First order logic
rushdishams
14,714 views
49 slides
Sep 30, 2013
Slide 1 of 49
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
About This Presentation
No description available for this slideshow.
Slide Content
Rushdi Shams, Dept of CSE, KUET, Bangladesh 1
Knowledge RepresentationKnowledge Representation
First Order LogicFirst Order Logic
Artificial IntelligenceArtificial Intelligence
Version 2.0Version 2.0
There are 10 types of people in this world- who understand binary There are 10 types of people in this world- who understand binary
and who do not understand binaryand who do not understand binary
Knowledge RepresentationKnowledge Representation
First Order LogicFirst Order Logic
Artificial IntelligenceArtificial Intelligence
Version 2.0Version 2.0
There are 10 types of people in this world- who understand binary There are 10 types of people in this world- who understand binary
and who do not understand binaryand who do not understand binary
Rushdi Shams, Dept of CSE, KUET, Bangladesh 2
Introduction
Propositional logic is declarative
Propositional logic allows partial/disjunctive/negated
information
(unlike most data structures and databases)
Meaning in propositional logic is context-independent
(unlike natural language, where meaning depends on context)
Propositional logic has very limited expressive power
(unlike natural language)
E.g., cannot say “if any student sits an exam they either pass or
fail”.
Propositional logic is compositional
(meaning of B ^ P is derived from meaning of B and of P)
Introduction
Propositional logic is declarative
Propositional logic allows partial/disjunctive/negated
information
(unlike most data structures and databases)
Meaning in propositional logic is context-independent
(unlike natural language, where meaning depends on context)
Propositional logic has very limited expressive power
(unlike natural language)
E.g., cannot say “if any student sits an exam they either pass or
fail”.
Propositional logic is compositional
(meaning of B ^ P is derived from meaning of B and of P)
Rushdi Shams, Dept of CSE, KUET, Bangladesh 3
Introduction
You see that we can convert the sentences into
propositional logic but it is difficult
Thus, we will use the foundation of propositional
logic and build a more expressive logic
Introduction
You see that we can convert the sentences into
propositional logic but it is difficult
Thus, we will use the foundation of propositional
logic and build a more expressive logic
Rushdi Shams, Dept of CSE, KUET, Bangladesh 4
Introduction
Whereas propositional logic assumes the world
contains facts,
first-order logic (like natural language) assumes the
world contains
Objects: people, houses, numbers, colors, baseball
games, wars, …
Relations: red, round, prime, brother of, bigger than,
part of, comes between, …
Functions: father of, best friend, one more than, plus, …
Introduction
Whereas propositional logic assumes the world
contains facts,
first-order logic (like natural language) assumes the
world contains
Objects: people, houses, numbers, colors, baseball
games, wars, …
Relations: red, round, prime, brother of, bigger than,
part of, comes between, …
Functions: father of, best friend, one more than, plus, …
Rushdi Shams, Dept of CSE, KUET, Bangladesh 5
Syntax of FOL: Basic Elements
Constants KingJohn, 2, NUS,...
Predicates Brother, >,...
Functions Sqrt, LeftLegOf,...
Variables x, y, a, b,...
ConnectivesØ, Þ, Ù, Ú, Û
Equality =
Quantifiers ", $
Syntax of FOL: Basic Elements
Constants KingJohn, 2, NUS,...
Predicates Brother, >,...
Functions Sqrt, LeftLegOf,...
Variables x, y, a, b,...
