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CS 363 Comparative Programming Languages Logic Programming Languages Slide 2 CS 363 Spring 2005 GMU2 Chapter 16 Topics An Overview of Logic Programming The Origins of Prolog The Basic Elements of Prolog Applications of Logic Programming Slide 3 CS 363 Spring 2005 GMU3 Introduction Logic (declarative) programming languages express programs in a form of symbolic logic Runtime system uses a logical inferencing process to produce results Declarative rather that procedural: only specification of results are stated (not detailed procedures for producing them) Slide 4 CS 363 Spring 2005 GMU4 Example: Sorting a List Describe the characteristics of a sorted list, not the process of rearranging a list sort(old_list, new_list) permute (old_list, new_list) sorted (new_list) sorted (list) for all j, 1 j < n, list(j) list (j+1) Slide 5 CS 363 Spring 2005 GMU5 Overview of Logic Programming Declarative semantics There is a simple way to determine the meaning of each statement Simpler than the semantics of imperative languages Programming is nonprocedural Programs do not state now a result is to be computed, but rather the form of the result Based on Propositional logic Slide 6 CS 363 Spring 2005 GMU6 Propositional Logic A proposition is formed using the following rules: Constants true and false are propositions Variables (p,q,r,) which have values true or false are propositions Operators ^, v, , , and (conjunction, disjunction, implication, equilivance and negation) are used to form more complex propositions. p v q ^ r s v t Slide 7 CS 363 Spring 2005 GMU7 Predicate Logic Expressions Include: Propositions Variables in domains such as integer, real Boolean valued functions Ex: prime(n), 0 CS 363 Spring 2005 GMU21 Example speed(ford,100). speed(chevy,105). speed(dodge,95). speed(volvo,80). time(ford,20). time(chevy,21). time(dodge,24). time(volvo,24). distance(X,Y) :- speed(X,Speed), time(X,Time), Y is Speed * Time. Distance(ford,S). > S = 2000 Facts Rules Goal Slide 22 CS 363 Spring 2005 GMU22 Inferencing Process of Prolog Queries are called goals If a goal is a compound proposition, each of the facts is a subgoal To prove a goal is true, must find a chain of inference rules and/or facts. For goal Q: B :- A C :- B Q :- P Process of proving a subgoal called matching, satisfying, or resolution Slide 23 CS 363 Spring 2005 GMU23 Inferencing Process Bottom-up resolution, forward chaining Begin with facts and rules of database and attempt to find sequence that leads to goal works well with a large set of possibly correct answers Top-down resolution, backward chaining begin with goal and attempt to find sequence that leads to set of facts in database works well with a small set of possibly correct answers Prolog implementations use backward chaining Slide 24 CS 363 Spring 2005 GMU24 Inferencing Process When goal has more than one subgoal, can use either Depth-first search: find a complete proof for the first subgoal before working on others Breadth-first search: work on all subgoals in parallel Prolog uses depth-first search Can be done with fewer computer resources Slide 25 CS 363 Spring 2005 GMU25 Inferencing Process With a goal with multiple subgoals, if fail to show truth of one of subgoals, reconsider previous subgoal to find an alternative solution: backtracking Begin search where previous search left off Can take lots of time and space because may find all possible proofs to every subgoal Slide 26 CS 363 Spring 2005 GMU26 Example mother(Susan,Emily). mother(Susan,Lucy). mother(Anne,Susan). mother(Anne,Mary). father(Jim,Emily). father(Jim,Lucy). father(Russell,Susan). father(Russell,Mary). parent(X,Y):-mother(X,Y). parent(X,y):-father(X,y). sibling(X,Y):-mother(M,X),mother(M,Y), father(F,X),father(F,Y). sibling(Emily,Y). Y = Lucy Sibling(Susan,Anne). > no Facts Rules Goals (queries) Slide 27 CS 363 Spring 