For example, consider an agent concerned with predicting the weather, with variable R indicating whether or not it is likely to rain, variable C indicating whether or not it is cloudy, and variable L indicating low pressure. Given knowledge base K:
L (Pressure is low)
C (It is cloudy)
C ∧ L ⇒ R, (Clouds and low pressure imply rain)
the agent may conclude R; thus, the agent’s knowledge implies that R is true, because K |= R.
Similarly, given knowledge base L:
¬L (Pressure is high)
C (It is cloudy)
C ∧ L ⇒ R, (Clouds and low pressure imply rain)
the agent cannot conclude that R is true; L 6|= R
Deriving a truth table:
L C r ((L ∧ C) → r)
F F F T
F F T T
F T F T
F T T T
T F F T
T F T T
T T F F
T T T T
but this does not make sense.
