Artificial Intelligence － Prolog Programming －

Artificial Intelligence

－ Prolog Programming －

Ryo HatanoJAIST

Oct 16, 2012

About this Lecture

• Today only• No report, no examination today

– But midterm examination contains some quiz about Prolog

• TA: Ryo Hatano, D1 student of Tojo [email protected]

• Lecture matelials:https://www.jaist.ac.jp/~s1220010/

2

mailto:[email protected]

https://www.jaist.ac.jp/~s1220010/

Objectives

• Study about the basic usage of Prolog– Understand the basics of logic programming

• Become able to study Prolog by yourself– Today, I’ll teach only introduction

3

4

Reference

• I. Bratko, Prolog Programming for Artificial Intelligence• Shapiro et al, The Art of Prolog• P. Blackburn et al, Learn Prolog Now!• S. Russell et al, Artificial Intelligence A Modern Approach

• I. Bratko, Prolog への入門• 古川康一他 , 帰納論理プログラミング• S. Russell 他 , エージェントアプローチ人工知能

You can find some books about Prolog in JAIST Library or online via Google.

( わかりやすい )

( 短くまとまっている )

(8 章が背景に詳しい )

(chap. 9 contains some background info)

(be available online)

(contains advanced topics)

(easy)

5

What is the Prolog ?

• PROgrammation en LOGique– Programming language which based on predicate logic– The implementation is a kind of automated proving system– It specializes in logical processing and knowledge

representation• It suitable for the problems to handle relation between some objects• Symbol processing is better

6

• There is a person in a room• He wants to catch a banana hanging from a ceiling • He have to find a way to the banana

Simple Planning System

Definition of predicates for solving

move(state(Before), command, state(After)).state(X, Y, BOX, Has).canget(state):- ←Recursion rule

The problem can solve using only these predicates ！

7

Monkey & Banana problem (details, for reference)

state(atdoor, onfloor, atwindow, hasnot)

state(atwindow, onbox, atwindow, hasnot)

state(P2’, onfloor, P2’, hasnot)

state(P2’, onbox, P2’, hasnot)

state(middle, onbox, middle, has)

walk(atdoor, P2)

push(atwindow, P2’)

climb

GraspP2’ = middle

state(P2, onfloor, atwindow, hasnot)

climb(onfloor, onbox)P2 = atwindow

state(atwindow, onfloor, atwindow, hasnot)Backtrack(onbox→onfloor)

Other backtracks are ommitted

Overview of the Prolog

• Using of the Prolog environment• start, stop, load, execution

• Many Syntaxes– Basics

• Data structure, operators and recursion• Evaluation process

– Advanced• list, cut, syntax sugar, user defined operator, extra logical predicates, set predicates, failure driven loop

8

Today’s Topics

and some samples

Overview of the Prolog (cont, for reference)

• Theoretical Backgrounds – History– Formal Semantics of Prolog– Warren Abstract Machine– Herbrand’s Theorem– Evaluation Algorithms

• Advanced topics – Meta programming (Higher order programming, Meta interpreter)– Grammar parsing with DCG (Definition Clauses Grammar)– Theorem proving and its application with user defined axiomatic

system– Other Logic programming (Inductive logic programming, Probabilistic

logic programming)– etc…

9

10

About the Prolog environment

• Implementation– SICStus Prolog – SWI Prolog– GNU Prolog

• Development environment– Prolog mode of Emacs– PDT of Eclipse– Text editor + Prolog interpreter

Not free, performance is good, but not easy to use

Free, easy to use, recommend

Note: some built-in libraries are not same

11

Basic Usage of the Prolog Environment

• Using interpreter– You can control the prolog system interactively– First we load the program first. Then input a query

after outputs of “?-”.

?- [sample_1e.pl].% sample_1e.pl compiled 0.00 sec, 1,004 bytes?- foo(bar).true.

?- foo(X).X = bar;X = baz

?- halt.

←load program by short notation

←query which input by user

←If other answer exists, input “;” then search next answer

←load then compile

Example

12

Basic usage of the Prolog Environment (cont.)

• Start– %prolog [-l] [filename]

• Exit– halt. – Ctrl + ‘d’

• Interrupt and termination– Ctrl + ‘c’ then ‘a’

• File load– chdir(‘dir_path’). Change the current directory (ex.‘c:\\test’)– consult[‘file_name’]. or [‘file_name’]. Execute the file load

• File reload– make. Reload the edited file

• Trace– trace. It shows all steps of evaluation. “notrace” is for exit.

