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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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Chapter 7

King Saud University

College of Computer and Information Sciences

Information Technology Department

IT422 - Intelligent systems

Chapter 7

Part 2

Introduction to Prolog



  • 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.



  • 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



  • 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.



  • Prolog basic concepts by an example:

  • Let’s consider the Parent relation








Defining relations by facts

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.

Using prolog program

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

Using prolog program1

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

Using prolog program2

Using Prolog Program

  • Question: who are omar’s children?

    In prolog ?- parent(omar,X).

    Answer: X= meriam

    X= khaled


  • 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;

Using prolog program3

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;

Using prolog program4

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 ?


What can we conclude from this example

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.

Data objects in prolog

Data objects in Prolog

Prolog syntax

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.

Prolog syntax1

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’…

Prolog syntax2

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.

Prolog syntax3

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.

Prolog syntax4

Prolog Syntax

  • Structures



1 may 2007

  • point pointpoint

  • Date(1,may,2007)

3 1 4 3 6 0




Defining relations by rules

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

Defining relations by rules1

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

Defining relations by rules2

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)

Defining relations by rules3

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).


  • 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.

Defining relations by rules4

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).

Defining relations by rules5

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.















Defining relations by rules6

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).







Defining relations by rules7

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).

To summarize

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).

Defining relations by rules8

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.

Defining relations by rules9

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),


Defining relations by rules10

Defining Relations By Rules

  • Complete program for predecessor relation:

    predecessor (X,Z):-

    parent (X,Z).

    predecessor (X,Z):-

    parent (X,Y),


  • This is a recursive definition of the relation predecessor.

  • Question: who are ali’s successors?

Lists in prolog

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 */

Lists in prolog1

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

Lists in prolog2

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]


?- p([a], X, Y).

X=a Y=[]


?- p([], X, Y).




  • 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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