Ways to Prove Theorems
Given a set of facts ( ground literals) and a set of rules,
a desired theorem can be proved in several ways:
- Truth Table: Write Premises &rarr Conclusion
and show that this sentence is true for every interpretation.
This is also called model checking.
- Algebra: Write Premises &rarr Conclusion and
reduce it to True using laws of Boolean algebra.
- Backward Chaining: Work backward from the desired conclusion by
finding rules that could deduce it; then try to deduce the premises of
- Forward Chaining: Use known facts and rules to deduce additional
known facts. If the desired conclusion is deduced, stop.
- Resolution: This is a proof by contradiction. Using ground facts,
rules, and the negation of the desired conclusion, try to derive ``box''
(false or contradiction) by resolution steps.