Luís Moniz Pereira Centro de Inteligência Artificial - CENTRIA Universidade Nova de Lisboa, Portugal Pierangelo Dell’Acqua Dept. of Science and Technology - ITN Linköping University, Sweden Ulf Nilsson Dept. of Computer and Information Science - IDA Linköping University, Sweden

Contribution The paper presents an asynchronous multi-agent system for logic based agents, and provides its semantics. The interaction among agents is expressed via a transition rule system that characterizes the global behaviour of the system.

Our agents FWe proposed a LP approach to agents that can: 3Reason and React to other agents 3Prefer among possible choices 3Update their own knowledge, reactions, and goals 3Interact by updating the theory of another agent 3Decide whether to accept an update depending on the requesting agent 3Abduce hypotheses to explain observations

Framework FThis agent framework builds on the works: 3 Dynamic Logic Program - J. J. Alferes et al KR’98 3 Updating Agents - P. Dell’Acqua & L. M. Pereira MAS’99 3 Updates plus Preferences - J. J. Alferes & L. M. Pereira JELIA’00 3 A compilation of Updates plus Preferences - J. J. Alferes et al JELIA’00

Enabling agents to update their KB FUpdating agent: a rational, reactive agent that can dynamically change its own knowledge and goals. 8makes observations 8reciprocally updates other agents with goals and rules 8thinks (rational) 8selects and executes an action (reactive)

Agent’s language  Atomic formulae: A objective atoms not A default atoms  :C projects updates CC FFormulae: L i is an atom, an update or a negated update active rule generalized rules Z j is a project integrity constraint false  L 1  L n  Z 1  Z m A  L 1  L n not A  L 1  L n L 1  L n  Z

Projects and updates  A project  2 :C denotes the intention of some agent  1 of proposing the updating the theory of agent  2 with C.  denotes an update proposed by  1 of the current theory of some agent  2 with C. wilma:C 1C1C fred  C

Example: active rules A   2 : not B B   1 : C Consider the following active rules in the theory of an agent  1.

Agents’ language  A project  :C can take one of the forms: FNote that a program can be updated with another program, i.e., any rule can be updated.  : ( A  L 1  L n )  : ( L 1  L n  Z )  : ( ?- L 1  L n )  : ( not A  L 1  L n )  : ( false  L 1  L n  Z 1  Z m )

Agents’ knowledge states FKnowledge states represent dynamically evolving states of agents’ knowledge. They undergo change due to updates.  Given the current knowledge state P s, its successor knowledge state P s+1 is produced as a result of the occurrence of a set of parallel updates. FUpdate actions do not modify the current or any of the previous knowledge states. They only affect the successor state: the precondition of the action is evaluated in the current state and the postcondition updates the successor state.

Abductive agents FThe initial theory of an agent  is a tuple (P,A,R): - P is a set of generalized rules and integrity constraints. - A is a set of abducibles. - R is a set of active rules. FAn updating program is a finite set of updates. FLet S be a set of natural numbers. We call the elements s  S states. FAn agent  at state s, written   s, is a pair (T,U): - T is the initial theory of . - U={U 1,…, U s } is a sequence of updating programs.

Semantics of abductive agents Let   s = (T,U) and  be the hypotheses assumed by  at state s. FAn abductive stable model of  at state s with hypotheses  is a stable model of the program that extends T to contain: - the updates in U, - the rules whose updates (in U) are neither distrusted nor rejected, - the projects of active rules with true body, and - the hypotheses in .

Example: abductive agent Consider the following theory of an agent  2. AB  AAB  A T = (P,A,R) = (P,{},{}) and P =   2 0 = (T,{})M = {A, B}   2 1 = (T,{U 1 }) with U 1 = {  1  not B } M = {A, not B,  1  not B} M is the unique abductive stable model of  at state s with hypotheses  ={}

Multi-agent systems A MAS consists of a number of agents acting concurrently and transition rules that characterize the global behaviour of the system. FThe interaction among the agents is asynchronous and modelled via buffers. FA buffer [U 1,…,U i ] is a sequence of updating programs U 1,…,U i (i  0). FEach agent  is equipped with a buffer   s [U 1,…,U i ]

Multi-agent systems FA multi-agent system  consists of a number of abductive agents  1,…,  n acting concurrently:  =   1 s1 [ U 1,…,U i ] | … |   n sn [ V 1,…,V j ] together with the transition rules: EXTP, INTP and INCUP. F  characterizes a fixed society of evolving agents.