In OS shell, -l is option for loading a prolog program

(See also: official manual)

13

Syntax of the Prolog program

• Arithmetic, Comparison, Substitution, User defined• Unification, Control of backtrack• Comment

Operators+

Data structuresClauses

Head :- Body.

Predicate(Term, Term, …, Term)

Variable Constant Function

+ Some technics (ex. Recursion)

14

Comment

• One line comment– From “%” to end of the line

• Multi line comment– From “/*” to “*/”

Write the comment in the source code and give the readability.It is important habit in software engineering.

/* Multi line comment*/foo(bar) %comment to end of the line

Example in Prolog programs

15



Operators+


Head :- Body.




16

• Prolog program consists of the set of “Horn clauses”– Horn clause is clause which has zero or one positive conclusion

• Prolog system has 3 types of clauses– Facts, Rules, Goals(Query)

Clauses

These formula are expressed to the form of Prolog In the real program

m

n

AAAC

BAAA

21

21

Example in predicate logic

Program clauses

17

Example of Program

• Notation of clauses in PrologHead :- Body.

% All of these are horn clauses ！vegetable(carrot).fruit(apple).vegetable(tomato). fruit(tomato).

plant(X) :- vegetable(X).plant(X) :- fruit(X).plant(X) :- fruit(X), vegetable(X).

?- plant(X).

Program

Interpreter

← Goal clauses(query)

Rule clauses

Fact clauses

It is equivalent to implication operator “→” in predicate logic.But the direction is opposite (Body→Head).

Write the period end of the each clauses

18

Fact clauses

vegetable(carrot). %Carrot is a kind of vegetablesfruit(apple). %Apple is a kind of fruitsvegetable(tomato). fruit(tomato). %Tomato is a kind of fruits and vegetables

Example of Prolog program

Explain about predicates is later

C

Equivalent form of predicate formula

• The clause express about the facts– Clauses has empty body (condition) ⇔ Head (conclusion) only.– It contains predicates and constants which value is always true

Empty value means “true” in Prolog system

19

Rule clauses

plant(X) :- vegetable(X).plant(X) :- fruit(X).plant(X) :- vegetable(X), fruit(X).

Example in Prolog programs


• The clauses express about rules– The clause has head and non empty body– It offers the function of Modus Ponens like implication operator– True/False value is depends on the contents of the body

BAAA n 21

Comma “,” means “and” condition.Semi colon “;” means “or” condition.

If there are some same heads of fact and rule clauses, it means “or” condition

Important notations are“ ．” , “ ，” and “:-”.

20

Goal clauses

?- vegetable(carrot).true.

Example in interpreter (“Yes/No” type of query)


• The clause express about query– The clause has only body– It consists of at least one goal– There are 2 types of queries

• Yes/No type, What type

←Query which ask the fact exists←System answers Yes or No

Example in interpreter (“What” type of query)

mAAA 21

Prolog system tries to find the answerof this arrow.

?- vegetable(X).X = carrot.

←Query which contains valiable←System answers the value of variable　 If the answer doesn’t exists, system answers error.

21



Operators+


Head :- Body.




22

Data structures

• All data objects treats as “term” in Prolog system• There are 3 types of terms

– Constant– Variable– Function (= It is the complex data structure which

consists of some elements)

23

Atoms

• There are 3 types of atoms– Character string which starts with lower case or

number– Special character string +, -, *, /, <, >, =, :, ., &, _, ~– Quoted string

←This is exceptional case. It depends on environment

carrot.miss_mary.1234.======>.‘Mr. Tom’.日本語の定数 .

←If you need constants which starts with upper case, “‘” is suitable←Some atoms already used by system such as “:-”

Example of constants

There are some special constants such as “true”, “end_of_file”.It depends on environment.

24

Variables

• There are 2 types of variables– Normal variables which starts with upper case or

under score– Anonymous variables which only express in under

score• Temporary name of variables which appears only one time in

the clause• When it appear, it allocates different number by the system• Anonymous variables in query ignores when answer

←Anonymous variable excludes from evaluation

XResult_Arg1hoge( _ , X):- ...

Memory allocates when variables evaluated

Example of variables

25

Function

• Structural data which has some elements– Functor(Term1, Term2, …)– The naming rule is same as constants– The number of arguments calls “arity”– Function only refers other terms. It doesn’t have truth

value.

fruit(apple).plant(eatable(X)):- fruit(X).

Example of function

FunctorTerm

←Function and predicate are not same

Another name is “Compound term”

Predicate

Interpreter

?- plant(Func).Func = eatable(apple). ←It only directs other terms.

　 “ eatable(apple)” is not returns true.

