CS621: Artificial Intelligence

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CS621 Artificial Intelligence

• Pushpak BhattacharyyaCSE Dept., IIT Bombay
• Lecture 34 Predicate Calculus and Himalayan Club
  example
• (lectures 32 and 33 were on HMMViterbi combined
  AI and NLP)

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Resolution - Refutation

• man(x) ? mortal(x)
• Convert to clausal form
• man(shakespeare) mortal(x)
• Clauses in the knowledge base
• man(shakespeare) mortal(x)
• man(shakespeare)
• mortal(shakespeare)

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Resolution Refutation contd

• Negate the goal
• man(shakespeare)
• Get a pair of resolvents

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Resolution Tree

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Search in resolution

• Heuristics for Resolution Search
• Goal Supported Strategy
• Always start with the negated goal
• Set of support strategy
• Always one of the resolvents is the most recently
  produced resolute

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Inferencing in Predicate Calculus

• Forward chaining
• Given P, , to infer Q
• P, match L.H.S of
• Assert Q from R.H.S
• Backward chaining
• Q, Match R.H.S of
• assert P
• Check if P exists
• Resolution Refutation
• Negate goal
• Convert all pieces of knowledge into clausal form
  (disjunction of literals)
• See if contradiction indicated by null clause
  can be derived

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• P
• converted to
• Draw the resolution tree (actually an inverted
  tree). Every node is a clausal form and branches
  are intermediate inference steps.

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Terminology

• Pair of clauses being resolved is called the
  Resolvents. The resulting clause is called the
  Resolute.
• Choosing the correct pair of resolvents is a
  matter of search.

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Predicate Calculus

• Introduction through an example (Zohar Manna,
  1974)
• Problem A, B and C belong to the Himalayan club.
  Every member in the club is either a mountain
  climber or a skier or both. A likes whatever B
  dislikes and dislikes whatever B likes. A likes
  rain and snow. No mountain climber likes rain.
  Every skier likes snow. Is there a member who is
  a mountain climber and not a skier?
• Given knowledge has
• Facts
• Rules

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Predicate Calculus Example contd.

• Let mc denote mountain climber and sk denotes
  skier. Knowledge representation in the given
  problem is as follows
• member(A)
• member(B)
• member(C)
• ?xmember(x) ? (mc(x) ? sk(x))
• ?xmc(x) ? like(x,rain)
• ?xsk(x) ? like(x, snow)
• ?xlike(B, x) ? like(A, x)
• ?xlike(B, x) ? like(A, x)
• like(A, rain)
• like(A, snow)
• Question ?xmember(x) ? mc(x) ? sk(x)
• We have to infer the 11th expression from the
  given 10.
• Done through Resolution Refutation.

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Club example Inferencing

• member(A)
• member(B)
• member(C)
• Can be written as

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• Negate

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• Now standardize the variables apart which results
  in the following

• member(A)
• member(B)
• member(C)

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10
7
12
5
4
13
14
2
11
15
16
13
2
17
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Assignment

• Prove the inferencing in the Himalayan club
  example with different starting points, producing
  different resolution trees.
• Think of a Prolog implementation of the problem
• Prolog Reference (Prolog by Chockshin Melish)

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Problem-2

• From predicate calculus

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A department environment

• Dr. X is the HoD of CSE
• Y and Z work in CSE
• Dr. P is the HoD of ME
• Q and R work in ME
• Y is married to Q
• By Institute policy staffs of the same department
  cannot marry
• All married staff of CSE are insured by LIC
• HoD is the boss of all staff in the department

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Diagrammatic representation
CSE
ME
Dr. P
Dr. X
Z
Y
R
Q
married
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Questions on department

• Who works in CSE?
• Is there a married person in ME?
• Is there somebody insured by LIC?

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Text Knowledge Representation
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A Semantic Graph
The student bought a new computer in June.
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UNL representation
Representation of Knowledge
Ram is reading the newspaper
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UNL a United Nations project
Dave, Parikh and Bhattacharyya, Journal of
Machine Translation, 2002

• Started in 1996
• 10 year program
• 15 research groups across continents
• First goal generators
• Next goal analysers (needs solving various
  ambiguity problems)
• Current active language groups
• UNL_French (GETA-CLIPS, IMAG)
• UNL_Hindi (IIT Bombay with additional work on
  UNL_English)
• UNL_Italian (Univ. of Pisa)
• UNL_Portugese (Univ of Sao Paolo, Brazil)
• UNL_Russian (Institute of Linguistics, Moscow)
• UNL_Spanish (UPM, Madrid)

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Knowledge Representation
UNL Graph - relations
read
agt
obj
Ram
newspaper
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Knowledge Representation
UNL Graph - UWs
read(iclgtinterpret)
obj
agt
newspaper(iclgtprint_media)
Ram(iofgtperson)
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Knowledge Representation
UNL graph - attributes
_at_entry _at_present _at_progress
read(iclgtinterpret)
obj
agt
_at_def
newspaper(iclgtprint_media)
Ram(iofgtperson)
Ram is reading the newspaper
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The boy who works here went to school
Another Example
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What do these examples show?

• Logic systematizes the reasoning process
• Helps identify what is mechanical/routine/automata
  ble
• Brings to light the steps that only human
  intelligence can perform
• These are especially of foundational and
  structural nature (e.g., deciding what
  propositions to start with)
• Algorithmizing reasoning is not trivial

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About the SA/GA assignments
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Key points

• 1. SA and GA are randomized search algorithms
       (a) why does one do randomized search?
       (b) To QUICKLY find a solution even if the
  the solution is not FULLY accurate2. For
  example, TSP is NP hard so any algorithm that
  purports to give the correct tour ALWAYS is going
  to take exponential amount of time.3. But it
  may be alright to get the solution certain
  percentage of time. Then one can use SA/GA.4.
  For sorting , consider getting the sorted
  sequences for any set of of numbers of any
  sequence length, say 200,000 numbers.

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Key points cntd

• 5. It may be OK to get an ALMOST sorted sequence
  QUICKLY so see if SA and GA can be used6. SO
  what is coming out strongly is TIME vs. ACCURACY
  TRADE-OFF7. THE ABOVE HAS TO COME OUT IN
  YOUR ASSIGNMENT8. What about 8 puzzle? Optimal
  path is not needed.

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Key points cntd

• 9. But you HAVE TO demonstrate randomness. That
  means Ther are times when the goal state will not
  be reached10. The above will be the case when
  randomness is INTRODUCED in the system by making
  the tempearure HIGH.11. Thus a key point of the
  assignment is the EFFECT OF HIGH TEMPERATURE on
  the system.12. Another point about the next
  state make sure you pick it up RANDOMLY and not
  deterministically.13. Think about the
  connection between BFS and random search. The
  former will guarantee finding the goal state, the
  latter not. But there may be gain in time
  complexity.