Transition rules - EXTP EXTP to execute external projects of  1 : if  (  2 :C)  P  1 where  1   2 and V j+1 ={  1  C | for every  2 :C  P  1 }   1 s1 [ U 1,…,U i ] |   2 s2 [ V 1,…,V j ]    1 s1 [ U 1,…,U i ] |   2 s2 [ V 1,…,V j, V j+1 ] Let P  i be the set of executable projects of an agent  i

Transition rules - INTP INTP to execute internal projects of  : if  (  :C)  P  where U i+1 ={   C | for every  :C  P  }   s [ U 1,…,U i ]    s [ U 1,…,U i, U i+1 ]

Transition rules - INCUP INTP to incorporate updates into  from its buffer Let   s = (T,{U 1,…,U s }) where i  1 and   s+1 = (T,{U 1,…,U s,U s+1 }) with U s+1 =V 1   s [ V 1,…,V i ]    s+1 [ V 2,…,V i ]

Multi-agent system at state s A multi-agent system  at state 0 (initial configuration):  0 =   1 0 [ ] | … |   n 0 [ ] A multi-agent system  at state s:  s =   1 s1 [ U 1,…, U i ] | … |   n sn [ V 1,…, V j ] where s= s 1 +…+s n

Multi-agent system at state s FThe MAS remains at the same state when the transition rule INTP or EXTP is applied. FIf INCUP is employed (by an agent  i ), then the MAS  s =   1 s1 [ U 1,…, U i ] | … |   i si [T 1, T 2,…, T k ] | … |   n sn [ V 1,…, V j ] moves to the next state:  s+1 =   1 s1 [ U 1,…, U i ] | … |   i si+1 [ T 2,…, T k ] | … |   n sn [ V 1,…, V j ]

Semantics of multi-agent systems FThe declarative semantics S  of MAS  characterizes the relationship among the agents in  and how the system evolves. FThe declarative semantics S  s of  at state s is the set of sets M  i si of all the abductive stable models of every agent  i in  at state si with hypotheses  i : S  s = { M  1 s1,…, M  n sn }

Executable projects FThe set P  of executable projects of an agent  contains the projects that occur in every abductive stable model of  at state s with hypotheses .

Example: MAS Consider the following two agents  1 and  2. AB  AAB  A T  2 = A A   2 : not B B   1 : C T  1 =

Example: MAS  0 =   1 0 [ ] |   2 0 [ ]  0 =   1 0 [ ] |   2 0 [ U 1 ] with U 1 = {  1  not B }  1 =   1 0 [ ] |   2 1 [ ] by EXTP by INCUP

Example: MAS  0 =   1 0 [ ] |   2 0 [ ] M  1 0 = { {A,  2 : not B} } P  1 = {  2 : not B } M  2 0 = { {A, B} } P  2 = { } S  0 = {M  1 0, M  2 0 } EXTP is applicable

Example: MAS S  0 = {M  1 0, M  2 0 }  0 =   1 0 [ ] |   2 0 [ U 1 ] with U 1 = {  1  not B } INCUP is applicable

Example: MAS M  1 0 = { {A,  2 : not B} } M  2 1 = { {A, not B,  1  not B} } S  1 = {M  1 0, M  2 1 }  1 =   1 0 [ ] |   2 1 [ ]

Future work FOngoing implementation of our agent framework: - its logical parts (logical reasoning, updating, preferring, etc.) are implemented in XSB Prolog, and - its non-logical parts are implemented in Java. - InterProlog is then used to interface XSB and Java. FHow to represent organisational structures, and how to animate them with agents in a way that each agent will have a view of the organisational structure and the externally visible events. FInvestigate whether there are invariants and other properties of the MAS that can guarantee the behaviour of the entire system.