Prolog
Programming in Logic
2
SWI-Prolog
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SWI-Prolog is a good, standard Prolog for Windows
and Linux
Can be installed on Macintosh with a little more effort
(requires X11 and Mac developer tools)
It's licensed under GPL, therefore free
Downloadable from:
http://www.swi-prolog.org/
3
Syllogisms
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“Prolog” is all about programming in logic.
Aristotle described syllogisms 2300 years ago
Sample syllogism:
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Socrates is a man.
All men are mortal.
Therefore, Socrates is mortal.
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Syllogisms are a form of logic. Can Prolog do them?
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Note: If a word or term is in red, you should learn and remember its
meaning
4
Forward and backward reasoning
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A syllogism gives two premises and a conclusion
Forward reasoning: Given some premises, ask “What can we
conclude?”
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Backward reasoning: Given some premises and a conjectured
conclusion, try to derive the conclusion from the premises
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Forward reasoning is inefficient when you are trying to get a particular
conclusion
You start from the conclusion and try to work backward to prove it
You use Prolog by asking it specific questions
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This is backward reasoning -- from (potential) conclusions to facts
5
Syllogisms in Prolog
Syllogism
Prolog
Socrates is a man.
man(socrates).
All men are mortal.
mortal(X) :- man(X).
Is Socrates mortal?
?- mortal(socrates).
6
Facts, rules, and queries
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Fact: Socrates is a man.
man(socrates).
Rule: All men are mortal.
mortal(X) :- man(X).
Query: Is Socrates mortal?
mortal(socrates).
Queries have the same form as facts
7
Variables and atoms
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Variables begin with a capital letter:
X, Socrates, _result
A variable can have a value
An atom is a value; it just stands for itself
Atoms do not begin with a capital letter:
x, socrates
8
Running Prolog I
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Create your “database” (program) in any editor
Save it as text only, with a .pl extension
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If you have Perl installed, you may have to use the .pro
extension instead
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Google “swi prolog file extension” for instructions
Here's the complete program:
man(socrates).
mortal(X) :- man(X).
9
Running Prolog II
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SWI-Prolog is interpreted and completely interactive
You may be able to run your program by double-clicking
your .pl file
Here are two ways you can run the interpreter:
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Double-click on the swipl file, or
If your PATH is set correctly, enter swipl at the command line
At the ?- prompt in the interpreter, enter:
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Then, ask your question at the prompt:
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?- consult('Complete path to your .pl file').
?- mortal(socrates).
Prolog responds:
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true.
10
Prolog is a theorem prover
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Prolog’s true. means “I can prove it”
Prolog’s false. really means “I can’t prove it”
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It does not mean “I can prove it is untrue.”
?- mortal(plato).
false.
This is the closed world assumption: the Prolog
program knows everything it needs to know
Prolog supplies values for variables when it can
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?- mortal(X).
X = socrates
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Given this (complete) program:
man(socrates).
What will Prolog respond if you
ask it
?- man(Aristotle).
0%
0%
te
s.
se
.
so
cr
a
=
Ar
is t
ot
le
tru
e.
0%
fa
l
A. true.
B. false.
C. Aristotle = socrates.
12
Given this program:
man(socrates).
mortal(X) :- man(X).
What will Prolog respond if you
ask it
?- mortal(Aristotle).
0%
0%
te
s.
se
.
so
cr
a
=
Ar
is t
ot
le
tru
e.
0%
fa
l
A. true.
B. false.
C. Aristotle = socrates.
13
Structures
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A structure consists of a name and zero or more
arguments.
Omit the parentheses if there are no arguments
Example structures:
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sunshine
man(socrates)
path(garden, south, sundial)
14
Base Clauses
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A base clause is just a structure, terminated with a
period.
A base clause represents a simple fact.
Example base clauses:
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debug_on.
loves(john, mary).
loves(mary, bill).
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What does this base clause mean?
loves(john, mary).
33%
33%
33%
an
ti
t.
.
sJ
oh
n.
w
ov
e
yo
u
yl
W
ha
t
ev
er
M
ar
Jo
h
n
lo
ve
sM
ar
y.
A. John loves Mary.
B. Mary loves John.
C. Whatever you want it
to mean.
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16
.
ov
e
ya
sB
..
i ll
.
33% 33%
ar
y
yl
M
ar
yl
ov
e
se
ve
M
ar
M
es
ov
ll l
Bi
A. Bill loves Mary.
B. Mary loves Bill.
C. Mary loves everybody
and everything.
