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Logical Reasoning with Prolog: The Himalayan Club Example in Artificial Intelligence

This lecture discusses logical reasoning in Prolog through the Himalayan Club example, based on Zohar Manna's framework. The scenario involves three club members—A, B, and C—who are either mountain climbers or skiers. Key relationships and preferences are explored, such as A liking rain and snow, while no mountain climber enjoys rain. The goal is to infer whether there exists a member who is a mountain climber but not a skier, employing resolution refutation. The lecture highlights Prolog's features, problem formulation, and applications in knowledge representation.

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Logical Reasoning with Prolog: The Himalayan Club Example in Artificial Intelligence

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  1. CS621: Artificial Intelligence Pushpak BhattacharyyaCSE Dept., IIT Bombay Lecture 35–Himalayan Club example; introducing Prolog

  2. Himalayan Club example • Introduction through an example (Zohar Manna, 1974): • Problem: A, B and C belong to the Himalayan club. Every member in the club is either a mountain climber or a skier or both. A likes whatever B dislikes and dislikes whatever B likes. A likes rain and snow. No mountain climber likes rain. Every skier likes snow. Is there a member who is a mountain climber and not a skier? • Given knowledge has: • Facts • Rules

  3. Example contd. • Let mc denote mountain climber and sk denotes skier. Knowledge representation in the given problem is as follows: • member(A) • member(B) • member(C) • ∀x[member(x) → (mc(x) ∨ sk(x))] • ∀x[mc(x) → ~like(x,rain)] • ∀x[sk(x) → like(x, snow)] • ∀x[like(B, x) → ~like(A, x)] • ∀x[~like(B, x) → like(A, x)] • like(A, rain) • like(A, snow) • Question: ∃x[member(x) ∧ mc(x) ∧ ~sk(x)] • We have to infer the 11th expression from the given 10. • Done through Resolution Refutation.

  4. Club example: Inferencing • member(A) • member(B) • member(C) • Can be written as

  5. Negate–

  6. member(A) • member(B) • member(C) • Now standardize the variables apart which results in the following

  7. 10 7 12 5 4 13 14 2 11 15 16 13 2 17

  8. Assignment • Prove the inferencing in the Himalayan club example with different starting points, producing different resolution trees. • Think of a Prolog implementation of the problem • Prolog Reference (Prolog by Chockshin & Melish)

  9. Prolog

  10. Introduction • PROgramming in LOGic • Emphasis on what rather than how Problem in Declarative Form LogicMachine Basic Machine

  11. Prolog’s strong and weak points • Assists thinking in terms of objects and entities • Not good for number crunching • Useful applications of Prolog in • Expert Systems (Knowledge Representation and Inferencing) • Natural Language Processing • Relational Databases

  12. A Typical Prolog program Compute_length ([],0). Compute_length ([Head|Tail], Length):- Compute_length (Tail,Tail_length), Length is Tail_length+1. High level explanation: The length of a list is 1 plus the length of the tail of the list, obtained by removing the first element of the list. This is a declarative description of the computation.

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