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Intro to Logic

Intro to Logic. Propositional logic. Inference Rules. First-order Logic. 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.

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Intro to Logic

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  1. Intro to Logic

  2. Propositional logic

  3. Inference Rules

  4. First-order Logic

  5. 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.

  6. 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.

  7. 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.

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