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Understanding Propositional and First-Order Logic: Inference Rules and Limitations

Dive into the fascinating world of logic with our introduction to propositional logic and first-order logic. Explore inference rules that help deduce unknowns from known facts, and understand their complexity. Learn about automatic theorem provers and the implications of decidability in propositional logic versus first-order logic. Discover the limitations highlighted by Gödel's incompleteness and the challenges posed by formalizing intuition. Finally, we will touch on Prolog, a programming language that translates first-order logic statements into resolutions, simplifying the logic process.

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Understanding Propositional and First-Order Logic: Inference Rules and Limitations

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Presentation Transcript

  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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