©agent technology, 2008, ai lab nju agent technology agent model and theory
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©Agent Technology, 2008, Ai Lab NJU
Agent Technology
Agent model and
theory
Nov., 2008©Gao Yang, Ai Lab NJU2
Agent model and theory
6.1 Logical Background– 6.1.1 Basic Concepts– 6.1.2 Propositional and Predicate Logic– 6.1.3 Modal Logic– 6.1.4 Dynamic Logic– 6.1.5 Temporal Logic
6.2 Cognitive Primitives– 6.2.1 Knowledge and Beliefs– 6.2.2 Desires and Goals– 6.2.3 Intentions
Nov., 2008©Gao Yang, Ai Lab NJU3
Chapter 4: Agent model and theory
– 6.2.4 Commitments– 6.2.5 Know-how
6.3 Belief Revision– 6.3.1 AGM Framework– 6.3.2 Epistemic entrenchment
6.4 Social Primitives– 6.4.1 Team and Organizational Structure– 6.4.2 Mutual Beliefs and Joint Intentions– 6.4.3 Social Commitments– 6.4.4 Group Know-how and Intentions
Nov., 2008©Gao Yang, Ai Lab NJU4
6.1 Logical Background
6.1.1 Basic Concepts– Why need formal method?
As internal specification languages to be used by the agent in its reasoning or action;
As external metalanguages to be used by the designer to specify, design, and verify certain behavioral properties of agents situated in a dynamic environment.
– Differents between these languages One would like to have the same logical language server
both of the above purpose. The internal language should be computationally efficie
nt. The external language should be more expressive.
Nov., 2008©Gao Yang, Ai Lab NJU5
6.1 Logical Background
6.1.1 Basic Concepts– Three aspects to logic
Well-formed formulas: some statements; Proof-theory: is also called the syntax; Model-theory: is also called the semantics.
– Purpose of the semantics
iM p
M p
Nov., 2008©Gao Yang, Ai Lab NJU6
6.1 Logical Background
6.1.2 Propositional and Predicate Logic– How to use this logic in agent
Is simplest Represent factual information, often about the agents’
environment.
– Example 6.1 The facts “it rains” and ‘road is wet”; Atomic propositions
– Rain– Wet-road
Implication that “if it rains, then the road is wet” can be captured by the propositional formula
– Rain -> wet-road
Nov., 2008©Gao Yang, Ai Lab NJU7
6.1 Logical Background
6.1.2 Propositional and Predicate Logic
– The language of propositional logic Assume a set is given atomic propositions;
SYN-1.
SYN-2.
– The formal model Let L identifies the set of atomic propositions that are
true.
SEM-1.
SEM-2.
SEM-3.
implies that pL
pL
, implies that ,p pp q L p q p L
0 iff ,where M L
0 0 0 iff and M p q M p M q
0 0 iff M p M p
0defM L
Nov., 2008©Gao Yang, Ai Lab NJU8
6.1 Logical Background
6.1.2 Propositional and Predicate Logic
– Imply is true if p is false irrespective of q
– Predicate logic Do not use predicate logic in the specification language.
Use it in metalanguage, which is used in semantic condi
tions.
Universal quantifier
Existential quantifier
p q
Nov., 2008©Gao Yang, Ai Lab NJU9
6.1 Logical Background
6.1.3 Modal Logic
– Objective To investigate different modes of truth, such as
possibly true and necessarily true.
In agents’ study, it is used to give meaning to concepts
such as belief and knowledge.
– Modal language Classical propositional logic is extended with two modal
operators: for possibility and for necessity.
SYN-3.
SYN-6.
ML
the rules for pL
implies that , p Mp L p p L
Nov., 2008©Gao Yang, Ai Lab NJU10
6.1 Logical Background
6.1.3 Modal Logic
– Example 6.2 “it is possible that it rains” as
“it is necessary that the sun rises in the east” as
– Model is the set of the worlds
gives the set of formulas true at a world
is an accessibility relation
SEM-6.
rain
sun rises in the east
1 , ,defM W L R W
: 2L W
R W W
1 iff ,where wM L w
Nov., 2008©Gao Yang, Ai Lab NJU11
6.1 Logical Background
SEM-5.
SEM-6.
SEM-6.
SEM-8.
– Algebric properties of the accessibility relation R is reflexive iff
R is serial iff
R is transitive iff
R is symmetric iff
R is euclidean iff
1 1 1 iff w w wM p q M p and M q
1 1 iff w wM p M p
1 1 iff : , &w wM p w R w w M p
1 1 iff : ,w wM p w R w w M p
: ,w w w R
: : ,w w w w R
1 2 1 2 2 1, : , ,w w w w R w w R
1 2 3 1 2 2 3 1 3, , : , & , ,w w w w w R w w R w w R
1 2 3 1 2 1 3 2 3, , : , & , ,w w w w w R w w R w w R
Nov., 2008©Gao Yang, Ai Lab NJU12
6.1 Logical Background
6.1.4 Dynamic Logic
– What is dynamic logic Can be thought of as the modal logic of action
The necessity and possibility of dynamic logic are
based upon the kinds of actions available
Can be used in a number of areas of DAI.
