344-302...

344-302

การเขี�ยนโปรแกรมเชิ�งตรรกะและภาษาโพรล�อก(Logic

Programming and Prolog)

ดร.วิ�ภาดา เวิทย�ประสิ�ทธิ์�� ภาควิ�ชิาวิ�ทยาการคอมพ�วิเตอร� คณะวิ�ทยาศาสิตร�

มหาวิ�ทยาล$ยสิงขีลานคร�นทร� ห%องท&างาน : CS 320 โทรศ$พท� :

-074288596

E-mail : wwettayaprasit@yahoo.comWebsite :

http://www.cs.psu.ac.th/wiphada

Chapter 1 2344-302 LP and Prolog

วั�ตถุ�ประสงค์ 1. ให้�นั�กศึ�กษามี�ค์วัามีร� �ค์วัามีเข้�าใจเก��ยวัก�บการเข้�ยนัโปรแกรมีเชิ#ง

ตรรกะ 2. ให้�นั�กศึ�กษาสามีารถุเข้�ยนัโปรแกรมีภาษาโพรล็'อกได้�วิ�ธิ์�การเร�ยนการสิอน : การบรรยาย ปฏิ#บ�ต#การการวิ$ดผล : Assignment 25%

สอบกล็างภาค์ 35%สอบปล็ายภาค์ 40%

เวิลาเร�ยน : จั$นทร� 11-12 ห%อง วิท3ศ*กร� 11-12 ห%อง วิท3

ศ*กร� 13-15 ห%อง CS105 (LAB)

Chapter 1 3344-302 LP and Prolog

Chapter 1 : Introduction to LogicChapter 2 : Syntax and Meaning of Prolog ProgramsChapter 3 : Input and OutputChapter 4 : Knowledge RepresentationChapter 5 : Expert SystemChapter 6 : Controlling BacktrackingChapter 7 : Lists Operator Chapter 8 : Arithmetic and Program Examples

เนั,-อห้าวั#ชิา

Chapter 1 4344-302 LP and Prolog

PROLOG Programming for Artificial Intelligence, Second Edition, Ivan Bratko, Addison-Wesley, Pulishing, 1990.Prolog : A Relational language and its Applications, John Malpas, Prentice-Hall, Inc. 1987.Expert Systems and Applied Artificial Intelligence, Efraim Turban, Macmillan Publishing Company, 1992.

เอกสิารอ%างอ�ง

Chapter 1

Introduction

• Propositional logic Formal Logic

Predicate Logic Predicate Calculus Symbolic Logic Logic Programming

Content

Chapter 1 7344-302 LP and Prolog

A statement that affirms or denies something.

Proposition

Chapter 1 8344-302 LP and Prolog

Proposition : a logical statement that may or may not be true.

objectrelationships of objects

A = I like banana. trueB = I like orange. falseC = I like mango. trueA and B = I like banana and orange. false

Proposition

Chapter 1 9344-302 LP and Prolog

All men are mortal Socrates is a man

Therefore, Socrates is mortal into propositional logic yieldsA

B C ( means "therefore ").

Propositional Logic

Chapter 1 10344-302 LP and Prolog

Propositional expression

implicationa b ~a v b~a b a V b

equivalencea b (a & b) v (~a & ~b)

tautologies : always truea v ~a

contradiction : always falseb & ~b

Chapter 1 11344-302 LP and Prolog

Propositional expression

contrapositive law

a b ~b ~a

Chapter 1 12344-302 LP and Prolog

A B C : propositions1. property of and, or

A and True = AA and False = FalseA or True = TrueA or False = A

2. property of negationA and ~A = FalseA or ~A = True

Proposition expression

Chapter 1 13344-302 LP and Prolog

3. commutative law (กฎการสิล$บท�-)A and B = B and AA or B = B or A

4. associative law (กฎการเปล�-ยนกล*.ม)A and (B and C) = (A and B) and CA or (B or C) = (A or B) or C

5. distributive law (กฎการแจักแจัง)A and (B or C) = (A and B) or (A and C)A or (B and C) = (A or B) and (A or C)

Proposition expression

Chapter 1 14344-302 LP and Prolog

6. de morgan’s lawsnot (A and B) = not A or not B not (A or B) = not A and not B

7. inference rule (กฎการอน*มาน) chain rule modus ponens

1 A B 1 A

2 B C 2 A BA C B

Proposition expression

Chapter 1 15344-302 LP and Prolog

Chain rule

(1) All California are American. เห้ต�(2) All American are Car-Drivers. เห้ต�(3) All California are Car-Drivers. ผล็

C AA DC D

Chapter 1 16344-302 LP and Prolog

Modus Ponens

If P implies Q, and P is true, then Q is true.

