1. Propositional Logic: Truth Table for (P -> Q)
P Q (P -> Q)
--------------True True True
True False False
False True True
False False True
2. First-Order Logic (FOL) Representation:
For all x: If Student(x), then Studies(x)
3. Conversion to Clausal Form:
Not Student(x) OR Studies(x)
4. Inference Rule: Modus Ponens
Given: P -> Q, P
Conclusion: Q
Example: If it rains, the ground is wet. It rains -> The ground is wet
5. Resolution Principle Example:
Clauses:
(Not P OR Q)
(P)
Resolution:
(Not P OR Q), P -> Q