Dynamic Logic Programming for Agents' Societal Knowledge Representation

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

2. Summary • Goals and Motivation • Overview of MDLP (Multi-Dimensional LP) • Inter- and Intra- Agent Societal Viewpoints • Equal Role Representation • Time Prevailing Representation • Hierarchy Prevailing Representation • Combining Inter- and Intra- Agent’s viewpoints • Conclusions and Current work

3. Goal Explore the applicability of MDLP to represent agents’ view of societal knowledge dynamics • 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.

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

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

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

7. L2 L1 L1 L2 MDLP Motivating Example • Parliament issues law L1 at time t1 • A local authority issues law L2 at time t2 > t1 • Parliamentary laws override local laws, but not vice-versa: • More recent laws have precedence over older ones: • How to combine these two dimensions of knowledge precedence? • DLP with Multiple Dimensions (MDLP)

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

9. Generalized Logic Programs • To represent negative info in LP updates, we need LPs allowing not in heads • Programs are sets of generalized LP rules: A ¬ B1,…, Bk, not C1,…,not Cm not A ¬ B1,…, Bk, not C1,…,not Cm • The semantics is a generalization of SMs

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

11. j1 j2 j3 s MDLP - semantics 1 • Definition: Let P=(PD,D) be a MDLP. An interpretation Ms is a stable model of the multi-dimensional update at state sV iff, where Ps= is Pi: Ms= least( [Ps – Reject(s, Ms)]  Defaults (Ps, Ms) )

12. Defaults (Ps, Ms)={not A | $r Ps: head(r)=A  Ms |=body(r)} j1 j2 j3 s MDLP - semantics 2 Ms= least( [Ps – Reject(s, Ms)]  Defaults (Ps, Ms) ) where: Reject(s, Ms) = {r Pi | r’ Pj , ijs, head(r)=not head(r’)  Ms |=body(r’)}

13. MDLP for Agents • Flexibility, 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. Hierarchy of agents Temporal evolution of one agent Two basic dimensions of a multi-agent system How to combine these dimensions into one DAG ?

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

16. Equal Role - 2 • In legal reasoning: • Lex Superior : rules issued by a higher authority override those of a lower one • Lex Posterior : more recent rules override older ones • It potentiates contradiction: • There are many pairs of unrelated programs

17. Time Prevailing Representation • Assigns priority to the time dimension:

18. Time Prevailing - 2 • Useful in very dynamic situations, where competence is distributed, i.e. ¹ agents normally provide rules about ¹ literals • Drawback: • It requires all agents to be fully trusted, since all newer rules override older ones irrespective of their mutual hierarchical position

19. Hierarchy Prevailing Representation • Assigns priority to the hierarchy dimension:

20. Hierarchy Prevailing - 2 • Useful when some agents are untrustworthy • Drawback: • One 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. A sub-agent Hierarchy Inter- and Intra- Agent Relationships • The above representations refer to a community of agents • But they can be used as well for relating the several sub-agents of an agent

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

23. Conclusions • We’ve explored MDLP to combine knowledge from several agents and multiple dimensions • Depending 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: • Is based on a modular design • It has a common internal KB (a MDLP), concurrently manipulated by its specialized sub-agents • Every agent is composed of specialized sub-agents that execute special tasks, e.g. • reactivity • planning • scheduling • belief revision • goal management • learning • preference evaluation • strategy