Chapter 1 17344-302 LP and Prolog

Transitive

(1) All baseball player are gum-chewers. เห้ต�(2) Some baseball players are from Boston. เห้ต�(3) Some (people) from Boston are gum-chewers. ผล็

21

Chapter 1 18344-302 LP and Prolog

any logical system that abstracts the form of statements away from their content in order to establish abstract criteria of consistency and validity

Formal Logic

Chapter 1 19344-302 LP and Prolog

Formal Logic

Logic (ตรรก): true, false truth table : and, or, not, xor, implies, if and only if

A B A and B A or B A xor B AB AB ~A

T T T T F T T FT F F T T F F FF T F T T T F TF F F F F T T T

Formal Logic : use to describe propositions

check proposition for validation

Chapter 1 20344-302 LP and Prolog

Name Symbol Example Meaning Precedencenegation ~ ~a not a 1conjunction & a & b a and b 2disjunction V a v b a or b 2equivalence a b a is equivalent to b 2implication a b a implies b (if a then b) 3

double negation : ~ ~ a = a compound propositions

a & b ca & ~b d : (a & (~b)) d

well-formed formula (wff) : a complex formula that includes logical connectives

Formal Logic

Chapter 1 21344-302 LP and Prolog

predicate logic or First-order logic (FOL) is a language in symbolic science,

which is used by mathematicians, philos ophers, linguists, and computer scientist

s. FOL is a system of deduction extending

propositional logic by the ability to express relations betwe

en individuals (e.g. people, numbers, an d "things") more generally.

Predicate Logic

Chapter 1 22344-302 LP and Prolog

x (Man(x ) → Mortal(x ))Man(Socrates ) Mortal(Socrates)

Predicate Logic

Chapter 1 23344-302 LP and Prolog

constants : a symbol that represent an object.manjohn

variables : a symbol that can represent different objects at different times

man(X) . (ต�วัอ�กษรต�วัให้ญ่0) compound term 1. functor :function symbol that name the relation2. an ordered list of parameters

man(john) like(bob,steak)

Predicate Logic

Chapter 1 24344-302 LP and Prolog

variable can be appear in propositions using

quantifiers (ต�วับ0งปร#มีาณ). Name Example Meaning

universal XP For all X, P is trueexistential XP There exists a value of X

such that P is true. quantifiers have highest precedence than any of the operators

Predicate Logic

Chapter 1 25344-302 LP and Prolog

Traditional Logic

All S is P. No S is P. ~ Some S is P. Some S is not P. ~

All baseball player are gum-chewers.Some taxi-driver are not aggressive.

X(woman(X) human(X))X(mother(mary,X) & male(X))

Chapter 1 26344-302 LP and Prolog

Quantifiers

p, q : predicates X, Y : variables~Xp(X) = X~p(X)~Xp(X) = X~p(X)Xp(X) = Yp(Y) Xp(X) = Yp(Y) X(p(X) & q(Y)) = Yp(Y) & Yq(Y)X(p(X) & q(Y)) = Yp(Y) & Yq(Y)

Chapter 1 27344-302 LP and Prolog

Predicate calculus

The branch of symbolic logic that deals not only with relations between propositions as a

whole but also with their internal structure, e specially the relation between subject and pr

edicate. Symbols are used to represent the s ubject and predicate of the proposition, and t

he existential or universal quantifier is used t o denote whether the proposition is universal or particular in its application.

