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Updating Agents

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Title: Updating Agents Author: s1 Last modified by: Lu s Moniz Pereira Created Date: 11/23/1999 1:01:53 PM Document presentation format: On-screen Show – PowerPoint PPT presentation

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Title: Updating Agents


1
A logical framework for modelling eMAS
  • Pierangelo DellAcqua
  • Dept. of Science and Technology - ITN
  • Linköping University, Sweden
  • Luís Moniz Pereira
  • Centro de Inteligência Artificial - CENTRIA
  • Universidade Nova de Lisboa, Portugal

PADL03
2
Motivation
  • To provide control over the epistemic agents in
    a Multi-Agent System (eMAS) the need arises to
  • - explicitly represent its organizational
    structure,
  • - and its agent interactions.
  • We introduce a logical framework F, suitable for
  • representing organizational structures of eMAS.
  • we provide its declarative and procedural
    semantics.
  • - F having a formal semantics, it permits us to
    prove
  • properties of eMAS structures.

3
Our agents
  • We have been proposing a LP approach to agents
    which can
  • Reason on their own or in collaboration
  • React to other agents and to the environment
  • Update their own knowledge, reactions, and goals
  • Interact by updating the theory of any other
    agent
  • Decide whether to accept an update subject to the
    requesting agent
  • Capture the representation of social evolution

4
Framework
  • This framework builds on the works
  • Updating Agents
  • P. DellAcqua L. M. Pereira - MAS99
  • Multi-dimensional Dynamic Logic Programming
  • L. A. Leite J. J. Alferes L. M. Pereira
    - CLIMA01
  • and subsequent ones.

5
Updating agents cycle
  • Updating agent a rational, reactive agent that
    dynamically changes its own knowledge and goals.
  • In its cycle, in some order, it

6
Logic framework
  • Atomic formulae

A atom not A default atom
generalized rule
Integrity constraints Action rules
7
Agents knowledge state sequences
  • Knowledge states represent dynamically evolving
    states of an agents knowledge. They undergo
    change due to updates (DLP).
  • Given the current knowledge state Ps , its
    successor knowledge state Ps1 is produced as a
    result of the occurrence of a set of parallel
    updates.
  • Update actions do not modify the current or any
    of the previous knowledge states.
  • They affect only the successor state the
    precondition of an action is evaluated in the
    current state, and its postcondition updates the
    successor state.

8
MDLP Motivating Example
  • Parliament issues law L1 at time t1
  • A local authority issues law L2 at time t2 gt 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)

9
Multi-Dimensional Logic Programming
  • 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.

10
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 agents evolving knowledge, along its
multiple dimensions ?
11
Two basic dimensions of a MAS
How to combine these dimensions into one DAG ?
12
Equal Role Representation
  • Assigns equal role to the two dimensions

13
Time Prevailing Representation
  • Assigns priority to the time dimension

14
Hierarchy Prevailing Representation
  • Assigns priority to the hierarchy dimension

15
Inter- and Intra- Agent Relationships
  • The above representations refer to a community of
    agents
  • But they can be employed as well for relating the
    several sub-agents of an agent

16
Intra- and Inter- Agent Example
  • Prevailing hierarchy for inter-agents
  • Prevailing time for sub-agents

17
MDLPs revisited
  • Def. MDLP Multi-Dimensional Logic Program
  • A MDLP ? is a pair (?D,D), where
  • D(V,E,w) is a
  • WDAG - Weighted directed acyclic graph
  • and,
  • ?DPv v?V is a set of generalized logic
    programs indexed by the vertices of D.

18
Weighted directed acyclic graphs
  • Def. Weighted directed acyclic graph (WDAG)
  • A weighted directed acyclic graph is a tuple
    D(V,E,w)
  • - V is a set of vertices,
  • - E is a set of edges,
  • - w E ? R maps edges into positive real
    numbers,
  • - no cycle can be formed with the edges of E.