– Model Language and its sublanguage Sublanguage define action regular expressions
is a set of atomic action symbols
SYN-5.
SYN-6.
DL RL
RL
B
the rules for applied to p DL L
implies that RL B
Nov., 2008©Gao Yang, Ai Lab NJU13
6.1 Logical Background
SYN-6.
SYN-8.
SYN-9.
Notes:
– a;b means doing a and b in sequence.
– a+b means doing either a or b.
– p? is an action based on confirming the truth value of p
roposition p.
– a* means 0 or more (but finitely many) iterations of a.
– Example 6.3 “If q then a else b endif”
, implies that a;b, a+b , * R Ra b L a L
implies that ? D Rp L p L
and implies that a , R D Ra L p L p a p L
?; ?;q a q b
Nov., 2008©Gao Yang, Ai Lab NJU14
6.1 Logical Background
– Model Here W, L defined as model logic;
Is a transition relation.
RP-1.
RP-2.
RP-3.
RP-6.
SEM-9.
SEM-10.
2 , ,defM W L
W W B
, iff , ,R w w w w
; , iff : , & ,a b a bR w w w R w w R w w
, iff , or ,a b a bR w w R w w R w w
*
0 0 1
, iff
, , : & & : 0 ,
a
n n a i i
R w w
w w w w w w i i n R w w
2 2 iff : , &w a wM a p w R w w M p
2 2 iff : ,w a wM a p w R w w M p
Nov., 2008©Gao Yang, Ai Lab NJU15
6.1 Logical Background
6.1.5 Temporal Logic
– Several variants about temporal logic Linear versus Branching
Discrete versus Dense
Moment-Based versus Period-Based
– Some terms in temporal logic Moments: associated with possible state of the world,
has a strict partial order.
Path: set of moments containing the given moments.
Nov., 2008©Gao Yang, Ai Lab NJU16
6.1 Logical Background
t 0
t 1
t 2
t 3
t 4
q
q. . .
q. . .
q. . .
q. . .q. . .r . . .
. . .
. . .
. . .
. . .
r eal i t y
a| | c
a| | d
b| | c
b| | d
An exampl e st r uct ur e of t i me
Nov., 2008©Gao Yang, Ai Lab NJU17
6.1 Logical Background
– Linear-time temporal logic language SYN-10. SYN-11. Notes:
– means at a moment t on a path, q holds at a
future moment t’ on the given path, and p holds on
all moments between t and t’.
– means p holds sometime in the future on the
given path and abbr. with .
– means p always holds in the future on the given
path
– means p holds in the next moment.
– means q held in a past moment.
LL
the rules for pL
, implies that , , L p qp q L p q P L
p q
pF
pG
p
qP
true p
Nov., 2008©Gao Yang, Ai Lab NJU18
6.1 Logical Background
– Model Here T is the set of moments, < the temporal ordering
relation, and gives the denotations of the atomic
propositions.
SEM-11.
SEM-12.
SEM-13.
Note: M3 is linear, < is a total ordering.
3 , ,defM T
3 3 iff : and pt tM P t t t M p
3 3 1 iff pt t
M M p
3
3 3
iff
: and and :
t
t t
M p q
t t t M q t t t t M p
Nov., 2008©Gao Yang, Ai Lab NJU19
6.1 Logical Background (optional)
– Branching temporal and Action logic Builds on top of and , especially uses the ideas of
the well-known language CTL*.
captures the essential properties of actions and time
that are of value in specifying agents. SYN-12. SYN-13. SYN-16. SYN-15.
SYN-16. SYN-16.
BL
LL DL
BL
the rules for pL , implies that , :B p Bp q L P a p L
B sL L
, , , implies that
, , , , ,s
s
p q L x a
p q p p q p x a p x a p L
A B
implies that ,s p p Bp L A R L
\ and implies that :s B sp L L a a p L X
Nov., 2008©Gao Yang, Ai Lab NJU20
6.1 Logical Background (optional)
– Notes about syntax The branching-time operator, A, denotes “in all paths at
the present moment.”
E, denotes “in some path at the present moment.”
R, denotes “in the real path at the present moment.”
The constructor (V a:p) means that “there is an action u
nder which p becomes true.”
– Examples 6.4 EFr , AF(q v r) , RFq hold at t0.
