João Alexandre Leite Luís Moniz Pereira Centro de Inteligência Artificial - CENTRIA Universidade Nova de Lisboa { jleite, lmp Pierangelo Dell’Acqua Dept. of Science and Technology Linköping University Porto, Dec Epia01

Our agents We propose a LP approach to agents that can: 3Reason and React to other agents 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 3Capture the representation of social evolution

Framework This framework builds on the work: 3 Updating Agents P. Dell’Acqua & L. M. Pereira - MAS’99 3 Multi-dimensional Dynamic Logic Programming L. A. Leite & J. J. Alferes & L. M. Pereira - CLIMA’01

Updating agents 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)

Multi-Dimensional Logic Programming FIn MDLP knowledge is given by a set of programs. FEach program represents a different piece of updating knowledge assigned to a state. FStates are organized by a DAG ( Directed Acyclic Graph ) representing their precedence relation. FMDLP determines the composite semantics at each state according to the DAG paths. FMDLP allows for combining knowledge updates that evolve along multiple dimensions.

Contribution 1 To extend the framework of MDLP with integrity constraints and active rules. 2 To incorporate the framework of MDLP into a multi-agent architecture. 3 To make the DAG of each agent updatable.

DAG A directed acyclic graph DAG is a pair D=(V,E) where V is a set of vertices and E is a set of directed edges.

Agent’s language Atomic formulae: A objective atoms not A default atoms i:C projects i  C updates Formulae: 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 j:C denotes the intention of some agent i of proposing the updating the theory of agent j with C. i  C denotes an update proposed by i of the current theory of some agent j with C. wilma:C fred  C

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.

Agent’s language A project i:C can take one of the forms: i : ( A  L 1  L n ) i : ( L 1  L n  Z ) i : ( ?- L 1  L n ) i : ( not A  L 1  L n ) i : ( false  L 1  L n  Z 1  Z m ) i : edge(u,v) i : not edge(u,v)

Initial theory of an agent A multi-dimensional abductive LP for an agent  is a tuple: T =  D, P D, A, R D  - D=(V,E) is a DAG s.t.  ´  V (inspection point of  ). - P D ={P V | v  V} is a set of generalized LPs. - A is a set of atoms (abducibles). - R D ={R V | v  V} is a set of set of active rules.

The agent’s cycle FEvery agent can be thought of as an abductive LP equipped with a set of inputs represented as updates. FThe abducibles are (names of) actions to be executed as well as explanations of observations made. FUpdates can be used to solve the goals of the agent as well as to trigger new goals.

Happy story - example inspection point of Alfredo alfredo judge motherfather girlfriend alfredo´ state 0The goal of Alfredo is to be happy DAG of Alfredo

Happy story - example alfredo judge motherfather girlfriend alfredo´ hasGirlfriend  not happy  father:(?-happy) not happy  mother:(?-happy) getMarried  hasGirlfriend  girlfriend:propose moveOut  alfredo:rentApartment custody(judge,mother)  alfredo:edge(father,mother) {moveOut, getMarried} state 0 abducibles

Happy story - example alfredo judge motherfather girlfriend alfredo´ state 0 hasGirlfriend  not happy  father:(?-happy) not happy  mother:(?-happy) getMarried  hasGirlfriend  girlfriend:propose moveOut  alfredo:rentApartment custody(judge,mother)  alfredo:edge(father,mother) {moveOut, getMarried}

Agent theory The initial theory of an agent  is a multi-dimensional abductive LP. Let an updating program be a finite set of updates, and S be a set of natural numbers. We call the elements s  S states. An 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.

Multi-agent system A multi-agent system M={   1 s,…,   n s } at state s is a set of agents  1,…,  n at state s. M characterizes a fixed society of evolving agents. The declarative semantics of M characterizes the relationship among the agents in M, and how the system evolves. The declarative semantics is stable models based.

Happy story - 1 st scenario Suppose that at state 1, Alfredo receives from the mother: and from the father: mother  (happy  moveOut) mother  (false  moveOut  not getMarried) mother  (false  not happy) father  (happy  moveOut) father  (not happy  getMarried)

happy  moveOut false  moveOut  not getMarried alfredo judge motherfather girlfriend alfredo´ state 1 happy  moveOut not happy  getMarried Happy story - 1 st scenario In this scenario, Alfredo cannot achieve his goal without producing a contradiction. Not being able to make a decision, Alfredo is not reactive at all. false  not happy

Happy story - 2 nd scenario Suppose that at state 1 Alfredo’s parents decide to get divorced, and the judge gives custodity to the mother. judge  custody(judge,mother)

custody(judge,mother) Happy story - 2 nd scenario alfredo judge motherfather girlfriend alfredo´ state 1 hasGirlfriend  not happy  father:(?-happy) not happy  mother:(?-happy) getMarried  hasGirlfriend  girlfriend:propose moveOut  alfredo:rentApartment custody(judge,mother)  alfredo:edge(father,mother)

Happy story - 2 nd scenario alfredo judge girlfriend alfredo´ state 2 motherfather Suppose that when asked by Alfredo, the parents reply in the same way as in the 1 st scenario. Note that the internal update produces a change in the DAG of Alfredo.

Happy story - 2 nd scenario Now, the advice of the mother prevails over and rejects that of his father. alfredo judge girlfriend alfredo´ state 2 happy  moveOut false  moveOut  not getMarried happy  moveOut not happy  getMarried motherfather false  not happy

Happy story - 2 nd scenario Thus, Alfredo gets married, rents an apartment, moves out and lives happily ever after. alfredo judge girlfriend alfredo´ state 2 hasGirlfriend  not happy  father:(?-happy) not happy  mother:(?-happy) getMarried  hasGirlfriend  girlfriend:propose moveOut  alfredo:rentApartment custody(judge,mother)  alfredo:edge(father,mother) motherfather

Syntactical transformation The semantics of an agent  at state s,   s =(T,U), is established by a syntactical transformation  that maps   s into an abductive LP:    s =  P,A,R  1.   s   P´,A,R  P´ is a normal LP, A and R are a set of abducibles and active rules. 2. Default negation can then be removed from P´ via the abdual transformation (Alferes et al. ICLP99): P´  P P is a definite LP.

Agent architecture Rational P Reactive P+R CC    s =  P,A,R  can abduce XSB Prolog cannot abduce InterProlog (Declarativa) InterProlog (Declarativa) Java

Agent architecture Rational P Reactive P+R CC    s =  P,A,R  UpdateH projects External Interface ext.project Updates ActionH int.project

Future work FAt the agent level: 3How to combine logical theories of agents expressed over graph structures. 3How to incorporate other rational abilities, e.g., learning. FAt the multi-agent system level: 3Non synchronous, dynamic multi-agent system. 3How to formalize dynamic societies of agents. 3 How to formalize the notion of organisational reflection.