1. Stable Multi-Agent Systems Informatica, PISA. Computing, CITY. Computing, IMPERIAL. Andrea Bracciali, Paolo Mancarella, Kostas Stathis, Francesca Toni, ESAW’04, Toulouse 22-10-04.  

2. OutlineOutline n Motivation; n I/O Agent Semantics; n Stable Sets: –Examples of stable MAS; –MAS Properties; n Stable MAS construction; n Conclusions and future work. n Motivation; n I/O Agent Semantics; n Stable Sets: –Examples of stable MAS; –MAS Properties; n Stable MAS construction; n Conclusions and future work.

3. MotivationMotivation Previous work on Logic Programming (LP) to specify agents: n Toni & Stathis’ ESAW’02 Access-as-you-need framework; n Q: What does it take to build an abstract model of a MAS (in a way similar to the T p op. of van Emden & Kowalski for LP)? Previous work on Logic Programming (LP) to specify agents: n Toni & Stathis’ ESAW’02 Access-as-you-need framework; n Q: What does it take to build an abstract model of a MAS (in a way similar to the T p op. of van Emden & Kowalski for LP)? Current work (Bracciali et al DALT’04) based on the need to model declaratively a MAS. Approach: n has formal foundations; n is abstract (language independent); n is suitable to express and verify properties. Current work (Bracciali et al DALT’04) based on the need to model declaratively a MAS. Approach: n has formal foundations; n is abstract (language independent); n is suitable to express and verify properties.

4. ESAW’02: Access-as-you-need Real Social Environment Personal Agent Electronic Social Environment Artificial Society 1 Artificial Society 1 Artificial Society 2 Artificial Society 2 Artificial Society n Artificial Society n I must join a society to get a resource for the user

5. ESAW’02: Access-as-you-need (cntd) Agent a: P a : get(R, T)  request(a,b,R, T')  accept(b,a,R,T'')  T''  T'  T A a : request(a, X, R, T), accept(X,a,R,T) IC a :  Agent b: P b : have(r) A b : accept(b,X,R,T), request(X, b, R, T) IC c : request(X,b,R,T)  have(R)   T'[accept(b,X,R,T')  T'  T] Agent a: P a : get(R, T)  request(a,b,R, T')  accept(b,a,R,T'')  T''  T'  T A a : request(a, X, R, T), accept(X,a,R,T) IC a :  Agent b: P b : have(r) A b : accept(b,X,R,T), request(X, b, R, T) IC c : request(X,b,R,T)  have(R)   T'[accept(b,X,R,T')  T'  T] actionsobservables How do we model a MAS of this kind abstractly?

6. Multi-agent System Assumptions n Agents: 1..n; World: W, with E( W ) all possible events in W. n Each agent i is equipped with; –set of all possible actions A(i); –set of all possible observations O(i); s.t. O(i)   A(j)  E( W ) A(i)  A(j) i  j (e.g. agent i cannot act pretending to be j). i  j

7. I/O Agent Semantics private agent i public  in Observations  O(i)  out Actions  A(i) M “Mental State” (beliefs) 00 plan  A(i)

8. I/O Agent Semantics (cntd) Semantics for single agent i is then given as: S i (  0,  in ) = M may be  when: n agent i is unable to plan or achieve a goal; or n the observations of agent i are inconsistent with the constraints it wants to satisfy (e.g. rely on agent a1 for a resource that a1 does not posses); Inconsistent agents are required not to commit to any action.

9. Stable MAS A MAS = is stable if there exists a  =   i out s.t. for each i  A S i (  -i  W i,  i 0 ) = where n  -i =   ( j ) (actions by agents other than i); n  ( j )=   A(j) (actions by agent j); W i = W  O(i) (happened events observable by i). The set  is called a stable set for MAS. iAiA iAiA j  A, i  j j  A, i  j

10. Example of Stable Set n Agent 1 moves odd-numbered blocks and has goal mvToB. n Agent 2 moves even-numbered blocks and has goal mvToC. 1 1 2 2 3 3 A A B B C C 1 1 1 1 2 2  = { 1ToB 1, 2ToC 2, 3ToB 1 } is a stable set. S 1 ({ 2ToC 2 } U W 1, { 1ToB 1, 3ToB 1 }) = S 2 ({ 1ToB 1, 3ToB 1 } U W 2, { 2ToC 2 }) = with mvToB  M 1 and mvToC  M 2. S 1 ({ 2ToC 2 } U W 1, { 1ToB 1, 3ToB 1 }) = S 2 ({ 1ToB 1, 3ToB 1 } U W 2, { 2ToC 2 }) = with mvToB  M 1 and mvToC  M 2.

11. Example of Unstable Set n Agent 1 intends to move block 1 to B. n Agent 2 intends to move block 2 to B. 1 1 2 2 A A B B C C 1 1 2 2 No stable set, as agents become inconsistent.

12. What can we do with stable sets? n A MAS admitting stable sets is “good”/”well-behaved”; n DALT’04: properties of MAS can be specified in terms of stable sets, e.g. –A successful MAS is a stable MAS whose every agent is successful (it achieves its goals); –A robust MAS is a successful MAS such that, taking away any agent in it, the resulting MAS is still successful. n How can we guarantee the existence of stable sets for MAS? How can we construct stable sets? n A MAS admitting stable sets is “good”/”well-behaved”; n DALT’04: properties of MAS can be specified in terms of stable sets, e.g. –A successful MAS is a stable MAS whose every agent is successful (it achieves its goals); –A robust MAS is a successful MAS such that, taking away any agent in it, the resulting MAS is still successful. n How can we guarantee the existence of stable sets for MAS? How can we construct stable sets?

13. Constructing Stable Sets: One Step Operator Given MAS = and , let A + be the set of all agents i in A s.t. S i (  -i  W i,  (i))  A - = A - A + Then T A ( A ) = A if A = A + = A+  A- otherwise

14. Constructing Stable Sets: concrete semantics of a MAS Given MAS = and A (tuple of initial plans) the concrete semantics of MAS is given by applying (possibly infinitely many times) T A, starting from A : T A ( A ), T A (T A ( A )), … Conjecture: the concrete semantics of a MAS is stable, given any tuple of initial plans. Given MAS = and A (tuple of initial plans) the concrete semantics of MAS is given by applying (possibly infinitely many times) T A, starting from A : T A ( A ), T A (T A ( A )), … Conjecture: the concrete semantics of a MAS is stable, given any tuple of initial plans.

15. Conclusions & Future work n A language independent abstract semantics for agents. n Suitable to model and verify properties of agents & MAS. n Relies on the notion of stability to approximate well- behavedness (shown examples both positive and negative). n Initial steps towards a formal methodology. n Future work involves: – the application of the framework to more complex scenaria; –use stability to prove properties of these scenaria. n A language independent abstract semantics for agents. n Suitable to model and verify properties of agents & MAS. n Relies on the notion of stability to approximate well- behavedness (shown examples both positive and negative). n Initial steps towards a formal methodology. n Future work involves: – the application of the framework to more complex scenaria; –use stability to prove properties of these scenaria.