CSCE 580 Artificial Intelligence Ch.5 [P]: Propositions and Inference Sections 5.5-5.7: Complete Knowledge Assumption, Abduction, and Causal Models

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CSCE 580Artificial IntelligenceCh.5 P
Propositions and InferenceSections 5.5-5.7
Complete Knowledge Assumption, Abduction, and
Causal Models

• Fall 2009
• Marco Valtorta
• mgv_at_cse.sc.edu

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Acknowledgment

• The slides are based on AIMA and other sources,
  including other fine textbooks
• David Poole, Alan Mackworth, and Randy Goebel.
  Computational Intelligence A Logical Approach.
  Oxford, 1998
• A second edition (by Poole and Mackworth) is
  under development. Dr. Poole allowed us to use a
  draft of it in this course
• Ivan Bratko. Prolog Programming for Artificial
  Intelligence, Third Edition. Addison-Wesley,
  2001
• The fourth edition is under development
• George F. Luger. Artificial Intelligence
  Structures and Strategies for Complex Problem
  Solving, Sixth Edition. Addison-Welsey, 2009

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Example of Clarks Completion
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Negation as Failure
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Non-monotonic Reasoning
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Example of Non-monotonic Reasoning
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Bottom-up Negation as Failure Inference Procedure
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Top-down Negation as Failure Inference Procedure
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Top-down Negation as Failure Inference Procedure
(updated on 2009-10-29)
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Abduction

• Abduction is a form of reasoning where
  assumptions are made to explain observations.
• For example, if an agent were to observe that
  some light was not working, it can hypothesize
  what is happening in the world to explain why the
  light was not working.
• An intelligent tutoring system could try to
  explain why a student is giving some answer in
  terms of what the student understands and does
  not understand.
• The term abduction was coined by Peirce
  (18391914) to differentiate this type of
  reasoning from deduction, which is determining
  what logically follows from a set of axioms, and
  induction, which is inferring general
  relationships from examples.

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Abduction with Horn Clauses and Assumables
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Abduction Example
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Another Abduction Example a Causal Model
A causal network
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Consistency-based vs. Abductive Diagnosis

• Determining what is going on inside a system
  based on observations about the behavior is the
  problem of diagnosis or recognition.
• In abductive diagnosis, the agent hypothesizes
  diseases and malfunctions, as well as that some
  parts are working normally, in order to explain
  the observed symptoms.
• This differs from consistency-based diagnosis
  (page 187) in that the designer models faulty
  behavior as well as normal behavior, and the
  observations are explained rather than added to
  the knowledge base.
• Abductive diagnosis requires more detailed
  modeling and gives more detailed diagnoses, as
  the knowledge base has to be able to actually
  prove the observations.
• It also allows an agent to diagnose systems where
  there is no normal behavior. For example, in an
  intelligent tutoring system, observing what a
  student does, the tutoring system can hypothesize
  what the student understands and does not
  understand, which can the guide the action of the
  tutoring system.

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Example of Abductive Diagnosis

• In abductive diagnosis, we need to axiomatize
  what follows from faults as well as from
  normality assumptions. For each atom that could
  be observed, we axiomatize how it could be
  produced.

This could be seen in design terms as a way to
make sure the light is on put both switches up
or both switches down, and ensure the switches
all work. It could also be seen as a way to
determine what is going on if the agent observed
l1 is lit one of these two scenarios must hold.
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Inference Procedures for Abduction

• The bottom-up and top-down implementations for
  assumption-based reasoning with Horn clauses
  (page 190) can both be used for abduction.
• The bottom-up implementation of Figure 5.9 (page
  190) computes, in C, the minimal explanations for
  each atom. Instead of returning A ltfalse, Agt in
  C, return the set of assumptions for each atom.
  The pruning of supersets of assumptions discussed
  in the text can also be used.
• The top-down implementation can be used to find
  the explanations of any g by generating the
  conflicts, and, using the same code and knowledge
  base, proving g instead of false. The minimal
  explanations of g are the minimal sets of
  assumables collected to prove g that are not
  subsets of conflicts.

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Inference Procedures for Abduction, ctd.
Bottom up
Top down
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Causal Models

• There are many decisions the designer of an agent
  needs to make when designing knowledge base for a
  domain. For example, consider two propositions a
  and b, both of which are true. There are many
  choices of how to write this.
• A designer could specify have both a and b as
  atomic clauses, treating both as primitive.
• A designer could have a as primitive and b as
  derived, stating a as an atomic clause and giving
  the rule blt-a.
• Alternatively, the designer could specify the
  atomic clause b and the rule alt-b, treating b as
  primitive and a as derived.
• These representations are logically equivalent
  they cannot be distinguished logically. However,
  they have different effects when the knowledge
  base is changed. Suppose a was no longer true for
  some reason. In the first and third
  representations, b would still be true and in the
  second representation b would no longer true.
• A causal model is a representation of a domain
  that predicts the results of interventions. An
  intervention is an action that forces a variable
  to have a particular value.

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Causal vs. Evidential Models

• In order to predict the effect of interventions,
  a causal model represents how the cause implies
  its effect. When the cause is changed, its effect
  should be changed. An evidential model represents
  a domain in the other direction,from effect to
  cause.

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Another Causal Model Example
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Parts of a Causal Model
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Using a Causal Model