33%
ry
bo
d
If we decide that
loves(john, mary).
means “John loves Mary,” then
what does
loves(mary, Bill).
mean?
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17
Nonbase Clauses
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A nonbase clause is a structure, a turnstile
(meaning “if”), and a list of structures.
Example nonbase clauses:
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:-
mortal(X) :- man(X).
mortal(X) :- woman(X).
happy(X) :- healthy(X), wealthy(X), wise(X).
The comma between structures means “and”
“X is happy if X is healthy, wealthy, and wise.”
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Predicates
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A predicate is a collection of clauses with the same
functor (name) and arity (number of arguments).
loves(john, mary).
loves(mary, bill).
loves(chuck, X) :- female(X), rich(X).
The scope of a variable (such as X) is the single
clause in which it occurs.
19
Programs
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In Prolog, a program is just a collection of predicates.
Predicates can be in any order.
Clauses within a predicate are used in the order in
which they occur.
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Atoms
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You can make an atom containing any characters at all by
enclosing it in single quotes:
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'C:\\My Documents\\examples.pl'
If you use double quotes, you will get a list of ASCII values
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In a quoted atom, a single quote must be doubled or backslashed:
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?- X = "Hello".
X = [72, 101, 108, 108, 111].
You probably don’t want this!
'Can''t, or won\'t?'
Backslashes in file names must also be doubled:
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'C:\\My Documents\\examples.pl'
Better yet, use forward slashes in paths; every OS, including Windows,
understands this
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Common problems
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Capitalization is meaningful!
No space is allowed between a functor and its
argument list:
man(socrates), not man (socrates).
Double quotes indicate a list of ASCII character
values, not a string
Don’t forget the period! (But if you do, you can put it
on the next line.)
22
Backtracking
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loves(chuck, X) :- female(X), rich(X).
female(jane).
female(mary).
rich(mary).
---------- Suppose we ask: loves(chuck, X).
 female(X) = female(jane), X = jane.
 rich(jane) fails.
 female(X) = female(mary), X = mary.
 rich(mary) succeeds.
23
Backtracking and Beads
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Each Prolog call is like a “bead” in a string of beads:
call
fail
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exit
redo
Each structure has four ports: call, exit, redo, fail
Exit ports connect to call ports;
fail ports connect to redo ports
24
Calls as nested beads
loves(chuck, X) :- female(X), rich(X).
loves(chuck, X)
call
fail
female(X)
rich(X)
exit
redo
25
Additional answers
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female(jane).
female(mary).
female(susan).
?- female(X).
X = jane ;
X = mary
Yes
female(X)
female(jane)
female(mary)
female(susan)
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33%
of
. ..
X
be
al
ill
n
w
tu
r
er
Pr
ol
og
w
ill
re
ns
w
ef
ir s
ta
Th
33%
.. .
X.
.
be
ill
er
w
ns
w
ef
ir s
ta
Th
A. The first answer will be
X = steven
B. The first answer will be
X = stan
C. Prolog will return a list of all
ancestors of isaac
33%
ist
Given this program:
father(stan, chester).
father(chester, david).
father(david, steven).
father(steven, isaac).
ancestor(X, Y) :- father(X, Y).
ancestor(X, Y) :- ancestor(X, Z),
father(Z, Y).
How will Prolog respond to:
?- ancestor(X, isaac).
20
27
Negation
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Since Prolog is programming in logic, you would expect it to
support negation (the “not” operator)
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It does (the operator is \+), but negation isn’t as useful as you might
think
Consider \+loves(chuck, X)
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You might think that this would instantiate X with a value that chuck
doesn’t love
Here’s what really happens:
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Prolog tries to find a solution (an X) for loves(chuck, X)
If loves(chuck, X) succeeds, \+loves(chuck, X) fails, so the
instantiation for X is discarded
If loves(chuck, X) fails, there is no instantiation for X, but
\+loves(chuck, X) succeeds
Hence, whether the test succeeds or fails, X doesn’t get a value
28
Readings
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A clause can be read declaratively (as a statement of
fact) or procedurally (as a list of things to try to do)
loves(chuck, X) :- female(X), rich(X).
Declarative reading: Chuck loves X if X is female and
rich.
Approximate procedural reading:
To find an X that Chuck loves:
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First try to find a female X (fail and backtrack if you can’t)
Given a particular value for X, try to show that X is rich (fail
and backtrack if you can’t)
Declarative readings are almost always preferred.
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The End
that that is is that that is not is not is not that so
That that is, is; that that is not, is not.
Is not that so?
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