ConnectivesØ, Þ, Ù, Ú, Û
Equality =
Quantifiers ", $
Rushdi Shams, Dept of CSE, KUET, Bangladesh 6
Examples
King John and Richard the Lion heart are
brothers
Brother(KingJohn,RichardTheLionheart)
The length of left leg of Richard is greater than
the length of left leg of King John
> (Length(LeftLegOf(Richard)),
Length(LeftLegOf(KingJohn)))
Examples
King John and Richard the Lion heart are
brothers
Brother(KingJohn,RichardTheLionheart)
The length of left leg of Richard is greater than
the length of left leg of King John
> (Length(LeftLegOf(Richard)),
Length(LeftLegOf(KingJohn)))
Rushdi Shams, Dept of CSE, KUET, Bangladesh 7
Atomic Sentences
Atomic Sentences
Rushdi Shams, Dept of CSE, KUET, Bangladesh 8
Atomic Sentences
Atomic Sentences
Rushdi Shams, Dept of CSE, KUET, Bangladesh 9
Complex Sentences
Complex sentences are made from atomic sentences using
connectives:
ØS, S
1
Ù S
2
, S
1
Ú S
2
, S
1
Þ S
2
, S
1
Û
S
2
,
Example
Sibling(KingJohn,Richard) Þ Sibling(Richard,KingJohn)
Complex Sentences
Complex sentences are made from atomic sentences using
connectives:
ØS, S
1
Ù S
2
, S
1
Ú S
2
, S
1
Þ S
2
, S
1
Û
S
2
,
Example
Sibling(KingJohn,Richard) Þ Sibling(Richard,KingJohn)
Rushdi Shams, Dept of CSE, KUET, Bangladesh 10
Complex Sentences
Complex Sentences
Rushdi Shams, Dept of CSE, KUET, Bangladesh 11
FOL illustrated
Five objects-
1.Richard the Lionheart
2.Evil King John
3.Left leg of Richard
4.Left leg of John
5.The crown
FOL illustrated
Five objects-
1.Richard the Lionheart
2.Evil King John
3.Left leg of Richard
4.Left leg of John
5.The crown
Rushdi Shams, Dept of CSE, KUET, Bangladesh 12
FOL illustrated
Objects are related with
Relations
For example, King John and
Richard are related with
Brother relationship
This relationship can be
denoted by
(Richard,John),(John,Richard)
FOL illustrated
Objects are related with
Relations
For example, King John and
Richard are related with
Brother relationship
This relationship can be
denoted by
(Richard,John),(John,Richard)
Rushdi Shams, Dept of CSE, KUET, Bangladesh 13
FOL illustrated
Again, the crown and King
John are related with
OnHead Relationship-
OnHead (Crown,John)
Brother and OnHead are
binary relations as they
relate couple of objects.
FOL illustrated
Again, the crown and King
John are related with
OnHead Relationship-
OnHead (Crown,John)
Brother and OnHead are
binary relations as they
relate couple of objects.
Rushdi Shams, Dept of CSE, KUET, Bangladesh 14
FOL illustrated
Properties are relations that
are unary.
In this case, Person can be
such property acting upon
both Richard and John
Person (Richard)
Person (John)
Again, king can be acted
only upon John
King (John)
FOL illustrated
Properties are relations that
are unary.
In this case, Person can be
such property acting upon
both Richard and John
Person (Richard)
Person (John)
Again, king can be acted
only upon John
King (John)
Rushdi Shams, Dept of CSE, KUET, Bangladesh 15
FOL illustrated
Certain relationships are
best performed when
expressed as functions.
Means one object is related
with exactly one object.
Richard -> Richard’s left leg
John -> John’s left leg
FOL illustrated
Certain relationships are
best performed when
expressed as functions.
Means one object is related
with exactly one object.
Richard -> Richard’s left leg
John -> John’s left leg
Rushdi Shams, Dept of CSE, KUET, Bangladesh 16
Universal quantification
"<variables> <sentence>
"x P(x)
Translated into the English language, the expression is understood
as:
"For all x, P(x) holds",
"for each x, P(x) holds" or
“for every x, P(x) holds"
"All cars have wheels" could be transformed into the
propositional form, "x P(x)
P(x) is the predicate denoting: x has wheels, and
the universe of discourse is only populated by cars.
Universal quantification
"<variables> <sentence>
"x P(x)
Translated into the English language, the expression is understood
as:
"For all x, P(x) holds",
"for each x, P(x) holds" or
“for every x, P(x) holds"
"All cars have wheels" could be transformed into the
propositional form, "x P(x)
P(x) is the predicate denoting: x has wheels, and
the universe of discourse is only populated by cars.
Rushdi Shams, Dept of CSE, KUET, Bangladesh 17
Universal quantification
If all the elements in the universe of discourse can
be listed then the universal quantification "x P(x)
is equivalent to the conjunction:
P(x
1
)Ù P(x
2
)Ù P(x
3
) Ù ... Ù P(x
n
) .
For example, in the above example of "x P(x), if
we knew that there were only 4 cars in our
universe of discourse (c1, c2, c3 and c4) then we
could also translate the statement as:
P(c1) Ù P(c2) Ù P(c3) Ù P(c4)
Universal quantification
If all the elements in the universe of discourse can
be listed then the universal quantification "x P(x)
is equivalent to the conjunction:
P(x
1
)Ù P(x
2
)Ù P(x
3
) Ù ... Ù P(x
n
) .
