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Logic Programming and Prolog

Logic Programming and Prolog. Presenter: John Xu Date: Nov 09, 2004. 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

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Logic Programming and Prolog

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  1. Logic Programming and Prolog Presenter: John Xu Date: Nov 09, 2004 CAS 701, McMaster

  2. 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? CAS 701, McMaster

  3. 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 Σ: S => T, ¬P => ¬O, S Λ O Logic consequence: T Λ P CAS 701, McMaster

  4. 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 CAS 701, McMaster

  5. /* 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). CAS 701, McMaster

  6. Logic Programming – Prolog Query Queries: • ancestor(fred, sally). Yes • ancestor(fred, diane). Yes • ancestor(fred, bill). No CAS 701, McMaster

  7. 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 <) is a finite or infinite sequence of goals: g0->g1->g2…->gn … • 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 CAS 701, McMaster

  8. Logic Programming – Implementation • Soundness of SLD-resolution • Completeness of SLD-resolution • Cut: Pruning the SLD-tree CAS 701, McMaster

  9. 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/prolog-for-se.html • http://www.swi-prolog.org/ CAS 701, McMaster

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