KR: Formalizing Sentences and Queries

Study Notes

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 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

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