• transforms( moved( wolf ), situation(
  X, X, Z2, Z3 ), situation( Y, Y, Z2,
  Z3 ) ) - opposite( X, Y ).

continued
19
... case study (8)

• transforms( moved( goat ), situation(
  X, Z1, X, Z3 ), situation( Y, Z1, Y,
  Z3 ) ) - opposite( X, Y ).
• transforms( moved( cabbage ),
  situation( X, Z1, Z2, X ), situation(
  Y, Z1, Z2, Y ) ) - opposite( X, Y ).
• The safety rules are as discussed earlier
• safe( S ) - safe_for_goat( S ),
  safe_for_cabbage( S ).

20
... case study (9)

• The farmer and the goat together
• safe_for_goat( situation( X, Z1, X, Z3 ) ).
• The wolf and the goat separated
• safe_for_goat( situation( X, Z1, Y, Z3 ) )
  - opposite( Z1, Y ).

21
... case study (10)

• The same for the goat and the cabbage
• safe_for_cabbage( situation( X, Z1, Z2, X )
  ).
• safe_for_cabbage( situation( X, Z1, Z2, Y )
  ) - opposite( Z2, Y ).
• And finally here is a solution
• ?- successfulMoves( Mvs ).
• Mvs moved(goat), moved(nothing), moved(wolf),
  moved(goat), moved(cabbage), moved(nothing),
  moved(goat)
• Yes

22
... case study (11)

• This program requires cuts in the definitions of
  safe_for_cabbage and safe_for_goat if it is to
  lose its annoying nondeterminism. It will then
  quickly deliver the other optimal solution
• Mvs moved(goat), moved(nothing),
  moved(cabbage), moved(goat), moved(wolf),
  moved(nothing), moved(goat)
• After that, the program begins to deliver
  non-optimal solutions, longer and longer, with
  the unproductive moved(X), moved(X) inserted just
  about everywhere.