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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.

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