E<b>r, A[a]q, A[d](q v r), A[e]true hold at t0.
(V e: Ex<e>true ^ Ax[e]q) holds at t0.
Nov., 2008©Gao Yang, Ai Lab NJU21
6.1 Logical Background (optional)
– Model SEM-16.
SEM-15.
SEM-16.
SEM-16.
SEM-18.
SEM-19.
SEM-20.
SEM-21.
4 , , ,defM T R
4 iff , where t
M t
4 4 4 iff and t t t
M p q M p M q
4 4 iff t t
M p M p
4 4 ,A iff : tt S t
M p S S S M p
4 4 ,R iff
t R t tM p M p
4 4P iff : t and t t
M p t t M p
4 4, , 1X iff
S t S tM p M p
4 4: iff : and ,where a
t t bM a p b b M p p L B
Nov., 2008©Gao Yang, Ai Lab NJU22
6.1 Logical Background (optional)
SEM-22.
SEM-23.
SEM-26. SEM-25.
SEM-26.
SEM-26.
SEM-28.
4 4 4, , , iff and
S t S t S tM p q M p M q
4 4, , iff
S t S tM p M p
4 4, iff ,where
S t tM p M p p L
4 4, , iff : ; , &
x
S t S tM x a p t S S t t a M p
4 4, , iff : ; ,
x
S t S tM x a p t S S t t a M p
4 4, ,: iff : and ,where \
a
sS t S t bM a p b b M p p L L B
4 ,
4 4, ,
iff
: and and :
S t
S t S t
M p q
t t t M q t t t t M p
Nov., 2008©Gao Yang, Ai Lab NJU23
6.2 Cognitive Primitives
Origin
– Intentional stance
– Knowledge level
– Functional level
BDI logic
– Be used to reason about agent
– Their beliefs, intentions, and actions bring about
the satisfaction of their desires
Nov., 2008©Gao Yang, Ai Lab NJU24
6.2 Cognitive Primitives
Modal operators– Bel(belief), Des(desire), Kh(know-how) and Int(intention)
– SYN-18.
Semantics for
Example 6.5– Consider an agent who has the desire to win a lottery event
ually and intends to buy a lottery ticket sometime, but does not believe that will ever win the lottery.
IL
5 , , , , , ,defM T R B D I
win buy winDesAF IntEF BelAF
h t, , implies that Int , K , K , Dess Ip q L x x p x p x p x p L A
Nov., 2008©Gao Yang, Ai Lab NJU25
6.2 Cognitive Primitives
6.2.1 Knowledge and Beliefs– B, a belief accessibility relation, which behaves as a modal
necessity operator,
– Knowledge(know-that), is customarily defined as a true beli
ef.
– B is serial, symmetric, euclidean and reflecive.
– SEM-29.
– B depends on the given moments, and agent can change it
s beliefs over time.
5 5Bel iff : , B ,t t
M x p t t t x t M p
Nov., 2008©Gao Yang, Ai Lab NJU26
6.2 Cognitive Primitives
6.2.2 Desires and Goals– D, a desire accessibility relation, which represent the
desires of the agent.
– SEM-30.
– In the philosophical view Desires can be inconsistent
Agent need not know the means of achieving these desires
– The role of desires According to inputs, agent choose a subset of desires that are
both consistent and achievable
– Goals The consistent achievable desires are usually called goals.
5 5Des iff : , D ,t t
M x p t t t x t M p
Nov., 2008©Gao Yang, Ai Lab NJU27
6.2 Cognitive Primitives
6.2.3 Intentions– I, a intend accessibility relation, defined as the conditions
that inevitably hold on each of the selected paths.
– SEM-31.
– Example 6.6 Consider next figure, assume that –r and –p hold everywhere
other than as shown. Let the agent x at moment t0 prefer the
path S1 and S2. Then, we have that x intend q (because it
occurs eventually on both the preferred paths) and does not
intend r(because it never occurs on S2)
5 5 ,Int iff : I , F
t S tM x p S S x t M p
0 0
5 5Int , Intt t
M x p M x r
Nov., 2008©Gao Yang, Ai Lab NJU28
6.2 Cognitive Primitives
t 0
t 1
t 2
t 3
t 4
q
q. . .
q. . .r . . .
r . . .. . .
. . .
. . .
S2
a| | c
a| | d
b| | c
b| | d
I nt ent i ons
. . .
. . .
. . .
S1
Nov., 2008©Gao Yang, Ai Lab NJU29
6.2 Cognitive Primitives
Some useful conclusion– IC1 Satisfiability
This says that if p is intended by x, then it occurs eventually on some path.
