Formal Methods in DAI :Logic-Based Representation and

Reasoning

컴퓨터 공학과이인호

0. Contents

Introduction Logical Background Cognitive Primitives BDI Implementations Coordination Communications Social Primitives Conclusions

1. Introduction

Agents are being used in critical situations Ensuring that an agent behaves correctly is

important Formal methods offer an understanding of

the systems being designed at a level higher than their specific implementation

2. Logical Background (1/6)

Formalizations of agent systems are used for two quite distinct purpose• Specifying agent’s internal reasoning & action• Specifying agent’s external behavior in a

dynamic environment

2. Logical Background (2/6)

Propositional Logic Predicate Logic Modal Logic

• Possibly true / Necessarily true• Represents belief and knowledge

Deontic Logic• What an agent is obliged to do • Not mentioned in detail

2. Logical Background (3/6)

Dynamic Logic• Modal logic of action• necessity and possibility operators are based upon t

he kinds of actions available• a;b : doing a and b in sequence• a + b : doing either a or b, whichever works. (nond

eterministic)• p? : action based on the truth value of p• a * : 0 or finitely many iterations of a

2. Logical Background (4/6) Temporal Logic

• The logic of time• Set of moments with a strict partial order,

which denotes temporal precedence• Each moment is associated with a possible state

of the world• A path at a moment : any maximal set of

moments containing the given moment• A real path : the path on which the world

progresses

2. Logical Background (5/6) Linear Temporal Logic

• pUq is true at a moment t on a path : q holds at a future moment on the given path and p holds on all moments between t and that moment

• Fp : p holds sometimes in the future on the given path (true U p)

• Gp : p always holds in the future on the given path (¬F¬p)

• Xp : p holds in the next moment• Pq : q held in a past moment

2. Logical Background (6/6) Branching Temporal and Action Logic

• A : in all paths at the present moment• E : in some path at the present moment• R : in the real path at the present moment• x[a]p : if agent x performs action a, then p hold

s at the moment where a ends• x<a>p : agent x perfoms action a and p holds at

the moment where a ends• (V a : p) : there is an action under which p beco

me true

3. Cognitive Primitives (1/5) Agents given high-level cognitive specificat

ions such as Beliefs, Knowledge, Desires, and Intentions

Operators• Bel (Belief)• Des (Desire)• Kt (Know-that)• Kh (Know-how)• Int (Intention)

3. Cognitive Primitives (2/5)

Knowledge and Beliefs• xBelp : agent x believes p possible at the mome

nt• xKtp : agent x know that p is true (true belief)

Desires and Goals• xDesp : agent x desires p at the moment• goal : subset of desires chosen by an agent whic

h are both consistent and achievable

3. Cognitive Primitives (3/5)

Intentions• xIntp : agent x selected of preferred p. That is,

p is inevitably hold on each of the selected paths

• Satisfiability : xIntp EFp• Temporal Consistency

: (xIntp xIntq) xInt(Fp Fq)• Persistence does not entail success

: EG((xIntp) ¬p)

3. Cognitive Primitives (4/5)

Know-how• An agent acts to satisfy their intentions, but as s

hown above, intentions do not ensure success• xKhp : agent x knows how to achieve p. That is

, knows the action to be done to achieve p• For example, if it knows p already holds, then it

knows how to achieve p(by doing nothing).• And if it knows p at a moment, then it knows h

ow to achieve p at the moment immediately before the moment

3. Cognitive Primitives (5/5)

Reasoning with Cognitive Concepts• Using the above concepts needs efficient

reasoning techniques• There are two main approaches for reasoning

with a logic Theorem Proving : establishing a given formula by

following through a finite sequence of applications of axioms and inferences rules of a given logic

Model Checking :checking if a given formula is satisfied at a given model and index

4. BDI Implementations (1/8) Basic Interpreter

initialize-state();

do

options := option-generator(event-queue, S)

selected-poptions := deliberate(options, s);

update-state(selected-options, S);

execute(S);

event-queue := get-new-events();

until quit.