Chapter 1 28344-302 LP and Prolog

Predicate calculus

a system of symbolic logic that represents individuals and predicates and quantification over individuals (as well as the relations between propositions )

Chapter 1 29344-302 LP and Prolog

Predicate calculus

If it is not rain tomorrow, Tom will go to the mountains.~weather(rain,tomorrow) go(tom,mountain)

Emma is a Doberman and a good dog.gooddog(emma) & isa(emma,doberman)

Chapter 1 30344-302 LP and Prolog

Predicate calculus

All basketball player are tall.X(basketball_player(X) tall(X))

Some people like wine.X(person(X) & like(X,wine))

Nobody likes taxes ~Xlike(X,taxes)

Chapter 1 31344-302 LP and Prolog

a

c

d

b

A blocks world

Chapter 1 32344-302 LP and Prolog

A blocks world

on(c,a). on(b,d).ontable(a).ontable(d).clear(b).clear(c). hand_empty.

a

c

d

b

Chapter 1 33344-302 LP and Prolog

A blocks world

a block is clear :

X (~ Y on(Y,X) clear(X)).

pick up X and putdown X on Y :

XY ((hand_empty & clear(X) & clear(Y)

pick_up(X) & put_down(X,Y)) stack(X,Y))

ac

db

Chapter 1 34344-302 LP and Prolog

vertebrate

bird

bluebirdsmall

features flies

blue

ISA

ISA

hasproperty

hascolor

hascovering

hassize

Semantic network

Chapter 1 35344-302 LP and Prolog

Predicate Calculusvertebrate

bird

bluebirdsmall

features flies

blue

ISA

ISA

hasproperty

hascolor

hascovering

hassize

hassize(bluebird, small)hascovering(bird,features)hascolor(bluebird,blue)hadproperty(bird,flies)isa(bluebird,bird)isa(bird,vertebrate)

Semantic Network

Predicate Calculus

Chapter 1 36344-302 LP and Prolog

Predicate calculus

knows(mary, bob)knows(sam, bob)knows(sam, petricia).

Who knows bob?Who knows bob and petricia?Does mary know anybody?

Chapter 1 37344-302 LP and Prolog

Predicate calculus

Facts:father(bill, daniel)father(bill, kenneth)brother(daniel, kenneth)brother(john, bill)

Rule:uncle(U,N) :- brother(U,B), father(B,N)uncle(U,N) :- brother(U,B), mother(B,N)

U B

N

Chapter 1 38344-302 LP and Prolog

Facts:father(bill, daniel) father(bill, kenneth)brother(daniel, kenneth) brother(john, bill)

Rule:uncle(U,N) :- brother(U,B), father(B,N)

U B

N

john bill

daniel kenneth Predicate calculus

Chapter 1 39344-302 LP and Prolog

Predicate calculus

“george likes susie if george like kate.”likes(george, susie) :- likes(george, kate)“kate does not like wine.” not(likes(kate,wine))

Chapter 1 40344-302 LP and Prolog

Predicate calculus

Facts : likes(george,kate) likes(george,susie) likes(george,wine)

likes(susie,wine) likes(kate,beer) likes(kate,susie)

Rule : friend(X,Y) :- likes(X,Z), likes(Y,Z)

Chapter 1 41344-302 LP and Prolog

A treatment of formal logic in which a system of

symbols is used to represe nt quantities and relations

hips.

Symbolic Logic

Chapter 1 42344-302 LP and Prolog

express proposition.express the ......relationship between the prepositions.describe how new propositions can be inferred from other prepositions that are assumed to be true.EX : john is a man. man(john)

wichai is a man. man(wichai) EX : man(X)

Symbolic Logic

Chapter 1 43344-302 LP and Prolog

Logic Programming

B1 and … and Bn implies H treats the implications as

- goal reduction procedures to show/solve H,

show/solve B1 and … and Bn .

creating a program that enables the computer to reason logically

Chapter 1 44344-302 LP and Prolog

Logic Programming

Logic programming .....use a form of symbolic logic

Logic programming language .....language base on symbolic logic

Chapter 1 45344-302 LP and Prolog

Homework 1

I married a window (W) who has a grown-up daughter (D). My father (F) who visited us quite often, fell in love with my step-daughter and married her. Hence my father became my son-in-law and my step-daughter become my mother. Some months later, my wife gave birth to a son (S1), who became the brother–in-law of my father, as well as my uncle. The wife of my father, that is, my step-daughter, also had a son (S2).

Question 1. Is this statement true?

“I am my own grandfather.”

Question 2. Explain how to receive your solution.