Logic Proofs & Deduction • Use re-write rules to “deduce” from what is known to what is unknown. • These rules can be quite complex. • This idea can be used to create Automatic Theorem Provers.
Limitations • Search Space Size (Generate Heuristics!) • Formalizing Intuition (Generate Heuristics!) • Propositional Logic is decidable (statements provable in finite time), but FOL is semi-decidable (only decidable if true, otherwise may be infinite). • Higher-order logics are incomplete (true statements not provable) according to Godel. • Doesn’t apply to probabilistic situations.
Next up… • Prolog: Programming Logic • Takes First-order logic statements and does all of the resolution for you, finding what is true according to the premises and what is not.