For example, in the above example of "x P(x), if
we knew that there were only 4 cars in our
universe of discourse (c1, c2, c3 and c4) then we
could also translate the statement as:
P(c1) Ù P(c2) Ù P(c3) Ù P(c4)
Rushdi Shams, Dept of CSE, KUET, Bangladesh 18
Universal quantification
Remember, we had five
objects, let us replace them
with a variable x-
1.x ―›Richard the Lionheart
2.x ―› Evil King John
3.x ―› Left leg of Richard
4.x ―› Left leg of John
5.x ―› The crown
Universal quantification
Remember, we had five
objects, let us replace them
with a variable x-
1.x ―›Richard the Lionheart
2.x ―› Evil King John
3.x ―› Left leg of Richard
4.x ―› Left leg of John
5.x ―› The crown
Rushdi Shams, Dept of CSE, KUET, Bangladesh 19
Universal quantification
Now, for the quantified
sentence
"x King (x) Þ Person (x)
Richard is king Þ Richard is Person
John is king Þ John is person
Richard’s left leg is king Þ Richard’s
left leg is person
John’s left leg is king Þ John’s left leg
is person
The crown is king Þ the crown is
person
Universal quantification
Now, for the quantified
sentence
"x King (x) Þ Person (x)
Richard is king Þ Richard is Person
John is king Þ John is person
Richard’s left leg is king Þ Richard’s
left leg is person
John’s left leg is king Þ John’s left leg
is person
The crown is king Þ the crown is
person
Rushdi Shams, Dept of CSE, KUET, Bangladesh 20
Universal quantification
Richard is king Þ Richard is
Person
John is king Þ John is person
Richard’s left leg is king Þ
Richard’s left leg is person
John’s left leg is king Þ John’s left
leg is person
The crown is king Þ the crown is
person
Only the second
sentence is correct,
the rest is incorrect
Universal quantification
Richard is king Þ Richard is
Person
John is king Þ John is person
Richard’s left leg is king Þ
Richard’s left leg is person
John’s left leg is king Þ John’s left
leg is person
The crown is king Þ the crown is
person
Only the second
sentence is correct,
the rest is incorrect
Rushdi Shams, Dept of CSE, KUET, Bangladesh 21
Existential quantification
$ <variables> <sentence>
$ x P(x)
Translated into the English language, the expression is understood
as:
"There exists an x such that P(x)"
"There is at least one x such that P(x)"
"Someone loves you" could be transformed into the
propositional form, $ x P(x)
P(x) is the predicate meaning: x loves you,
The universe of discourse contains (but is not limited
to) all living creatures.
Existential quantification
$ <variables> <sentence>
$ x P(x)
Translated into the English language, the expression is understood
as:
"There exists an x such that P(x)"
"There is at least one x such that P(x)"
"Someone loves you" could be transformed into the
propositional form, $ x P(x)
P(x) is the predicate meaning: x loves you,
The universe of discourse contains (but is not limited
to) all living creatures.
Rushdi Shams, Dept of CSE, KUET, Bangladesh 22
Existential quantification
If all the elements in the universe of discourse can
be listed, then the existential quantification $ x
P(x) is equivalent to the disjunction:
P(x
1
)Ú P(x
2
) Ú P(x
3
) Ú ... Ú P(x
n
) .
For example, in the above example of $ x P(x), if
we knew that there were only 5 living creatures in
our universe of discourse (say: me, he, she, rex and
fluff), then we could also write the statement as:
P(me) Ú P(he) Ú P(she) Ú P(rex) Ú P(fluff)
Existential quantification
If all the elements in the universe of discourse can
be listed, then the existential quantification $ x
P(x) is equivalent to the disjunction:
P(x
1
)Ú P(x
2
) Ú P(x
3
) Ú ... Ú P(x
n
) .
For example, in the above example of $ x P(x), if
we knew that there were only 5 living creatures in
our universe of discourse (say: me, he, she, rex and
fluff), then we could also write the statement as:
P(me) Ú P(he) Ú P(she) Ú P(rex) Ú P(fluff)
Order of application of quantifiers
When more than one variables are quantified in a wff
such as $ y " x P( x, y ), they are applied from the
inside, that is, the one closest to the atomic formula is
applied first.
