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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 : [email protected] :

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 : 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


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


A statement that affirms or denies something.

Proposition


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


All men are mortal Socrates is a man

Therefore, Socrates is mortal into propositional logic yieldsA

B C ( means "therefore ").

Propositional Logic


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


Propositional expression

contrapositive law

a b ~b ~a


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


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)



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



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


Modus Ponens

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


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


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


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


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


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


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

Predicate Logic


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


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


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))


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)


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.


Predicate calculus

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


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)


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)


a

c

d

b

A blocks world


A blocks world

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

a

c

d

b


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


vertebrate

bird

bluebirdsmall

features flies

blue

ISA

ISA

hasproperty

hascolor

hascovering

hassize

Semantic network


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


Predicate calculus

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

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


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


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


Predicate calculus

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


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)


A treatment of formal logic in which a system of

symbols is used to represe nt quantities and relations

hips.

Symbolic Logic


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


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


Logic Programming

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

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


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.

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