1. Combining Societal Agents’ Knowledge João Alexandre Leite José Júlio Alferes Luís Moniz Pereira CENTRIA – Universidade Nova de Lisboa Universidade de Évora, 26-28 Sept. 2001AGP 2001

2. Summary zGoals and Motivation zOverview of MDLP (Multi-Dimensional LP) zInter- and Intra- Agent Societal Viewpoints yEqual Role Representation yTime Prevailing Representation yHierarchy Prevailing Representation yCombining Inter- and Intra- Agent’s viewpoints zConclusions and Current work

3. Goal  The representation is the core of the agent architecture and system MINERVA.  MINERVA was designed with the aim of providing a common agent framework based on the strengths of Logic Programming. Explore the applicability of MDLP to represent agents’ view of societal knowledge dynamics

4. Motivation - 1 zThe notion of agency has claimed a major role in modern AI research zLP and Non-monotonic Reasoning are appropriate for rational agents: yUtmost efficiency is not always crucial yClear specification and correctness are crucial yLP provides a general, encompassing, rigorous declarative and procedural framework for rational functionalities

5. Motivation - 2 zTill recently, LP could be seen as good for representing static non-contradictory knowledge zIn the agency paradigm we need to consider: yWays of integrating knowledge from different sources evolving in time yKnowledge expressing state transitions yKnowledge about the environment evolution, and each agent’s behavioural evolution zLP declaratively describes states well. LP must describe state transitions too.

6. Dynamic LP zDLP was introduced to express LP’s linear evolution in dynamic environments, via updates zDLP gives semantics to sequences of GLPs zEach program represents a distinct state of knowledge, where states may specify: ydifferent time points, different hierarchical instances, different viewpoints, etc. zDifferent states may have mutually contradictory or overlapping information, and DLP determines the semantics for each state sequence

7. MDLP Motivating Example zParliament issues law L1 at time t1 zA local authority issues law L2 at time t2 > t1 zParliamentary laws override local laws, but not vice-versa: zMore recent laws have precedence over older ones: L2L1 L2 zHow to combine these two dimensions of knowledge precedence? ë DLP with Multiple Dimensions (MDLP)

8. MDLP zIn MDLP knowledge is given by a set of programs zEach program represents a different piece of updating knowledge assigned to a state zStates are organized by a DAG (Directed Acyclic Graph) representing their precedence relation zMDLP determines the composite semantics at each state, according to the DAG paths zMDLP allows for combining knowledge updates that evolve along multiple dimensions

9. Generalized Logic Programs zTo represent negative info in LP updates, we need LPs allowing not in heads zPrograms are sets of generalized LP rules: A  B 1,…, B k, not C 1,…,not C m not A  B 1,…, B k, not C 1,…,not C m zThe semantics is a generalization of SMs

10. MDLP - definition  Definition: A Multi-Dimensional Dynamic Logic Program, P, is a pair ( P D,D) where: yD=(V,E) is an acyclic digraph  P D ={P V : v  V} is a set of generalized logic programs indexed by the vertices of D

11. MDLP - semantics 1  Definition: Let P =( P D,D) be a MDLP. An interpretation M s is a stable model of the multi-dimensional update at state s  V iff, M s = least( [ P s – Reject(s, M s )]  Defaults ( P s, M s ) ) where P s =  j  s P i : s j3j3 j2j2 j1j1

12. MDLP - semantics 2 where: Reject(s, M s ) = {r  P i |  r’  P j, i  j  s, head(r)=not head(r’)  M s  body(r’)} Defaults ( P s, M s )={not A |  r  P s : head(r)=A  M s  body(r)} M s = least( [ P s – Reject(s, M s )]  Defaults ( P s, M s ) ) s j3j3 j2j2 j1j1

13. MDLP for Agents zFlexibility, modularity, and compositionality of MDLP makes it suitable for representing the evolution of several agents’ combined knowledge How to encode, in a DAG, the relationships among every agent’s evolving knowledge along multiple dimensions ?

14. Two basic dimensions of a multi-agent system Hierarchy of agents Temporal evolution of one agent How to combine these dimensions into one DAG ?

15. Equal Role Representation zAssigns equal role to the two dimensions:

16. Equal Role - 2 zIn legal reasoning: yLex Superior : rules issued by a higher authority override those of a lower one yLex Posterior : more recent rules override older ones zIt potentiates contradiction: yThere are many pairs of unrelated programs

17. Time Prevailing Representation zAssigns priority to the time dimension:

18. Time Prevailing - 2  Useful in very dynamic situations, where competence is distributed, i.e.  agents normally provide rules about  literals zDrawback: yIt requires all agents to be fully trusted, since all newer rules override older ones irrespective of their mutual hierarchical position

19. Hierarchy Prevailing Representation zAssigns priority to the hierarchy dimension:

20. Hierarchy Prevailing - 2 zUseful when some agents are untrustworthy zDrawback: yOne has to consider the whole history of all higher ranked agents in order to accept/reject a rule from a lower ranked agent However, techniques are being developed to reduce the size of a MDLP

21. Inter- and Intra- Agent Relationships zThe above representations refer to a community of agents zBut they can be used as well for relating the several sub-agents of an agent A sub-agent Hierarchy

22. Intra- and Inter- Agent Example zPrevailing hierarchy for inter-agents zPrevailing time for sub-agents

23. Conclusions zWe’ve explored MDLP to combine knowledge from several agents and multiple dimensions zDepending on the situation, and relationships among agents, we’ve envisaged several classes of DAGs for their encoding  Based on this work, and on a language (LUPS) for specifying updates by means of transitions, we’ve launched into the design of an agent architecture MINERVA

24. Current Work  A MINERVA agent: yIs based on a modular design yIt has a common internal KB (a MDLP), concurrently manipulated by its specialized sub-agents zEvery agent is composed of specialized sub- agents that execute special tasks, e.g. yreactivity yplanning yscheduling ybelief revision ygoal management ylearning ypreference evaluation ystrategy