Thus $ y " x P( x, y ) reads $ y [" x P( x, y )], and
we say "there exists a y such that for every x, P( x,
y ) holds" or "for some y, P( x, y ) holds for every x".
Rushdi Shams, Dept of CSE, KUET, Bangladesh 23
When more than one variables are quantified in a wff
such as $ y " x P( x, y ), they are applied from the
inside, that is, the one closest to the atomic formula is
applied first.
Thus $ y " x P( x, y ) reads $ y [" x P( x, y )], and
we say "there exists a y such that for every x, P( x,
y ) holds" or "for some y, P( x, y ) holds for every x".
Rushdi Shams, Dept of CSE, KUET, Bangladesh 23
Order of application of quantifiers
The positions of the same type of quantifiers can be
switched without affecting the truth value as long as
there are no quantifiers of the other type between the
ones to be interchanged.
For example $ x $ y $ z P(x, y , z) is equivalent to
$ y $ x $ z P(x, y , z), $ z $ y $ x P(x, y , z),
etc.
It is the same for the universal quantifier.
Rushdi Shams, Dept of CSE, KUET, Bangladesh 24
The positions of the same type of quantifiers can be
switched without affecting the truth value as long as
there are no quantifiers of the other type between the
ones to be interchanged.
For example $ x $ y $ z P(x, y , z) is equivalent to
$ y $ x $ z P(x, y , z), $ z $ y $ x P(x, y , z),
etc.
It is the same for the universal quantifier.
Rushdi Shams, Dept of CSE, KUET, Bangladesh 24
Order of application of quantifiers
However, the positions of different types of
quantifiers can not be switched.
For example $ x " y P( x, y ) is not equivalent to $
y " x P( x, y ).
Rushdi Shams, Dept of CSE, KUET, Bangladesh 25
However, the positions of different types of
quantifiers can not be switched.
For example $ x " y P( x, y ) is not equivalent to $
y " x P( x, y ).
Rushdi Shams, Dept of CSE, KUET, Bangladesh 25
Rushdi Shams, Dept of CSE, KUET, Bangladesh 26
Order of application of quantifiers
" x $ y x < y
“for every number x, there is a number y that is greater than x ”
$ y " x x < y
“there is a number that is greater than every (any) number ”
Order of application of quantifiers
" x $ y x < y
“for every number x, there is a number y that is greater than x ”
$ y " x x < y
“there is a number that is greater than every (any) number ”
Rushdi Shams, Dept of CSE, KUET, Bangladesh 27
Properties of quantifiers
"x "y is the same as "y "x
$x $y is the same as $y $x
$x "y is not the same as "y $x
Properties of quantifiers
"x "y is the same as "y "x
$x $y is the same as $y $x
$x "y is not the same as "y $x
Rushdi Shams, Dept of CSE, KUET, Bangladesh 28
Properties of quantifiers
Quantifier duality: each can be expressed using the other
"x Likes(x,IceCream) is equivalent to
Ø$x ØLikes(x,IceCream)
$x Likes(x,Broccoli) is equivalent to
Ø"x ØLikes(x,Broccoli)
Properties of quantifiers
Quantifier duality: each can be expressed using the other
"x Likes(x,IceCream) is equivalent to
Ø$x ØLikes(x,IceCream)
$x Likes(x,Broccoli) is equivalent to
Ø"x ØLikes(x,Broccoli)
Rushdi Shams, Dept of CSE, KUET, Bangladesh 29
Properties of quantifiers
Equivalences-
1.$x P is equivalent to Ø"x ØP
2.Ø$x ØP is equivalent to "x P
3.$x ØP is equivalent to Ø"x P
4.Ø$x P is equivalent to "x ØP
Properties of quantifiers
Equivalences-
1.$x P is equivalent to Ø"x ØP
2.Ø$x ØP is equivalent to "x P
3.$x ØP is equivalent to Ø"x P
4.Ø$x P is equivalent to "x ØP
Rushdi Shams, Dept of CSE, KUET, Bangladesh 30
Rushdi Shams, Dept of CSE, KUET, Bangladesh 31
Example knowledge base
The law says that it is a crime for an
American to sell weapons to hostile nations.
The country Nono, an enemy of America,
has some missiles, and all of its missiles
were sold to it by Colonel West, who is
American.
Prove that Col. West is a criminal
Example knowledge base
The law says that it is a crime for an
American to sell weapons to hostile nations.