4. BDI Implementations (2/8) Abstract BDI-interpreter

initialize-state();

do

options := option-generator(event-queue, B, G, I)

selected-options := deliberate(options, B, G, I);

update-intentions(selected-options, I);

execute(I);

get-new-external-events();

drop-successful-attitudes(B, G, I);

drop-impossible-attitudes(B, G, I);

until quit.

4. BDI Implementations (3/8)

Practical System• To make abstract interpreter practical, some repres

entationsla choices is needed to make option generator and deliberaton procedures fast to satisfy the realtime demands placed upon the system

• Beliefs and Goals The system operates only on explicit beliefs and goals current : a subset of the agent’s beliefs ad goals

4. BDI Implementations (4/8)

Plans• Information about means and options as belifes

can be more directly represented as plans• A plan has…

– type : name of plan– body : method for executing (plan graph)– invocation condition (triggeing event) / precondition

: specify when the plan may be selected– add list / delete list : atomic propositions believed or

not believed upon its successful execution

4. BDI Implementation (5/8)

• Whenever a plans invocation condition and precondition are satisfied, its body is believed to be an option

• After successful execution, the propoitions in the add list will become true

• Resulting consequences can trigger further plans

4. BDI Implementation (6/8)

Intentions• Intentions are represented as sets of hierarchical

ly related plans• Intention frame : means (plan) - end (goal) pair

with variable bindings and contorl points• An intention towards a means results in another

end(subgoal) and means, thus creating another intention frame until subgoal can be directly executed as an atomic action

4. BDI Implementation (7/8)

A Practical Interpreter• option-generator(trigger-events)

option := {}

for trigger-event trigger-events do

for plan plan-library do

if matches(invocation(plan), trigger-event) then

if provable(precondition(plan), B) then

options := options U {plan};

return(options).

4. BDI Implementation (8/8)

• deliberate(options)if length(options) 1 then return(options);

else

metalevel-options :=

option-generator(b-add(option-set(options)));

selected-options := deliberate(metalevel-options);

if null(selected-options) then

return(random-choice(options));

else return(selected-options).

5. Coordination (1/3)

When agents are heterogeneous and auto-nomous, coordination becomes important

One Formal Approach developed by Singh• representing each agent as a small skeleton• each skeleton includes only the events or transit

ions made by the agent that are significant for coordination

5. Coordination (2/3)

Event Classes• flexible : the agent is willing to delay or omit• inevitable : the agent is willing only to delay• immediate : the agent is willing neither to delay

nor to omit• triggerable : the agent is willing to perform bas

ed on external request

5. Coordination (3/3) Common Coordination Relationships

Name Description Formal notation

R1 e is required by fIf f occurs, e must occur before or

after f e _f

R2 e disables fIf e occurs, then f must occur

before e_e_f f e

R3 e feeds or enables f f requires e to occur beforee f

_f

R4 e conditionally feeds f If e occurs, it feeds f _e e f

_f

R5 Guaranteeing e enables ff can occur only if e has occurred or

will occur e f _e_f

R6 e initiates f f occurs iff e precedes it _e_f e f

R7 e and f jointly require gIf e and f occur in any order, then g

must also occur (in any order)_e_f g

R8 g compensates for efailing f

If e happens and f does not, thenperform g (

_e f g) (

_g e) (

_g_f )

6. Communications Communication : a natural way in which th

e agents may interact with one another Speech Act theroy : with language, we do n

ot only make statements, but also perform actions

3 main aspects of a speech act• locution : the string transmitted• illocution : intrinsic meaning• perlocution : possible effects on the recipients

7. Social Primitives (1/2)

Group : system of agents that are somehow constrained in their mutual interactions

Team : a group in which the agents are restricted to having a common goal of some sort

7. Social Primitives (2/2)

Mutual Belief(a) believe p, (b) believe that others believe p(c) believe that (b) holds of the others

Joint Intentions(a) each have a goal p(b) each will persist with this goal until it is mutu

ally believed that p is achievd or that p canot be achieved

(c) (a) and (b) are mutually believed

8. Conclusions

Formal mehods in DAI are still in their infancy

But, some techniques have also been used to influence a variety of practical systems

A range of future challenge :to develop formal techniques• that cover the phenomena that emerge in practic

e• are more accurate in real systems• can be used to analyze and design them