Logic Programming March 27, 2012 Tom Lever

1. Logic ProgrammingMarch 27, 2012 Tom Lever

2. What is Logic Programming? • Roots in automatic theorem proving • Describe the problem, not the solution • Let the computer decide how to solve it • Describe problem in language native to the field • Write declarative sentences in a dialect of FOL • Computer follows simple rules to analyze • Correct description  correct solution (?!)

3. What is PROLOG? • PROgramming en LOGique • Early 1970s work on natural language processing • Alain Colmerauer – Montreal and Marseille • Robert Kowalski – Imperial College, London • David H D Warren – University of Edinburgh • Warren Abstract Machine (WAM) interpreted code • Declarations are in the form of Horn clauses (see section 17.3 of our textbook - clauses in CNF with at most one positive literal in each disjunction)

4. What do declarations look like? • Material conditionals (implications) facing left () • Literal :- Literal ^ Literal ^…^ Literal • Each literal takes the form of Predicate(arguments) • Each declaration has the form Head :- Body. • A declaration with only a Head is a Fact owns(max,pris). • A declaration without a head is a Query ? – owns(max,Who). • A complete declaration is a Rule ownsCat(Who, Pet) :- owns(Who, Pet), animal(Pet, cat).

5. Basic Housekeeping • Predicates and constants begin with lower-case • Variables begin with upper-case • A comma between predicates means AND • Variables are instantiated with values when a predicate is examined (executes) • Predicates in the same declaration are examined left to right. • Facts and rules are preloaded from files.

6. Fact = an assertion or premise • owns(max, carl). • owns(max, pris). • owns(claire, scruffy). • owns(claire, folly). • animal(carl, dog). • animal(scruffy, cat). • animal(folly, dog). • animal(pris, cat).

7. Query = interactive way to access data • Queries continue executing until the entire database has been examined. Continue after pauses with Tab or terminate with Enter. • ? – owns(max, folly). • ? – owns(Who, folly). • ? – owns(Who, Pet). • ? – animal(Pet, dog). • ? – ownsCat(Person, Pet). • ? – owns(Person, Pet), animal(Pet, What).

8. Definite Programs and Goals • Definite program – a set of definite clauses (facts & rules) • Definite goal – a query consisting of atomic formulas as subgoals which must each be satisfied • Query – analogous to relational database query, posing an existential question whether all subgoals can be satisfied • Rules containing variables imply universal quantification • Rules defined recursively can give a model infinite depth • PROLOG code specifies “what” exists but not “how” to find the solution

9. Backtracking? – animal(Pet, _), owns(Person, Pet). • When a predicate succeeds, it instantiates its variables and control passes to the right • The rightmost predicate pauses after it succeeds, then continues where it left off • When the rightmost predicate fails, control passes back to its predecessor • If it succeeds again, it re-instantiates its variables and control passes to the right again • The rightmost predicate starts from the top

10. Unification • The process of matching up references and definitions of predicates (argument passing) • Sophisticated pattern matching to instantiate variables in two directions. For example: T = p( X, f(a,b), g(Z,F)) U = p(t(e), W, g(3,C)) • Combining these changes both to this: T = U = p(t(e), f(a,b), g(3,C) where only variable C (or F) remains uninstantiated

11. Recursion • Used in list processing (similar to LISP) • Defining something in terms of itself • Must define a stop condition append([], List, List). append([Head|Tail], List, [Head|NewTail]) :- append(Tail, List, NewTail). • Sample uses ? – append([a,b,c], [d,e,f], What). ? – append(First, Second, [mary, anne, john]).

12. Quicksort Pseudocode function quicksort('array') if length('array') ≤ 1 return 'array' // 0 or 1 elements already sorted select and remove a pivot value 'pivot' from 'array' create empty lists 'less' and 'greater' for each 'x' in 'array' if 'x' ≤ 'pivot' then append 'x' to 'less' else append 'x' to 'greater' return concatenate(quicksort('less'), 'pivot', quicksort('greater')) // two recursive calls

13. Quicksort in PROLOG partition([], _, [], []). partition([X|Xs], Pivot, Smalls, Bigs) :- ( X @< Pivot -> Smalls = [X|Rest], partition(Xs, Pivot, Rest, Bigs) ; Bigs = [X|Rest], partition(Xs, Pivot, Smalls, Rest) ). quicksort([]) --> []. quicksort([X|Xs]) --> { partition(Xs, X, Smaller, Bigger) }, quicksort(Smaller), [X], quicksort(Bigger).

14. Applications • Natural language processing • Artificial intelligence • Theorem proving • Ontologies (information frameworks) • Expert systems • Automated answering systems • Control systems • Games

15. References • Bharath, R. An Introduction to PROLOG, Tab Books 1986 • Saint-Dizier, P. An Introduction to Programming in PROLOG, Springer-Verlag, 1990 • http://www.learnprolognow.org/ - a free online introductory course to PROLOG, with links to free downloadable implementations • http://en.wikipedia.org/wiki/Prolog- overview with abundant links leading in many directions • http://www.cs.bham.ac.uk/~pjh/prolog_course/sem223_se.html - Logic Programming with Prolog – An Introduction for Software Engineers - course overview