1. A I (Artificial Intelligence)
Professor I. J. Chung

2. AI (Artificial Intelligence)
Knowledge Representation
Logical representation :
Formal logic ( 1st order predicate calculus )
Inference rules and proof procedures
Prolog
Logic program as KBS / ES
Variety : parallel logic program.
Declarative representation.
cf: Ada ( spec. + body )
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3. AI (Artificial Intelligence)
Procedural representation :
set of instructions for solving problems.
If … then … else structure in RBS.
Production system.
Procedure for solving a goal in a problem domain.
Network representation :
Graph representation with nodes (objects) and arcs (representation).
Semantic network, conceptual dependencies, conceptual graphs.
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4. AI (Artificial Intelligence)
Structured representation :
Extension of network representation With a complex data structure consisting of slots and attached values.
Script, frame, objects
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Logical representation schemes :
English predicate calculus prolog
and ∧ ,
or ∨ ;
only if ← :=
not not
E.g. spot is a dog dog ( spot ).
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E.g.
1) Marcus was a person.
person ( marcus ).
2) Marcus was a pompeian.
pompeian (marcus ).
3) All pompeian were Romans.
∀x pompeian(x) → roman(x)
pompeian(x) ∨ roman (x)
4) Caesar was a ruler.
ruler(caesar)
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7. AI (Artificial Intelligence)
5) All Romans were either loyal to Ceasar or hated him.
∀x roman(x) → (loyalto(x,caesar) ∨ hate(x,caesar))
~roman(x) ∨ loyalto(x,caesar) ∨ hate(x,caesar) : clausal form
6) everyone is loyal to someone.
∀x ∃y loyalto (x,y)
loyalto (x,f(x))
Skolem function
7) People only try to assassinate rulers they are not loyal to
∀x ∀y : person(x) ∧ ruler(y) ∧ trytoassassinate(x,y)
→ ~loyalto (x,y)
~person(x) ∨ ~ruler(y) ∨ ~trytoassassinate(x,y) ∨ ~loyalto(x,y)
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8. AI (Artificial Intelligence)
8) Marcus tried to assassinate Caesar.
trytoassassinate(marcus,caesar)
Question : “Did Marcus hate Caesar?”
hate(marcus, caesar)
9) ~hate(marcus,caesar)
Robinson’s resolution (pf. By contradiction)
: negate the hypothesis to be proved & derive the
contradiction (empty clause)
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Refutation graph
: unsatisfiable set S={B(x),~B(x)∨C(x),~C(a)∨D(b),
~C(c)∨E(d),~D(x)∨~E(y)}
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11. AI (Artificial Intelligence)
Clausal form : well-formed formula of predicate calculus → clause form
(∀x){P(x) ⇒ {(∀y){P(y) ⇒ P(f(x,y))} ∧ ~(∀y){Q(x,y) ⇒ P(y)}}}
Eliminate implication sign A ⇒ B ⇔ ~A∨B
(∀x){~P(x)∨{(∀y){~P(y) ∨ P(f(x,y))} ∧ ~(∀y){~Q(x,y) ∨ P(y)}}}
Reduce scopes of negation signs
∴ (∀x){~P(x)∨{(∀y){~P(y)∨P(f(x,y))}∧(∃y){~{~Q(x,y)∨P(y)}}}}
(∀x){~P(x)∨{(∀y){~P(y)∨P(f(x,y))}∧(∃y){Q(x,y)∧~P(y)}}}
Standardize variables
(∀x){~P(x)∨{(∀y){~P(y)∨P(f(x,y))}∧(∃w){Q(x,w)∧~P(w)}}}
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Eliminate existential quantifier
(∀y) (∃x) P(x,y) (∀y) P(g(y),y)
Skolem function
∴(∀x){~P(x)∨{(∀y){~P(y)∨P(f(x,y))}∧{Q(x,g(x))∧~P(g(x))}}}
Convert to prenext form
: (∀x∀y){~P(x)∨{{~P(y)∨P(f(x,y))}∧{Q(x,g(x))∧~P(g(x))}}}
prefix
Put matrix in CNF
(∀x∀y){~P(x)∨~P(y)∨P(f(x,y))}
∧{~P(x)∨Q(x,g(x))}∧{~P(x)∨~P(g(x))}}
Eliminate the universal quantifier & ‘and’ sign
∴ ~P(x)∨~P(y)∨P(f(x,y))
~P(x)∨Q(x,g(x))
~P(x)∨~P(g(x))
matrix
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Logic program
Program paradigm where logical assertions are viewed as programs (Declarative Semantics)
ATP with formal knowledge representation defined over 1st order calculus.
Robinson’s resolution rule
Logic itself is a PL. (declarative semantics)
Prolog : verification, validation, proving them.
Produce call : -q1,q2,…,qk
~q1∨~q2∨…∨~qk
Logic : ‘what’ part control : ‘how’ part
cf.Ada
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Problem of logic program
Control problem : needs to provide a control information with extra-logical control features.
Negation problem : imperfect version of NAF
NAF : p.176 下
CWA : if ground atom A is not a logical consequence of program then infer ~A
E.g. student (Kim)
student (park)
since student (lee) is not a logical consequence., we infer ~student (lee)
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Prolog : logical assertions Horn clause
p:-q1,q2,…,qk ≡ p∨~q1∨~q2∨…∨~qk
List: [ ] rather than ( )
sum ([ ],0)
sum ([H|T],X) :- sum (T,Y),
add (H,Y,X) sum of elements of the list
add (X,Y,Z) :- Z is X+Y
max ([ ],0) :-
max ([H|T],X) :- max (T,N),
comp (H,N,X) max of the list
comp (X,Y,Z) :- X >= Y, Z is X
comp (X,Y,Z) :- Z is Y
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fibo (0,0) :- !
fibo (1,1) :- !
fibo (X,Y) :- X1 is X-1,
X2 is X-2,
fibo (X1,Y1),
fibo (X2,Y2),
y is Y1+Y2
power (m,o,1) :- !
power (m,n,c) :- n1 is n-1,
power (m,n1,c1), mn
c is c1*m
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append ([ ],X,X)
append ([X|XS],YS,[X|ZS]) :- append (XS,YS,ZS)
:- append ([a,b],[c],[a,b,c]) 2
:- append ([b],[c],[b,c])
:- append ([ ],[c],[c]) 1
(SLD-tree)
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SLD-tree for PU{G} via R
P: program, G:goal, R:rule
∀ node of the tree is a goal
root is G
:- A1,A2,…,Am,Ak Am :- Ba,…,Bq
:- (A1,…,Am-1,B1,…,Bq,Am+1,…,Ak) Θ
E.g.
p(x,z) :- q(x,y), p(y,z)
p(x,x)
q(a,b)
goal : :- p(x,b)
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19. AI (Artificial Intelligence)
AND-parallelism : computation rule in which pwc. Are evaluated concurrently.
OR-parallelism : parallelism in the search rule → several clauses can be fired an currently
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