26

Function (cont.)

• The data structure consider as tree– When all elements of some trees are same, they treat

as same data

Example of tree structure father(parent(X, Y), male(X))

father

parent male

X Y X

The root of tree calls to Principal functor

It depends on matching operation

27

Predicates

• Structural data which express relation between terms– Predicate symbol(Term1, Term2, …)– The naming rule is same as constants– Predicate symbols and terms constructs atomic

formula. It has truth value.

fruit(carrot).plant(X):- fruit(X).father(X):- parent(X, Y), male(X).

Example of predicates

Predicate symbol Terms

←It can contains some variables and constants.

28

Predicate (cont.)

• Distinguish the same predicate or not is by predicate symbol and arity– Short notation “predicate symbol/arity” has used

plant(X) :- vegetable(X).plant(Y) :- vegetable(Y), fruit(Y).

Example

Body and variable name are same, but each predicate Treat as same by plant/1

Note: The problem of distinguish predicates and tree structure of functions are not same.

29



Operators+


Head :- Body.




30

Arithmetic operator

• X + Y Addition• X - Y Subtraction• X * Y Multiplication• X / Y Division• X // Y Quotient of the natural number division• X mod Y Remainder of the natural number division• X is Y Y substitute to X (Y need to be bind)

?- Result is 2 + 3.Result = 5.

?- Result = 2 + 3.Result = 2 + 3

Example of arithmetic formula

In general, the arithmetic operator writes in infix notation

←it is not correct. “ ＝” is not arithmetic operation. So it is not evaluated.

←example of correct arithmetic operation and substitution

31

Comparison operators

• X > Y X is greater than Y• X < Y X is less than Y• X >= Y X is greater than or equal to Y• X =< Y X is less than or equal to Y• X =:= Y (Arithmetic formula) value of X and Y are

equals• X =\= Y (Arithmetic formula) value of X and Y are

not equals• X == Y Terms X and Y are equals• X \== Y Terms X and Y are not equals

32

Unification

• X = Y Matching X and Y, then if it matches true otherwise false

Matching of the Prolog is near to predicate logic

?-date(_Day, _Month, 2012) = date(9, april, _Year)._Day = 9_Month = april_Year = 2012

Example of unification

←it returns most general solution

33

Recursion

• The evaluation process calls itself– The rule which calls itself in the body– Usually, it uses as loop– The condition (address of variables and values) of each

predicates are saved on memoryWhen returns, the process take the values from memory

Example of recursion

factorial(0, 1).factorial(N, Result):-

N2 is N – 1,factorial(N2, Result2), Result is N * Result2.

←Stop condition. It needs to write above recursion.

Outline of the evaluation process

• Prolog system is a kind of automated theorem proving system

• It mainly consists of 4 technics– Depth first backward search– Unification– Backtracks– Closed world assumption

34

35

Depth first backward search

%Definition of factsfruit(apple).fruit(tomato). vegetable(tomato).

%Definition of rulesplant(X) :- fruit(X).plant(X) :- vegetable(X).

InterpreterSource code?- trace.true.

?- plant(X). Call: (6) plant(_G466) ? creep Call: (7) fruit(_G466) ? creep Exit: (7) fruit(apple) ? creep Exit: (6) plant(apple) ? creepX = apple

plant

fruit vegetableIt searches from query to defined factsby depth first

apple tomato tomato

Search tree

36

Unification



InterpreterSource code?- trace.true.

?- plant(X). Call: (6) plant(_G466) ? creep Call: (7) fruit(_G466) ? creep Exit: (7) fruit(apple) ? creep Exit: (6) plant(apple) ? creepX = apple

plant

fruit vegetableIt matches variables and terms.The scope is only same clause.

apple tomato tomato

X= apple

Search tree

37

Backtracks



InterpreterSource code

X = apple ; Redo: (7) fruit(_G466) ? creep Exit: (7) fruit(tomato) ? creep Exit: (6) plant(tomato) ? creepX = tomato

plant

fruit vegetable

It backs to former branch then search other answers.

apple tomato tomato

Search tree

38

Closed world assumption



InterpreterSource code

?- plant(X).X = apple ;X = tomato ;X = tomato ;X = tomato.

?-

plant

fruit vegetable

There are no more things substitute to X.In the prolog, there are assumption whichMeans not defining things are all false.Therefore, the result of this example is false.

apple tomato tomato

←Waiting for next query

It is called closed world assumption

No more choices

Search tree

Artificial Intelligence － Prolog Programming －

Documents

Transcript of Artificial Intelligence － Prolog Programming －