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Chapter 7

King Saud University College of Computer and Information Sciences Information Technology Department IT422 - Intelligent systems . Chapter 7. Part 2 Introduction to Prolog. Introduction. PRO LOG = PRO gramming in LOG ic

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Chapter 7

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  1. King Saud University College of Computer and Information Sciences Information Technology Department IT422 - Intelligent systems Chapter 7 Part 2 Introduction to Prolog

  2. Introduction • PROLOG = PROgramming in LOGic • 1970: using logic as a programming language (R. Kowalski, M. Van Emden, A. Colmerauer from Edinburg and Marseille). • 1972: First Prolog interpreter (Prolog0), Aix-Marseille, P. Roussel. • 1982: Prolog software product in markets. • 1995: extension CLP Constraint Logic Programming.

  3. Introduction • Procedural/Object Oriented Programming (PP/OOP) vs. Declarative Programming • PP/OOP:a program instructs the computer • what to do • how to do • in what order • Declarative Programming:a program describes what to do without a detailed plan of how to do

  4. Introduction • Prolog is the most widely used logic programming language. • Prolog programs are set of definite clauses written in a notation somewhat different from standard FOL. • Three basic mechanisms among others: • Pattern Matching, • Tree based data structuring • Back-Tracking. • Suitable for problems that involve structured objects and relations between them. • The execution of Prolog programs is done through depth-first backward chaining search with no checks for infinite recursion. • It allows symbolic computation. • Examples: • Red sphere is behind green box. • If object X is closer to the observer than object Y and object Y is closer than object Z than X is closer than Z.

  5. Introduction • Prolog basic concepts by an example: • Let’s consider the Parent relation ali layla nour omar meriam khaled zahra

  6. Defining Relations By Facts • This relation can be defined by the following Prolog program: • parent(leyla, omar). • parent(ali, omar). • parent(omar, meriam). • parent(omar, khaled). • parent(ali, nour). • parent(khaled, zahra). • This program consists of 6 Clauses. Each clause declares one fact about the relation parent. • The clause parent(omar, meriam) is an instance of the relation parent. A relation is defined as a set of instances.

  7. Using Prolog Program • What can we do with this program? • Let’s ask the system questions about the relation parent: • Question: is omar parent of khaled? • In prolog ?- parent(omar, khaled). • Answer: yes

  8. Using Prolog Program • Question: is leyla parent of meriam? In prolog ?- parent(leyla, meriam). • Answer: no • Question: who is zahra’s parent? In prolog ?- parent(X, zahra). The system tells what is the value of X for which the statement is true. • Answer: X= khaled

  9. Using Prolog Program • Question: who are omar’s children? In prolog ?- parent(omar,X). Answer: X= meriam X= khaled no • Question: Who is parent of whom? In prolog ?- parent(X,Y). Answer: X= leyla Y=omar; X=ali Y=omar; X=omar Y=meriam; X=omar Y= khaled; X=ali Y=nour; X=khaled y=zahra;

  10. Using Prolog Program • Question: who is grandparent of khaled? In prolog ?- parent(X, khaled), parent(Y, X). Note: the logical meaning remains the same if we change the order of the two requirements. Answer: X= omar Y= ali; X= omar Y=leyla • Question: Who are ali grandchildren? In prolog ?- parent(ali,X), parent (X,Y). Answer: X= omar y=khaled; X=omar Y=meriam;

  11. Using Prolog Program • Question: Do meriam and nour have a common parent? In prolog ?- parent(X, meriam), parent(X,nour). First who is parent of meriam (X) ? Second is it (X) the same parent of nour ? Answerno

  12. What can we conclude from this example • It is easy in Prolog to define a relation such as parent by stating the n-tuples of objects that satisfy the relation. In this case we have defined a relation by a set of facts represented by clauses. • We can easily express queries in Prolog. • A Prolog program consists of clauses. Each clause terminates with a full stop. • The arguments of relations can be: concrete objects, constants, general objects such as X and Y. • Questions to the system consist of one or more goals. The answer can be positive (goal satisfiable) or negative (goal unsatisfiable). • If several answers satisfy the question than Prolog will find as many of them as desired by the user.

  13. Data objects in Prolog

  14. Prolog Syntax • Prolog system recognizes the type of an object in the program by its syntactic form. • The syntax of Prolog specifies different forms for each type of data object. • All data objects in Prolog are called TERMS.

  15. Prolog Syntax • Atoms and numbers: • An atom can be constructed in three ways: • String of letters, digits and the underscore ‘_’ starting with a lower case e.g. ali, x25, x_y… • Strings of special characters e.g. <__>,::=, .. Predefined string: ‘:-’ • Strings of characters enclosed in single quotes e.g.‘Ali’, ‘Saudi-Arabia’…

  16. Prolog Syntax • Numbers: • Used in Prolog include integer numbers and real numbers e.g.1997, -94, 0, 3.14, 0.0035…. • Variables: • Strings of letters, digits and underscore characters. They start with an upper case letter or an underscore character e.g.X, Result, _23, _x33, _ , …. • Note: Prolog uses anonymous variables _ that are represented by underscores in clauses.

  17. Prolog Syntax • Structures • Structured objects = object that has several components. The components themselves can, in turn, be structures. • e.g. date(1,may,2001), date(Day,may,2007) • Note: This method for data structuring is simple and powerful symbolic manipulation. • All structured objects can be pictured as trees.

