Answering Complex Questions and Performing Deep Reasoning in Advance QA Systems

1
Answering Complex Questions and Performing Deep
Reasoning in Advance QA Systems Reasoning with
logic and probability

• Chitta Baral
• Arizona State university
• Co-Investigators
• Michael Gelfond and
• Richard Scherl.
• Other collaborator
• Nelson Rushton.

2
Developing formalisms for Reasoning with logic
and probability

• One of the research issues that we are working
  on.
• A core component of our deep reasoning goals.
  
• What if reasoning
• Reasoning about counterfactuals
• Reasoning about causes, etc.
• In parallel
• We are also using existing languages and
  formalisms (AnsProlog) to domain knowledge and do
  reasoning.

3
Reasoning with counterfactuals.

• Text (From Pearls Causality)
• If the court orders the execution then the
  captain gives a signal.
• If the captain gives a signal then the rifleman A
  shoots and rifleman B shoots.
• Rifleman A may shoot out of nervousness.
• If either of rifleman A or B shoots then the
  prisoner dies.
• The probability that the court orders the
  execution is p.
• The probability that A shoots out of nervousness
  is q.
• A counterfactual question
• What is the probability that the prisoner would
  be alive if A were not to have shot, given that
  the prisoner is in fact dead?

4
Pictorial representation

• U court orders execution (p)
• C Captain gives the signal
• A Rifleman A shoots
• B Rifleman B shoots
• V Rifleman A is nervous (q)
• D The prisoner dies
• Logic
• U causes C
• C causes A
• V causes A
• C causes B
• A causes D
• B causes D
• Probability
• Pr(U) p
• Pr(V) q

U
V
C
A
B
D
5
Bayes Nets, Causal Bayes Nets, and Pearls
structural causal models

• Bayes nets do not have to respect causality
• They only succinctly represent the joint
  probability distribution
• One can not reason about causes and effects with
  Bayes nets. (One can with causal Bayes nets)
• Even then, one needs to distinguish between doing
  and observing.
• This distinction is important to do
  counterfactual reasoning.
• Pearls structural causal models gives an
  algorithm to do counterfactual reasoning. But
• The logical language is weak.
• (Need a more general knowledge representation
  language that can express defaults, normative
  statements etc.)
• The variables with probabilities are assumed to
  be independent.

6
Further Motivation for a richer language The
Monty Hall problem

• http//www.remote.org/frederik/projects/ziege/bewe
  is.html
• A player is given the opportunity to select one
  of three closed doors, behind one of which there
  is a prize, and the other 2 rooms are empty.
• Once the player has made a selection, Monty is
  obligated to open one of the remaining closed
  doors, revealing that it does not contain the
  prize.
• Monty gives a choice to the player to switch to
  the other unopened door if he wants.
• Question Does it matter if the player switches,
  or
• Which unopened door has the higher probability of
  containing the prize?

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Illustration-1

• First, let us assume that the car is behind door
  no. 1.
• We can do this without reducing the validity of
  our proof, because if the car were behind door
  no. 2, we only had to exchange all occurrences of
  "door 1" with "door 2" and vice versa, and the
  proof would still hold.
• The candidate has three choices of doors.
• Because he has no additional information, he
  randomly selects one.
• The possibility to choose each of the doors 1,
  2, or 3 is 1/3 each
•   Candidate chooses p  
• Door 1 1/3
• Door 2 1/3
• Door 3 1/3
• Sum 1 

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Illustration-2

• Going on from this table, we have to split the
  case depending on the door opened by the host.
• Since we assume that the car is behind door no.
  1, the host has a choice if and only if the
  candidate selects the first door - because
  otherwise there is only one "goat door" left!
• We assume that if the host has a choice, he will
  randomly select the door to open.  
• Candidate chooses Host opens p  
• Door 1 Door 2 1/6
• Door 1 Door 3 1/6
• Door 2 Door 3 1/3
• Door 3 Door 2 1/3
• Sum 1 

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Illustration-3

• candidate who always sticks to his original
  choice no matter what happens  
• Candidate chooses Host opens final choice win
  p  
• Door 1 Door 2 Door 1
  yes 1/6
• Door 1 Door 3 Door 1
  yes 1/6
• Door 2 Door 3 Door 2 no
  1/3
• Door 3 Door 2 Door 3 no
  1/3
• Sum1 Sum of cases where candidate wins 1/3 
• candidate who always switches to the other door
  whenever he gets the chance
•  Candidate chooses Host opens final choice win
  p  
• Door 1 Door 2 Door 3 no 1/6
• Door 1 Door 3 Door 2 no 1/6
• Door 2 Door 3 Door 1 yes 1/3
• Door 3 Door 2 Door 1 yes 1/3
• Sum1 Sum of cases where candidate wins
  2/3

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Key Issues

• The existing languages of probability do not
  really give us the syntax to express certain
  knowledge about the problem
• Lot of reasoning is done by the human being
• Our goal Develop a knowledge representation
  language and a reasoning system such that once we
  express our knowledge in that language the system
  can do the desired reasoning
• P-log is such an attempt

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Representing the Monty Hall problem in P-log.

• doors 1, 2, 3.
• open, selected, prize, D doors
• can_open(D) ?selected D.
• can_open(D) ? prize D.
• can_open(D) ?not can_open(D).
• pr(openD c can_open(D), can_open(D1), D / D1
  ) ½
• By default pr(open D c can_open(D) ) 1 when
  there is no D1, such that
• 
  
  can_open(D1) and D / D1 .
• random(prize), random(selected).
• random(open X can_open(X)).
• pr(prize D) 1/3.
• pr(selected D) 1/3.
• obs(selected 1). obs(open 2). obs(prize
  2).

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General Syntax of P-log

• Sorted Signature
• objects and function symbols (term building
  functions and attributes)
• Declaration
• Definition of Sorts and typing information for
  attributes
• Eg. doors 1, 2, 3. open, selected, prize, D
  doors
• Regular part Collection of AnsProlog rules
• Random Selection
• r random(a(t) Y p(Y) ) ? B.
• Probabilistic Information
• Prr(a(t) y) c B) v.
• Observations and Actions
• obs(l).
• do(a(t) y).

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Semantics the main ideas

• The logical part is translated into an AnsProlog
  program.
• The answer sets correspond to possible worlds
• The probabilistic part is used to define a
  measure over the possible worlds.
• It is then used in defining the probability of
  formulas, and
• conditional probabilities.
• Consistency conditions.
• Sufficiency conditions for consistency.
• Bayess nets and Pearls causal models are
  special cases of P-log programs.

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Rifleman Example --various P-log encodings
(Encoding 1)

• U, V, C, A, B, D boolean
• random(U). random(V). random(C). random(A).
  random(B). random(D).
• Pr(U) p. Pr(V) q.
• Pr(CCU) 1. Pr(ACC) 1. Pr(ACV) 1.
• Pr(BCC) 1. Pr(DCA) 1. Pr(DCB) 1.
  
• Pr(CCU) 1. Pr(ACV,C) 1.
• Pr(BCC) 1. Pr(DCA,B) 1.
• Prediction, Explanation works as expected
• Formulating counterfactual reasoning work in
  progress.

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Conclusion highlights of progress

• Modules and generalizations
• Travel module first milestone reached.
• Generalization of the methodology in progress.
• Develop couple of other modules about to start.
• Further generalize the process next step.
• AnsProlog enhancements and its use in various
  kinds of reasoning
• P-log and reasoning using it -- in progress.
• CR-Prolog (Consistency restoring Prolog) in
  progress.
• GUIs, Modular AnsProlog, etc. in progress.