The country Nono, an enemy of America,
has some missiles, and all of its missiles
were sold to it by Colonel West, who is
American.
Prove that Col. West is a criminal
Rushdi Shams, Dept of CSE, KUET, Bangladesh 32
Example knowledge base
... it is a crime for an American to sell weapons to hostile nations:
American(x) Ù Weapon(y) Ù Sells(x,y,z) Ù Hostile(z) Þ Criminal(x)
Nono … has some missiles,
Owns(Nono,x)
Missile(x)
… all of its missiles were sold to it by Colonel West
Missile(x) Ù Owns(Nono,x) Þ Sells(West,x,Nono)
Missiles are weapons:
Missile(x) Þ Weapon(x)
An enemy of America counts as "hostile“:
Enemy(x,America) Þ Hostile(x)
West, who is American …
American(West)
The country Nono, an enemy of America …
Enemy(Nono,America)
Example knowledge base
... it is a crime for an American to sell weapons to hostile nations:
American(x) Ù Weapon(y) Ù Sells(x,y,z) Ù Hostile(z) Þ Criminal(x)
Nono … has some missiles,
Owns(Nono,x)
Missile(x)
… all of its missiles were sold to it by Colonel West
Missile(x) Ù Owns(Nono,x) Þ Sells(West,x,Nono)
Missiles are weapons:
Missile(x) Þ Weapon(x)
An enemy of America counts as "hostile“:
Enemy(x,America) Þ Hostile(x)
West, who is American …
American(West)
The country Nono, an enemy of America …
Enemy(Nono,America)
Rushdi Shams, Dept of CSE, KUET, Bangladesh 33
Forward Chaining
American(x) Ù Weapon(y) Ù Sells(x,y,z) Ù Hostile(z) Þ
Criminal(x)
Owns(Nono,x)
Missile(x)
Missile(x) Ù Owns(Nono,x) Þ Sells(West,x,Nono)
Missile(x) Þ Weapon(x)
Enemy(x,America) Þ Hostile(x)
American(West)
Enemy(Nono,America)
Forward Chaining
American(x) Ù Weapon(y) Ù Sells(x,y,z) Ù Hostile(z) Þ
Criminal(x)
Owns(Nono,x)
Missile(x)
Missile(x) Ù Owns(Nono,x) Þ Sells(West,x,Nono)
Missile(x) Þ Weapon(x)
Enemy(x,America) Þ Hostile(x)
American(West)
Enemy(Nono,America)
Rushdi Shams, Dept of CSE, KUET, Bangladesh 34
Forward Chaining
American(x) Ù Weapon(y) Ù Sells(x,y,z) Ù Hostile(z) Þ
Criminal(x)
Owns(Nono,x)
Missile(x)
Missile(x) Ù Owns(Nono,x) Þ Sells(West,x,Nono)
Missile(x) Þ Weapon(x)
Enemy(x,America) Þ Hostile(x)
American(West)
Enemy(Nono,America)
Forward Chaining
American(x) Ù Weapon(y) Ù Sells(x,y,z) Ù Hostile(z) Þ
Criminal(x)
Owns(Nono,x)
Missile(x)
Missile(x) Ù Owns(Nono,x) Þ Sells(West,x,Nono)
Missile(x) Þ Weapon(x)
Enemy(x,America) Þ Hostile(x)
American(West)
Enemy(Nono,America)
Rushdi Shams, Dept of CSE, KUET, Bangladesh 35
Forward Chaining
American(West) Ù Weapon(y) Ù Sells(x,y,z) Ù Hostile(z)
Þ Criminal(x)
Owns(Nono,x)
Missile(x)
Missile(x) Ù Owns(Nono,x) Þ Sells(West,x,Nono)
Missile(x) Þ Weapon(x)
Enemy(x,America) Þ Hostile(x)
American(West)
Enemy(Nono,America)
Forward Chaining
American(West) Ù Weapon(y) Ù Sells(x,y,z) Ù Hostile(z)
Þ Criminal(x)
Owns(Nono,x)
Missile(x)
Missile(x) Ù Owns(Nono,x) Þ Sells(West,x,Nono)
Missile(x) Þ Weapon(x)