– IC2 Temporal Consistency
This says that if an agent intends p and intends q, then it (implicitly) intends achieving them in some undetermined temporal order: p before q, q before p , or both simultaneously.
– IC3 Persistence does not entail success
Just because an agent persists with an intention does not mean that it will succeed.
Int EFx p p
Int Int Int F Fx p x q x p q
EG Int is satisfiablex p p
Nov., 2008©Gao Yang, Ai Lab NJU30
6.2 Cognitive Primitives
6.2.4 Commitments
– Goals and intentions Are quite similar, and difference arises in their
relationship with other modalities and how they evolve
over time.
Commitment can separate them.
– Commitment Be treated as constraining how intentions are revised
and updated.
– Handling commitment IC4 shows how commitment may be expressed in the
present framework.
Nov., 2008©Gao Yang, Ai Lab NJU31
6.2 Cognitive Primitives
– IC4 Persist while succeeding
This constraint requires that agents desist from revising their intentions as long as they are able to proceed properly. If an agent selects some paths, then at future moments on those paths, it selects from among the future components of those paths.
I , ; ,
I , I ,
xS x t and S t t a
S x t S x t and S S
Nov., 2008©Gao Yang, Ai Lab NJU32
6.2 Cognitive Primitives
6.2.5 Know-how– Motivation
Intentions have an obvious connection with actions – agents
act to satisfy their intentions.
But intentions do not ensure success.
A key ingredient is know-how.
– Example 6.7 Consider former figure, at t0, x may do either action a or
action b, since both can potentially lead to one of the
preferred paths being realized. However if the other agent
does action d, then no matter which action x chooses, x will
not succeed with its intentions, because none of its preferred
paths will be realized.
Nov., 2008©Gao Yang, Ai Lab NJU33
6.2 Cognitive Primitives
– Let be the set of tree, and is defined as follows
– SYN-19.
1 1
1
1.
2.
3. ,..., , ,..., ,
; ,...,
m m
m
T is the empty tree
T a implies that a
T have different radices and a
implies that a
, , I
I
x A and p L implies that
x p L
Nov., 2008©Gao Yang, Ai Lab NJU34
6.2 Cognitive Primitives
– SEM-32.
– SEM-33.
– SEM-36.
– SEM-35.
tt tM p iff M K p
t tt tM a p iff M K E a true A a K p
1
1
; ,...
:
mt
t i m i it
M a p iff
M K E a true A a p
:
ht
t
M xK p iff
M x p
Nov., 2008©Gao Yang, Ai Lab NJU35
6.3 Belief Revision
Beliefs– The bird caught in the trap is a swan– The bird caught in the trap comes from Sweden– Sweden is part of Europe– All European swans are white
Consequences– The bird caught in the trap is white
New information– The bird caught in the trap is black
Which sentence would you give up?
Nov., 2008©Gao Yang, Ai Lab NJU36
6.3.1 AGM Framework
Alchourron, Gardenfors, and Makinson (1985)
– Epistemic states: sets of formulas K.
– Epistemic attitudes: - α accepted
- α rejected
Otherwise - α undetermined
– Input: formula
– Change operations: expansion, contraction, and r
evision
K
K
Nov., 2008©Gao Yang, Ai Lab NJU37
6.3.1 AGM Framework
Belief sets
Three operations:
– Expansion
– Contraction
– Revision
(Levi identity)
(Levi identity)
For contraction and revision, rationality postulates.
K Cn K
K Cn K
K
*K
*K K
*K K K
Nov., 2008©Gao Yang, Ai Lab NJU38
6.3.1 AGM Framework
Contraction Postulates
1 ( )
2 ( )
3 ,
4 ,
5 , cov
6 ,
7
K K is a belief set closure
K K K inclusion
K If K then K K vacuity
K If not then K success
K If K then K K re ery
K If then K K equivalence
K K
8 ,
K K
K if K then K K
Nov., 2008©Gao Yang, Ai Lab NJU39
6.3.1 AGM Framework
Revision Postulates
*1
*2 *
*3 *
*4 * , *
*5 *
*6 , * *
*7 * *
*8 * , * *
K K * α = Cn K * α
K K
K K K
K If K then K K
K K K if and onlyif
K If then K K
K K K
K if K then K K
Nov., 2008©Gao Yang, Ai Lab NJU40
6.4 Social Primitives
6.6.1 Team and Organizational Structure
Nov., 2008©Gao Yang, Ai Lab NJU41
6.4 Social Primitives
6.6.2 Mutual Beliefs and Joint Intentions
Nov., 2008©Gao Yang, Ai Lab NJU42
6.4 Social Primitives
6.6.3 Social Commitments
Nov., 2008©Gao Yang, Ai Lab NJU43
6.4 Social Primitives
6.6.4 Group Know-how and Intentions
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