  18. Prolog Syntax • Structures D=date T=triangle 1 may 2007 • point pointpoint • Date(1,may,2007) 3 1 4 3 6 0 functor arguments T=triangle(point(3,1),point(4,3),point(6,0))

  19. Defining Relations By Rules • Fact ≠ Rule • A fact is always, unconditionally, true. • A rule specifies a thing that is true if some condition is specified. It has: • a condition part (right hand side of the rule). • a conclusion part (left hand side of the rule). • A clause is written “backwards” from what we are used to. Instead of A B => C in Prolog we have C:- A, B. • e.g. let’s define the relation offspring: For all X and Y Y is an offspring of X if X is a parent of Y

  20. Defining Relations By Rules • Corresponding Prolog clause: offspring (Y,X):-parent (X,Y) head (conclusion part) body (condition part) • Interpretation: for all X and Y if X is parent of Y then Y is an offspring of X

  21. Defining Relations By Rules • If we ask the question: ?-offspring(khaled,omar). • Y is substituted with khaled and X with omar: the process is called instantiation Y=khaled X=omar • Offspring(khaled,omar):-parent(omar,khaled). • Try to find whether the condition is true. • The goal offspring(khaled,omar) is replaced with the goal parent(omar,khaled)

  22. Defining Relations By Rules • More complex rules: • Let’s add the following facts: female(leyla). male(omar). female(nour). male(khaled). female(meriam). male(ali). female(zahra). • Now, let’s define the relation mother: For all X and Y X is the mother of Y if X is female and X is parent of Y.

  23. Defining Relations By Rules • The corresponding Prolog rule is: Mother(X,Y):-female (X) , parent(X,Y). • Head (conclusion part): mother (X,Y) • Body (condition part): female (X), parent(X,Y) • ‘,’ : to express conjunction (AND operator).

  24. Defining Relations By Rules • Nodes correspond to objects: arguments of relations. • Arcs between nodes correspond to binary relations. Arcs are oriented so as to point from the first to the second argument. • Unary relations are represented by marking the corresponding node by the name of the relation. X X X offspring parent mother parent parent grandparent Y Y Y parent Z

  25. Defining Relations By Rules • Question: define the relation sister • For any X and Y • X is a sister of Y if • Both X and Y have the same parent • X is a female • sister(X,Y):- female(X), parent(Z,X), parent(Z,Y). Z parent parent X Y sister

  26. Defining Relations By Rules • Let’s ask the question: • is meriam sister of khaled? • ?-sister(meriam,khaled). • Another question: who is khaled’s sister? • ?-sister(X,khaled). • Think about ?-sister(X,meriam).

  27. To summarize • Prolog programs can be extended by simply adding new clauses. • Prolog clauses are of three types: facts, rules and questions. • Facts declare things that are always, unconditionally, true. • Rules declare things that are true depending on a given condition. • By means of questions the user can ask the program what things are true. • Prolog clauses consist of the head and the body. The body is a list of goals separated by commas. Commas are understood as conjunctions. • Facts are clauses that have a head and the empty body. Questions have only the body. Rules have a head and a body. • Variables are instantiated when the system answers questions. • Variables are assumed to be universally quantified (for all).

  28. Defining Relations By Rules • Recursive rules Let’s define the relation predecessor. First possibility For all X and Z X is a predecessor of Z if X is a parent of Z. Second possibility For all X and Z X is a predecessor of Z if X is a parent of Y and Y is a parent of Z.

  29. Defining Relations By Rules • Recursive rules • More general definition: • For all X and Z • X is a predecessor of Z • If there exits a Y such that • X is a parent of Y • Y is a predecessor of Z • Corresponding Prolog clause predecessor (X,Z):- parent (X,Y), predecessor(Y,Z).

  30. Defining Relations By Rules • Complete program for predecessor relation: predecessor (X,Z):- parent (X,Z). predecessor (X,Z):- parent (X,Y), predecessor(Y,Z). • This is a recursive definition of the relation predecessor. • Question: who are ali’s successors?

  31. Lists in Prolog • Prolog allows manipulation of lists. • Syntax: a list always starts and ends with square brackets, and each of the items they contain is separated by a comma. e.g. [first,second,third] • Prolog also has a special facility: • Split the first part of the list (called the head) away from the rest of the list (known as the tail). • Place a special symbol | (pronounced 'bar') in the list to distinguish between the first item in the list and the remaining list. • For example, consider the following. [first,second,third] = [X|Y]where X = first and Y=[second,third] • [ ] /* this is a special list, it is called the empty list because it contains nothing */

  32. Lists in Prolog • Now lets consider some comparisons of lists: • [a,b,c] unifies with [Head|Tail] resulting in Head=a and Tail=[b,c] • [a] unifies with [H|T] resulting in H=a and T=[] • [a,b,c] unifies with [a|T] resulting in T=[b,c] • [a,b,c] doesn't unify with [b|T] • [] doesn't unify with [H|T] • [] unifies with []. Two empty lists always match

  33. Lists in Prolog Consider the following fact. p([H|T], H, T). Lets see what happens when we ask some simple queries. ?- p([a,b,c], X, Y). X=a Y=[b,c] Yes ?- p([a], X, Y). X=a Y=[] Yes ?- p([], X, Y). no

  34. Conclusion • Clauses are statements about what is true about a problem, instead of instructions how to accomplish the solution. • The Prolog system uses the clauses to work out how to accomplish the solution by searching through the space of possible solutions. • Not all problems have pure declarative specifications. Sometimes extralogical statements are needed.

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