Prolog is a logic programming language well-suited for problems involving structured objects and relations. The document discusses how Prolog represents relations through facts and rules. Facts unconditionally declare true instances of a relation, like "parent(tom, bob)". Rules specify conclusions that are true if conditions are met, written as "conclusion :- conditions". Prolog can then answer questions by pattern matching or recursively applying rules to facts.

1. An Overview of Prolog
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2. What is Prolog
 Prolog is a powerful language for AI and non-
numerical programming
 Stands for programming in logic
 Centered around a small set of basic mechanisms,
including:
 Pattern matching
 Tree-based data structuring
 Automatic back tracking
 Well suited for problems that involves structured
objects and relations between them.
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3. Chapter One: Introduction to Prolog
1. Defining relations by facts
2. Defining relations by rules
3. Recursive rules
4. How Prolog answers questions
5. Declarative and procedural meaning of programs
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4. Chapter one:
1. Defining relations by facts
2. Defining relations by rules
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5. 1.1 Defining relations by facts
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Example
The fact that tom is a parent of bob
parent(tom, bob).
the name of a relation argument1 argument2
Fact clause

6. 1.1 Defining relations by facts
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 The family tree is defined by the following Prolog
program:
parent(pam, bob)
parent(tom, bob)
parent(tom, liz)
parent(bob, ann)
parent(bob, pat)
parent(pat, jim)
This program consists of six clauses.
 Each clause declares one fact about parent
relation (particular instance of the parent relation)
* a relation is the set of all its instances

7. 1.1 Defining relations by facts
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When the program communicated to Prolog system,
Prolog can be posed some questions about the
parent relation:
Is bob a parent of pat?
?- parent(bob, pat)
Prolog answer: True
?- parent(liz, pat)
Prolog answer: No solutions
?- parent(tom, pat)
Prolog answer: No solutions
tom
bob
ann
pat jim
liz
pam

8. 1.1 Defining relations by facts
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Who is liz’s parent?
?- parent(X, liz)
Prolog answer: X = tom
Who are bob’s children?
?- parent(bob, X)
Prolog answer:
X = ann.
X = pat.
tom
bob
ann
pat jim
liz
pam

9. 1.1 Defining relations by facts
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Find X and Y such that X is a parent of Y.
?- parent (X, Y).
Prolog answers:
X = pam.
Y = bob.
X = tom.
Y = bob.
X = tom.
Y = liz.
X = bob.
Y = ann.
X = bob.
Y = pat.
X = pat.
Y = jim.
tom
bob
ann
pat jim
liz
pam

10. 1.1 Defining relations by facts
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Who is a grandparent of jim?
Who is the parent of jim? Assume that this is Y
Who is the parent of Y? Assume that this is X
?- parent(Y, jim), parent (X, Y)
Prolog answer: X = bob
Y = pat
• Changing the order of the requirements will affect the
result.
?- parent(X, jim), parent (Y, X)
Prolog answer: X = pat.
Y = bob.
?- parent(X, jim), parent (X, Y)
Prolog answer: X = pat.
Y = jim.
√
x
x

11. 1.1 Defining relations by facts
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Do ann and pat have a common parent?
Who is a parent X of ann?
Is X a parent of pat?
?- parent (X, ann), parent(X, pat)
Prolog answer: X = bob
tom
bob
ann
pat jim
liz
pam

12. 1.2 Defining relations by rules
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 We can add the information on the sex of the people
that occur in the parent relation:
female(pam).
male(tom).
male(bob).
female(liz).
female(pat).
female(ann).
male(jim).
male and female are unary relations, whereas
parent is a binary relation.
Gender(pam, female).
Gender(tom, male).
Gender(bob, male).

13. 1.2 Defining relations by rules
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Let us introduce the offspring relation (inverse of
parent)
offspring(liz, tom).
offspring(bob, tom).
...
The logical statement is:
For all X and Y,
Y is an offspring of X if
X is a parent of Y
offspring(Y, X) :- parent(X, Y).
Rule clause
Fact
caluses

14. 1.2 Defining relations by rules
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There is an important difference between facts and
rules:
 Facts is something that is always, unconditionally,
true
parent(tom, liz).
 Rules specify things that are true if some condition
is satisfied. Rules have:
 Condition part (right-hand side) = body
 Conclusion part (left-hand side) = head
offspring(Y, X) :- parent(X, Y).
head body

15. 1.2 Defining relations by rules
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Questions
 Is liz an offspring of tom?
?- offspring(liz, tom).
Prolog answer: True
How Prolog answer this question using the rule:
Offspring(Y, X) :- parent(X, Y).
Prolog answer: True

16. 1.2 Defining relations by rules
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 How to express:
 Mother relation
 Grandparent relation
 Sister relation
in Prolog?

17. Important Points
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