Enemy(x,America) Þ Hostile(x)
American(West)
Enemy(Nono,America)
Rushdi Shams, Dept of CSE, KUET, Bangladesh 36
Forward Chaining
American(West) Ù Weapon(y) Ù Sells(West,y,z) Ù
Hostile(z) Þ Criminal(x)
Owns(Nono,x)
Missile(x)
Missile(x) Ù Owns(Nono,x) Þ Sells(West,x,Nono)
Missile(x) Þ Weapon(x)
Enemy(x,America) Þ Hostile(x)
American(West)
Enemy(Nono,America)
Forward Chaining
American(West) Ù Weapon(y) Ù Sells(West,y,z) Ù
Hostile(z) Þ Criminal(x)
Owns(Nono,x)
Missile(x)
Missile(x) Ù Owns(Nono,x) Þ Sells(West,x,Nono)
Missile(x) Þ Weapon(x)
Enemy(x,America) Þ Hostile(x)
American(West)
Enemy(Nono,America)
Rushdi Shams, Dept of CSE, KUET, Bangladesh 37
Forward Chaining
American(West) Ù Weapon(y) Ù Sells(West,y,z) Ù
Hostile(z) Þ Criminal(x)
Owns(Nono,x)
Missile(x)
Missile(x) Ù Owns(Nono,x) Þ Sells(West,x,Nono)
Missile(x) Þ Weapon(x)
Enemy(x,America) Þ Hostile(x)
American(West)
Enemy(Nono,America)
Forward Chaining
American(West) Ù Weapon(y) Ù Sells(West,y,z) Ù
Hostile(z) Þ Criminal(x)
Owns(Nono,x)
Missile(x)
Missile(x) Ù Owns(Nono,x) Þ Sells(West,x,Nono)
Missile(x) Þ Weapon(x)
Enemy(x,America) Þ Hostile(x)
American(West)
Enemy(Nono,America)
Rushdi Shams, Dept of CSE, KUET, Bangladesh 38
Forward Chaining
American(West) Ù Weapon(y) Ù Sells(West,y,z) Ù
Hostile(z) Þ Criminal(x)
Owns(Nono,x)
Missile(x)
Missile(x) Ù Owns(Nono,x) Þ Sells(West,x,Nono)
Missile(x) Þ Weapon(x)
Enemy(Nono,America) Þ Hostile(x)
American(West)
Enemy(Nono,America)
Forward Chaining
American(West) Ù Weapon(y) Ù Sells(West,y,z) Ù
Hostile(z) Þ Criminal(x)
Owns(Nono,x)
Missile(x)
Missile(x) Ù Owns(Nono,x) Þ Sells(West,x,Nono)
Missile(x) Þ Weapon(x)
Enemy(Nono,America) Þ Hostile(x)
American(West)
Enemy(Nono,America)
Rushdi Shams, Dept of CSE, KUET, Bangladesh 39
Forward Chaining
American(West) Ù Weapon(y) Ù Sells(West,y,z) Ù
Hostile(z) Þ Criminal(x)
Owns(Nono,x)
Missile(x)
Missile(x) Ù Owns(Nono,x) Þ Sells(West,x,Nono)
Missile(x) Þ Weapon(x)
Enemy(Nono,America) Þ Hostile(Nono)
American(West)
Enemy(Nono,America)
Forward Chaining
American(West) Ù Weapon(y) Ù Sells(West,y,z) Ù
Hostile(z) Þ Criminal(x)
Owns(Nono,x)
Missile(x)
Missile(x) Ù Owns(Nono,x) Þ Sells(West,x,Nono)
Missile(x) Þ Weapon(x)
Enemy(Nono,America) Þ Hostile(Nono)
American(West)
Enemy(Nono,America)
Rushdi Shams, Dept of CSE, KUET, Bangladesh 40
Forward Chaining
American(West) Ù Weapon(y) Ù Sells(West,y,z) Ù
Hostile(Nono) Þ Criminal(x)
Owns(Nono,x)
Missile(x)
Missile(x) Ù Owns(Nono,x) Þ Sells(West,x,Nono)
Missile(x) Þ Weapon(x)
Enemy(Nono,America) Þ Hostile(Nono)
American(West)
Enemy(Nono,America)
Forward Chaining
American(West) Ù Weapon(y) Ù Sells(West,y,z) Ù
Hostile(Nono) Þ Criminal(x)
Owns(Nono,x)
Missile(x)
Missile(x) Ù Owns(Nono,x) Þ Sells(West,x,Nono)
Missile(x) Þ Weapon(x)
Enemy(Nono,America) Þ Hostile(Nono)
American(West)
Enemy(Nono,America)