2005 GMU27 sibling(Emily,Y). mother(M,Emily),mother(M,Y),father(F,Emily), father(F,Y). After searching the db: mother(Susan,Emily),mother(Susan,Y), father(Jim,Emily),father(Jim,Y). Searching again: mother(Susan,Emily),mother(Susan,Lucy), father(Jim,Emily),father(Jim,Lucy) So Y = Lucy Slide 28 CS 363 Spring 2005 GMU28 sibling(Susan,Anne). mother(M,Susan),mother(M,Anne), father(F,Susan),father(F,Anne). If we choose M = Anne, we cant resolve the second mother clause (similar problem with father) fail Slide 29 CS 363 Spring 2005 GMU29 List Structures Other basic data structure (besides atomic propositions we have already seen): list List is a sequence of any number of elements Elements can be atoms, atomic propositions, or other terms (including other lists) [apple, prune, grape, kumquat] [] ( empty list) [X | Y] ( head X and tail Y) Slide 30 CS 363 Spring 2005 GMU30 Example Definition of member function: member(Elem,[Elem | _ ). member(Elem,[ _ | List]) :- member (Elem,List). Anonymous variable Slide 31 CS 363 Spring 2005 GMU31 member(a,[b,c,d]). member(a,[b,c,d]) member(a,[c,d]) member(a,[d]) member(a,[]) fails Slide 32 CS 363 Spring 2005 GMU32 Example Definition of append function: append([], List, List). append([Head | List_1], List_2, [Head | List_3]) :- append (List_1, List_2, List_3). Slide 33 CS 363 Spring 2005 GMU33 How append works append([a,b],[c,d],X). append([a|b],[c,d],_). append([b],[c,d],_). append([],[c,d],[c,d]). first rule! append([b],[c,d],[b,c,d]). append([a,b],[c,d],[a,b,c,d]). X = [a,b,c,d] Slide 34 CS 363 Spring 2005 GMU34 Example Definition of reverse function: reverse([], []). reverse([Head | Tail], List) :- reverse (Tail, Result), append (Result, [Head], List). Slide 35 CS 363 Spring 2005 GMU35 Cut Operator (!) Explicit control of backtracking ! Is a goal that always succeeds but cannot be resatisified by backtracking a,b,!,c,d if a and b succeed, but c fails, the whole goal fails. Slide 36 CS 363 Spring 2005 GMU36 Deficiencies of Prolog Resolution Order control Prolog always starts at the beginning of DB when searching Prolog always starts trying to resolve the leftmost subgoal (depth first) rule/definition order can affect performance! Slide 37 CS 363 Spring 2005 GMU37 Deficiencies of Prolog Easy to write infinite loops (due to resolution order) ancestor(X,X). ancestor(X,Y) :- ancestor(Z,y),parent(X,Z). Reversing rules fixes the problem Slide 38 CS 363 Spring 2005 GMU38 Deficiencies of Prolog Closed World assumption Prolog can only prove things to be true (based on the info) but it cannot be used to prove a goal is false Leads to a problem with negation Slide 39 CS 363 Spring 2005 GMU39 Deficiencies of Prolog Problems with negation: Given: parent(bill,jake). parent(bill, shelley). sibling(X,Y) :- parent(M,X),parent(M,Y). For goal: sibling(X,y). Prolog will respond with: X=jake, Y=jake sibling(X,Y) :- parent(M,X),parent(M,Y),not(X=Y). Slide 40 CS 363 Spring 2005 GMU40 Deficiencies of Prolog Problems with negation: Need to write the rule using negation: sibling(X,Y) :- parent(M,X),parent(M,Y),not(X=Y). However, must be done carefully not(not(goal)) is not the same as goal. Slide 41 CS 363 Spring 2005 GMU41 Trace Built-in structure that displays instantiations at each step Tracing model of execution - four events: Call (beginning of attempt to satisfy goal) Exit (when a goal has been satisfied) Redo (when backtrack occurs) Fail (when goal fails) Slide 42 CS 363 Spring 2005 GMU42 Applications of Logic Programming Relational database management systems Expert systems Natural language processing Education Slide 43 CS 363 Spring 2005 GMU43 Conclusions Advantages: Prolog programs based on logic, so likely to be more logically organized and written Processing is naturally parallel, so Prolog interpreters can take advantage of multi- processor machines Programs are concise, so development time is decreased good for prototyping