A Causal Knowledge-Driven Inference Engine for Expert System

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A Causal Knowledge-Driven Inference Engine for
Expert System

• Presenters Donna-Marie Anderson
• Oniel Charles

2
Introduction to Expert Systems

• Consists of 3 major components
• Dialogue Structure
• Inference Engine (CAKES)
• Knowledge Base

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Causal Knowledge Base

• Syntactically similar to IF-THEN rule but
  semantically different
• In most cases it is referred to as Fuzzy
  Cognitive Map (FCM)
• Used mainly to represent political, economic or
  decision making problems

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FCMs

• Fuzzy signed directed graph with feedback
• Model the world as a collection of concepts and
  causal relationship between the concepts
• Concept is depicted as a node
• Causal relation is represented as an edge
• Therefore, edge value between 2 concepts, i and
  j,
• written eij, indicates the causality value
  between
• the 2 concepts

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FCMs

• Causality values lies between 1 1
• eij 0 means no causal relation between concepts
  i and j.
• eij gt 0 indicates causal increase (positive
  causality)
• eij lt 0 indicates causal decrease (negative
  causality)
• Simple FCM has edge value in -1, 0, 1, i.e. if
  causality occurs it occurs at maximal positive or
  negative degree.

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FCM Reasoning Technique

• Uses modus ponens-based approximate reasoning
  method between the set of causal relationships
  between concepts.
• If x is G y is F with causality exy
• then if x is Gi y is Fi with causality
  exy
• Uses negation of the premises
• If x is G y is F with causality exy
• then if x is not G y is not F with
  causality exy

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Causal Knowledge Acquisition

• Matrix Multiplication Inference Method
• Define a concept node (row) vector, C, with the
  number of columns equal to the number of
  concepts, i.e., if there are L concepts then
• C (C1,C2,C3,.,CL-1,CL) , where each Ci
  represents a concept.
• Build an Adjacency matrix (FCM matrix), E, based
  on the causality value between the concepts.

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Traditional Causal Knowledge-Based Inference

• Forward-evolved inference
• Use the adjacency matrix to test the effect of
  one of the concept on the others.
• Get the row vector that represents the concept
  you wish to test.
• Decide on a threshold value in the interval
  -1,1, say .5
• Multiply the row vector by E.
• Compare the values received to the threshold. If
  lt then it becomes 0, otherwise it is 1.

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Traditional Causal Knowledge-Based Inference

• Forward-evolved inference
• Repeat until you find a vector that after
  multiplying it by E and applying the threshold
  operation on the product you get back the vector.
• At this point you you have obtained the set that
  the FCM has associatively inferred.
• The set is given by the position in the resultant
  vector that contains a 1.

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Traditional Causal Knowledge-Based Inference

• Backward inference
• Uses the transpose of E, Et, to yield a specific
  concept node value that should be accompanied
  with a given consequence.

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CAsual Knowledge-based Expert system Shell (CAKES)

• Core Menus
• Concept Nodes Menu
• Relationship Menu
• Inference Menu

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Fuzzy Causal Relationship

• Definition of FCR- A causally increases B means
  that if A increases then B increases and if A
  decreases then B decreases. On the other hand if
  A causally increases B means that if A
  increases then B decreases and if A decreases
  then B increases.
• In the concepts that constitute causal
  relationship, there must exist a quantitative
  elements that can increase or decrease.

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Fuzzy Causal Relationship (FCR)

• FCM fuzzy relations mean fuzzy causality.
  Causality can have a negative sign. The negative
  fuzzy relation between two concept nodes is the
  degree of relation with negation of a concept
  node.
• Example If the concept node Ci is noted as Cj
  the R(Ci,Cj)-0.6 which means that R(Ci,Cj)0.6
  conversely R(Ci,Cj)0.6 the R(Ci,Cj)-0.6

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Fuzzy Causal Relationship (example)

• Based on our Definition of FCR the following four
  FCRs are equivalent.
• Buying by institution investors -gt Increase of
  composite stock price
• 
  
• Selling by institution investors -gt Decrease
  composite stock price
• 
  
• Buying by institution investors -gt Decrease of
  composite stock price
• -
• Selling by institution investors -gt Increase
  composite stock price
• 
  -

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Fuzzy Causal Relationship (Causality Values)

• The following two FCRs with real valued
  causality are equivalent.
• Institute investors -gt Composite stock price
• 0.9
• Buying by Institute investors -gt
• 0.1
• Not Increase of composite stock
  price

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Fuzzy Causal Relationship(Theorems)

• There are 6 theorems that highlight the core
  principles of FCR. In the interest of time we
• will highlight only two.
• Theorem 3.
• When fuzzy causal concepts Ci, and
• Cj, are given, the following FCRs are all
  equivalent.
• Ci -gt Cj Ci -gt Cj Ci -gt Cj Ci
  -gt Cj
• r r -r
  -r
• where 1lt r lt1

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Fuzzy Causal Relationship(Theorems)

• Theorem 6.
• When Ci is a negative concept of Ci and the
  dis-quantity fuzzy set of Ci is equal to the
  complement of Ci s quantity fuzzy set, then the
  following FCRs are all equivalent.
• Ci -gt Cj implies Ci -gt Cj Ci -gt Cj
• 1 0
  -0
• Ci -gt Cj implies Ci -gt Cj Ci -gt Cj
• -1 -0
  0

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Fuzzy Partially Causal Relationship

• In reality, there exist many cases in which the
  definition of causality is not met.
• For example there might be a stock market
  situation in which institute investors buying
  causes increase of composite stock price but
  there selling cannot cause a decrease of
  composite stock price.

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Fuzzy Partially Causal Relationship

• Our FCR type discussed in the previous section
  should be adjusted to incorporate this situation.
  Hence -
• Buying by institution investors ---gt Increase of
  composite stock price
• 
  .09
• Selling by institution investors ----gt Decrease
  composite stock price
• 
  0.9
• where ---gt means partially causality. This
  constitutes Fuzzy Partially Causal Relationship

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Fuzzy Partially Causal Relationship (Example)
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Fuzzy Partially Causal Relationship (Example)
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CAKES Design and Implementation
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Advanced Inference Mechanism

• Refines FCM by using FCR and FPCR concepts
• Principles
• If two causal relationships support the same
  conclusion, then the addition of those 2
  causality value is gt each causality value.
• If a causal relationship is connected
  consecutively to a causal relationship, then the
  absolute value of its additive value of the 2
  causality values is lt the least of absolute
  value of the 2 causality

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Advanced Inference Mechanism

• Principles
• The final additive value remains same
  irrespective of the order of addition of
  causality values of interest.
• Both a ve and a ve causality value have the
  same amount of strength although they have the
  opposite direction with each other.
• The final causality value lies in the interval
  -1,1

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Conclusion

• Improved FCM theory was needed for a more
  sophisticated representation of causal knowledge
  and to arrive at more logical conclusions.
• Refined by using FCR and FPCR
• The Expert System used to test these concepts was
  CAKES.