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Combining Societal Agents’ Knowledge. João Alexandre Leite José Júlio Alferes Luís Moniz Pereira. CENTRIA – Universidade Nova de Lisboa. AGP 2001. Universidade de Évora, 26-28 Sept. 2001. Summary. Goals and Motivation Overview of MDLP ( M ulti- D imensional LP )

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Combining societal agents knowledge

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


  • 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


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.

Motivation 1
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

Motivation 2
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.

Dynamic lp
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

Mdlp motivating example





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)


  • 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

Generalized logic programs
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

Mdlp definition
MDLP - definition

  • Definition:

    A Multi-Dimensional Dynamic Logic Program, P, is a pair



    • D=(V,E) is an acyclic digraph

    • PD={PV : v  V} is a set of generalized logic programs indexed by the vertices of D

Mdlp semantics 1





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= js Pi:

Ms= least( [Ps – Reject(s, Ms)]  Defaults (Ps, Ms) )

Mdlp semantics 2

Defaults (Ps, Ms)={not A | $r Ps: head(r)=A  Ms |=body(r)}





MDLP - semantics 2

Ms= least( [Ps – Reject(s, Ms)]  Defaults (Ps, Ms) )


Reject(s, Ms) =

{r Pi | r’ Pj , ijs, head(r)=not head(r’)  Ms |=body(r’)}

Mdlp for agents
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 ?

Two basic dimensions of a multi agent system

Hierarchy of agents

Temporal evolution of one agent

Two basic dimensions of a multi-agent system

How to combine these dimensions into one DAG ?

Equal role representation
Equal Role Representation

  • Assigns equal role to the two dimensions:

Equal role 2
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

Time prevailing representation
Time Prevailing Representation

  • Assigns priority to the time dimension:

Time prevailing 2
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

Hierarchy prevailing representation
Hierarchy Prevailing Representation

  • Assigns priority to the hierarchy dimension:

Hierarchy prevailing 2
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

Inter and intra agent relationships

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

Intra and inter agent example
Intra- and Inter- Agent Example

  • Prevailing hierarchy for inter-agents

  • Prevailing time for sub-agents


  • 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

Current work
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