Rushdi Shams, Dept of CSE, KUET, Bangladesh 41
Backward Chaining
American(West) Ù Weapon(y) Ù Sells(West,y,z) Ù
Hostile(Nono) Þ Criminal(x)
Owns(Nono,x)
Missile(x)
Missile(x) Ù Owns(Nono,x) Þ Sells(West,x,Nono)
Missile(x) Þ Weapon(x)
Enemy(Nono,America) Þ Hostile(Nono)
American(West)
Enemy(Nono,America)
Backward Chaining
American(West) Ù Weapon(y) Ù Sells(West,y,z) Ù
Hostile(Nono) Þ Criminal(x)
Owns(Nono,x)
Missile(x)
Missile(x) Ù Owns(Nono,x) Þ Sells(West,x,Nono)
Missile(x) Þ Weapon(x)
Enemy(Nono,America) Þ Hostile(Nono)
American(West)
Enemy(Nono,America)
Rushdi Shams, Dept of CSE, KUET, Bangladesh 42
Backward Chaining
American(West) Ù Weapon(y) Ù Sells(West,y,z) Ù
Hostile(Nono) Þ Criminal(x)
Owns(Nono,x)
Missile(x)
Missile(x) Ù Owns(Nono,x) Þ Sells(West,x,Nono)
Missile(x) Þ Weapon(x)
Enemy(Nono,America) Þ Hostile(Nono)
American(West)
Enemy(Nono,America)
Backward Chaining
American(West) Ù Weapon(y) Ù Sells(West,y,z) Ù
Hostile(Nono) Þ Criminal(x)
Owns(Nono,x)
Missile(x)
Missile(x) Ù Owns(Nono,x) Þ Sells(West,x,Nono)
Missile(x) Þ Weapon(x)
Enemy(Nono,America) Þ Hostile(Nono)
American(West)
Enemy(Nono,America)
Rushdi Shams, Dept of CSE, KUET, Bangladesh 43
Backward Chaining
American(West) Ù Weapon(y) Ù Sells(West,y,z) Ù
Hostile(Nono) Þ Criminal(x)
Owns(Nono,x)
Missile(x)
Missile(x) Ù Owns(Nono,x) Þ Sells(West,x,Nono)
Missile(x) Þ Weapon(x)
Enemy(Nono,America) Þ Hostile(Nono)
American(West)
Enemy(Nono,America)
Backward Chaining
American(West) Ù Weapon(y) Ù Sells(West,y,z) Ù
Hostile(Nono) Þ Criminal(x)
Owns(Nono,x)
Missile(x)
Missile(x) Ù Owns(Nono,x) Þ Sells(West,x,Nono)
Missile(x) Þ Weapon(x)
Enemy(Nono,America) Þ Hostile(Nono)
American(West)
Enemy(Nono,America)
Rushdi Shams, Dept of CSE, KUET, Bangladesh 44
Backward Chaining
American(West) Ù Weapon(y) Ù Sells(West,y,z) Ù
Hostile(Nono) Þ Criminal(x)
Owns(Nono,x)
Missile(x)
Missile(x) Ù Owns(Nono,x) ÞSells(West,x,Nono)
Missile(x) Þ Weapon(x)
Enemy(Nono,America) Þ Hostile(Nono)
American(West)
Enemy(Nono,America)
Backward Chaining
American(West) Ù Weapon(y) Ù Sells(West,y,z) Ù
Hostile(Nono) Þ Criminal(x)
Owns(Nono,x)
Missile(x)
Missile(x) Ù Owns(Nono,x) ÞSells(West,x,Nono)
Missile(x) Þ Weapon(x)
Enemy(Nono,America) Þ Hostile(Nono)
American(West)
Enemy(Nono,America)
Rushdi Shams, Dept of CSE, KUET, Bangladesh 45
Backward Chaining
American(West) Ù Weapon(y) Ù Sells(West,y,z) Ù
Hostile(Nono) Þ Criminal(x)
Owns(Nono,x)
Missile(x)
Missile(x) Ù Owns(Nono,x) ÞSells(West,x,Nono)
Missile(x) Þ Weapon(x)
Enemy(Nono,America) Þ Hostile(Nono)
American(West)
Enemy(Nono,America)
Backward Chaining
American(West) Ù Weapon(y) Ù Sells(West,y,z) Ù
Hostile(Nono) Þ Criminal(x)
Owns(Nono,x)
Missile(x)
Missile(x) Ù Owns(Nono,x) ÞSells(West,x,Nono)
Missile(x) Þ Weapon(x)
Enemy(Nono,America) Þ Hostile(Nono)
American(West)
Enemy(Nono,America)
