1. Formal Methods in DAI : Logic-Based Representation and Reasoning
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2. 0. Contents Introduction Logical Background Cognitive Primitives
BDI Implementations
Coordination
Communications
Social Primitives
Conclusions

3. 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

4. 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

5. 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

6. 2. Logical Background (3/6)
Dynamic Logic
Modal logic of action
necessity and possibility operators are based upon the kinds of actions available
a;b : doing a and b in sequence
a + b : doing either a or b, whichever works. (nondeterministic)
p? : action based on the truth value of p
a * : 0 or finitely many iterations of a

7. 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

8. 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

9. 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 holds 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 become true

10. 3. Cognitive Primitives (1/5)
Agents given high-level cognitive specifications such as Beliefs, Knowledge, Desires, and Intentions
Operators
Bel (Belief)
Des (Desire)
Kt (Know-that)
Kh (Know-how)
Int (Intention)

11. 3. Cognitive Primitives (2/5)
Knowledge and Beliefs
xBelp : agent x believes p possible at the moment
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 which are both consistent and achievable

12. 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)

13. 3. Cognitive Primitives (4/5)
Know-how
An agent acts to satisfy their intentions, but as shown 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 how to achieve p at the moment immediately before the moment

14. 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

15. 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.

16. 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.

17. 4. BDI Implementations (3/8)
Practical System
To make abstract interpreter practical, some representationsla 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

18. 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

19. 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

20. 4. BDI Implementation (6/8)
Intentions
Intentions are represented as sets of hierarchically 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

21. 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).

22. 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).

23. 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 transitions made by the agent that are significant for coordination

24. 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 based on external request

25. 5. Coordination (3/3)
Common Coordination Relationships

26. 6. Communications
Communication : a natural way in which the agents may interact with one another
Speech Act theroy : with language, we do not 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

27. 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

28. 7. Social Primitives (2/2) Mutual Belief Joint Intentions
(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 mutually believed that p is achievd or that p canot be achieved
(c) (a) and (b) are mutually believed

29. 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 practice
are more accurate in real systems
can be used to analyze and design them