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 → Conclusion and show that this sentence is true for every interpretation. This is also called model checking.

• Satisfiability: Find an assignment of truth values to variables that will make a propositional calculus formula true. There are efficient SAT solvers that can solve systems with millions of propositional variables.

• Algebra: Write Premises → 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 those rules.

• 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.