Logic Programming and Prolog

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Logic Programming and Prolog

• Presenter John Xu
• Date Nov 09, 2004

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Logic Programming Example

• Suppose we have the following sentences
• 1) A graduate student of CAS must take the core
  course CAS 701
• 2) A student can not obtain a degree without
  passing the required core course
• I am a graduate student of CAS and want to
  obtain a degree, should I pass CAS 701?

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Logic Programming Example

• Structured solution
• S Being a graduate student of CAS
• T Taking core course CAS 701
• O Obtaining a degree
• P Passing required core course
• S S gt T, P gt O, S ? O
• Logic consequence T ? P

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Logic Programming Definition

• Logic programming is a declarative approach of
  writing computer programs based on Logic
• Prolog, which stands for PROgramming in LOGic, is
  the most widely available logic programming
  language

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• / Filename ancestor.pro
• This program creates a small set of facts and
  rules on who is the ancestor of whom. The user
  types the desired goal interactively when the
  program is run./
• / ancestor(A, B) means A is an ancestor of B /
• ancestor(bob, susan).
• ancestor(A, X) - parent(A, X).
• ancestor(A, X) - parent(A, C), ancestor(C, X).
• / parent(P, C) means P is a parent of C /
• parent(fred, sally).
• parent(tina, sally).
• parent(sally, diane).
• parent(sam, bill).

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Logic Programming Prolog Query

• Queries
• ancestor(fred, sally).
• Yes
• ancestor(fred, diane).
• Yes
• ancestor(fred, bill).
• No

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Logic Programming Implementation

• SLD-Resolution (inference mechanism)
• Unification a procedure that takes two atomic
  formulas as input, and either shows how they can
  be instantiated to identical atoms or, reports a
  failure
• An SLD-derivation of G0 (using P and lt) is a
  finite or infinite sequence of goals
  g0-gtg1-gtg2-gtgn
• SLD-refutation a finite derivation of the goal
  g0
• Failed derivation a derivation of the goal g0
  with the last element that is not empty and
  cannot be resolved by any clause of the program

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Logic Programming Implementation

• Soundness of SLD-resolution
• Completeness of SLD-resolution
• Cut Pruning the SLD-tree

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Logic Programming Reference

• Book
• Ralph P. Grimaldi, DISCRETE AND COMBINATORIAL
  MATHEMATICS, 5TH ED, Pearson Education, 2004
• Ulf Nilsson and Jan Ma luszy_nski, LOGIC,
  PROGRAMMING AND PROLOG, 2ND ED, Ulf Nilsson and
  Jan Ma luszy_nski, 2000
• Web
• http//cis.stvincent.edu/carlsond/prolog.html
• http//ktiml.mff.cuni.cz/bartak/prolog/index.html
  
• http//www.cs.auckland.ac.nz/j-hamer/07.363/prolo
  g-for-se.html
• http//www.swi-prolog.org/