Rushdi Shams, Dept of CSE, KUET, Bangladesh 46
Backward Chaining
American(West) Ù Weapon(y) Ù Sells(West,y,Nono) Ù
Hostile(Nono) Þ Criminal(x)
Owns(Nono,x)
Missile(x)
Missile(x) Ù Owns(Nono,x) ÞSells(West,x,Nono)
Missile(x) Þ Weapon(x)
Enemy(Nono,America) Þ Hostile(Nono)
American(West)
Enemy(Nono,America)
Backward Chaining
American(West) Ù Weapon(y) Ù Sells(West,y,Nono) Ù
Hostile(Nono) Þ Criminal(x)
Owns(Nono,x)
Missile(x)
Missile(x) Ù Owns(Nono,x) ÞSells(West,x,Nono)
Missile(x) Þ Weapon(x)
Enemy(Nono,America) Þ Hostile(Nono)
American(West)
Enemy(Nono,America)
Rushdi Shams, Dept of CSE, KUET, Bangladesh 47
Backward Chaining
American(West) Ù Weapon(y) Ù Sells(West,y,Nono) Ù
Hostile(Nono) Þ Criminal(x)
Owns(Nono,x)
Missile(x)
Missile(x) Ù Owns(Nono,x) ÞSells(West,x,Nono)
Missile(x) Þ Weapon(x)
Enemy(Nono,America) Þ Hostile(Nono)
American(West)
Enemy(Nono,America)
Backward Chaining
American(West) Ù Weapon(y) Ù Sells(West,y,Nono) Ù
Hostile(Nono) Þ Criminal(x)
Owns(Nono,x)
Missile(x)
Missile(x) Ù Owns(Nono,x) ÞSells(West,x,Nono)
Missile(x) Þ Weapon(x)
Enemy(Nono,America) Þ Hostile(Nono)
American(West)
Enemy(Nono,America)
Rushdi Shams, Dept of CSE, KUET, Bangladesh 48
…& the Inference
American(West) Ù Weapon(y) Ù Sells(West,y,Nono) Ù
Hostile(Nono) Þ Criminal(West)
Owns(Nono,x)
Missile(x)
Missile(x) Ù Owns(Nono,x) ÞSells(West,x,Nono)
Missile(x) Þ Weapon(x)
Enemy(Nono,America) Þ Hostile(Nono)
American(West)
Enemy(Nono,America)
…& the Inference
American(West) Ù Weapon(y) Ù Sells(West,y,Nono) Ù
Hostile(Nono) Þ Criminal(West)
Owns(Nono,x)
Missile(x)
Missile(x) Ù Owns(Nono,x) ÞSells(West,x,Nono)
Missile(x) Þ Weapon(x)
Enemy(Nono,America) Þ Hostile(Nono)
American(West)
Enemy(Nono,America)
Rushdi Shams, Dept of CSE, KUET, Bangladesh 49
References
Artificial Intelligence: A Modern Approach (2
nd
Edition)
by Russell and Norvig Chapter 8
http://www.cs.odu.edu/~toida/nerzic/content/logic/pred_logic/quantification/quantification.html
References
Artificial Intelligence: A Modern Approach (2
nd
Edition)
by Russell and Norvig Chapter 8
http://www.cs.odu.edu/~toida/nerzic/content/logic/pred_logic/quantification/quantification.html
Categories
TechnologyDownload
Download Slideshow Get the original presentation fileQuick Actions
Statistics
- Views 14,714
- Slides 49
- Favorites 7
- Age 4449 days
Related Slideshows
11
8-top-ai-courses-for-customer-support-representatives-in-2025.pptx
JeroenErne2
51 views
10
7-essential-ai-courses-for-call-center-supervisors-in-2025.pptx
JeroenErne2
49 views
13
25-essential-ai-courses-for-user-support-specialists-in-2025.pptx
JeroenErne2
38 views
11
8-essential-ai-courses-for-insurance-customer-service-representatives-in-2025.pptx
JeroenErne2
38 views
21
Know for Certain
DaveSinNM
24 views
17
PPT OPD LES 3ertt4t4tqqqe23e3e3rq2qq232.pptx
novasedanayoga46
27 views