KR: Formalizing Sentences and Queries

Knowledge Representation (KR)

• Formalize sentences using predicates:
  • child(tom, john) represents "Tom is John's child"
  • child(ann, tom) represents "Ann is Tom's child"
  • child(john, mark) represents "John is Mark's child"
  • child(alice, john) represents "Alice is John's child"
  • grandchild(X, Y) <=> child(X, Z) ∧ child(Z, Y) represents "The grandchild of a person is a child of a child of this person"

Query Answers

• Is Ann a child of Tom? -> Yes
• Who is a grandchild of Ann? -> No information provided
• Who is a grandchild of whom? -> No information provided

Example

• Formalize the scenario:
  • bird(tom) represents "Tom is a bird"
  • bird(sam) represents "Sam is a bird"
  • bird(donald) represents "Donald is a bird"
  • eagle(sam) represents "Sam is an eagle"
  • penguin(tom) represents "Tom is a penguin"
  • duck(donald) represents "Donald is a duck"
  • fly(x) <=> feather(x) ∧ bird(x) represents "Birds fly if they have feathers"
  • penguin(x) => ¬feather(x) represents "Penguins do not have feathers"

Definite Program

• grandfather(X, Z) <=> father(X, Y) ∧ parent(Y, Z) represents "A grandfather is a father of a parent"
• parent(X, Y) ∨ father(X, Y) represents "A parent is either a father or a mother"
• father(a, b) represents "A is the father of B"
• mother(b, c) represents "B is the mother of C"
• Query: grandfather(a, X) -> X = c

Backtracking

• Backtracking is the process of going back to a previous goal and trying to resatisfy it, i.e., find another way of satisfying it.
• Example:
  • Father(john, mary) represents "John is the father of Mary"
  • Father(john, mark) represents "John is the father of Mark"
  • Father(john, francis) represents "John is the father of Francis"
  • Father(gavin, lucy) represents "Gavin is the father of Lucy"
  • Rich(jane) represents "Jane is rich"
  • Rich(john) represents "John is rich"
  • Rich(gavin) represents "Gavin is rich"
  • Rich_father(X, Y) :- rich(X), father(X, Y) represents "A rich father is a father who is rich"
• Query: Rich_father(A, B) -> Solution using backtrack method

Fuzzy Logic

• Types of Belief:
  • Possible: no matter how remote, the hypothesis cannot be ruled out
  • Probable: there is some evidence favoring the hypothesis but not enough to prove it
  • Certain: evidence is logically true or false
  • Impossible: it is false
  • Plausible: more than a possibility exists
• Uncertainty:
  • Lack of information to formulate a decision
  • May result in making poor or bad decisions
  • Requires reasoning under uncertainty along with common sense
• Expert Systems:
  • Provide an advantage when dealing with uncertainty compared to decision trees
  • With decision trees, all facts must be known to arrive at an outcome
  • Probability theory is devoted to dealing with theories of uncertainty