We write v1 ? v2 to indicate a path from v1 to v2.
19
This paper MDLPs revisited
  • We generalize the definition of MDLP by
    assigning weights to the edges of a DAG.
  • In case of conflictual knowledge, incoming into
    a vertex v by two vertices v1 and v2, the weights
    of v1 and v2 may resolve the conflict.
  • If the weights are the same both
  • conclusions are false.
  • (Or, two alternative conclusions
  • can be made possible.)

a
v
0.1
a
not a
20
Path dominance
  • Def. Dominant path
  • Let a1 ? an be a path with vertices a1,a2,,an.
  • a1 ? an is a dominant path if there is no other
    path b1,b2,,bm such that
  • b1 a1, bm an, and
  • - ? i, j such that ai bj and w((ai-1,ai)) lt
    w((bj-1,bj)).

21
Example path dominance
a4
Let w((a5,a4)) lt w((a3,a4)). Then, a1, a2 , a3,
a4 is a dominant path.
a3
a5
a2
a1
22
Example formalizing agents
  • Epistemic agents can be formalized via MDLPs.
  • Example
  • Formalize three agents A, B, and C, where
  • B and C are secretaries of A
  • B and C believe it is not their duty to answer
    phone calls
  • A believes it the duty of a secretary to answer
    phone calls

23
Example formalizing agents
?A (?DA,DA) DA (v1,,wA) Pv1
answerPhone ? secretary ? phoneRing ?B
(?DB,DB) DB (v3,v4,(v4,v3),wB) wB((v4,v3))
0.6 Pv3 Pv4 phoneRing, secretary, not
answerPhone ?C (?DC,DC) DC
(v5,v6,(v6,v5),wC) wC((v6,v5)) 0.6 Pv5
and Pv6 Pv4
A
B
C
24
Logical framework F
  • Def. Logical framework F
  • A logical framework F is a tuple (A, L, wL)
    where
  • A?1,,?n is a set of MDLPs
  • L is a set of links among the ?i
  • and wL L ? R.

25
Semantics of F
  • Declarative semantics of F is stable model based.

Idea The knowledge of a vertex v1 overrides
the knowledge of a vertex v2 wrt. a vertex s iff
v1 prevails v2 wrt. s. Example Pv1
answerPhone Pv2 not answerPhone if
then MsanswerPhone
  • Procedural semantics based on a syntactic
    transformation.

26
Modelling eMAS
  • Multi-agent systems can be understood as
    computational
  • societies whose members co-exist in a shared
    environment.
  • A number of organizational structures have been
    proposed
  • - coalitions, groups, institutions,
    agent societies, etc.
  • In our approach, agents and organizational
    structures are
  • formalized via MDLPs, and glued together via
    F.

27
Modelling eMAS groups
  • A group is a system of agents constrained in
    their mutual
  • interactions.
  • A group can be formalized in F in a flexible
    way
  • - the agents behaviour can be restricted
    to different degrees.
  • - formalizing norms and regulations may
    enhance trustfulness of the group.

28
Example formalizing groups
  • Secretaries example
  • Formalize group G, of agents A, B, and C,
    where
  • B must operate (strictly) in accordance with A,
    while
  • C has a certain degree of freedom.

29
Example formalizing groups
F (A,L,wL) A ?A,?B,?C,?G ) L (v1,v2),
(v2,v3), (v2,v5) wL((v1,v2)) wL((v2,v5))
0.5 wL((v2,v3)) 0.7
?G (?DG,DG) DG (v2,,wG) Pv2
G
F
30
Example semantics
Model of agent B Mv3 phoneRing, secretary,
answerPhone
Model of agent C Mv5 phoneRing, secretary,
not answerPhone
31
Conclusions and future work
  • Novel logical framework to model structures of
    epistemic
  • agents
  • - declarative semantics is stable model
    based,
  • - procedural semantics based on a syntactical
    transformation.
  • To represent F within the theory of each agent
  • - to empower the agents with the ability to
    reason about and modify
  • the agents structure,
  • - to handle open societies where agents can
    enter/leave the system.

32
The End
33
Prevalence
  • Def. Prevalence wrt. a vertex an
  • Let a1 ? an be a dominant path with vertices
    a1,a2,,an. Then,
  • 1. every vertex ai prevails a1 wrt. an (1lt i ?
    n).
  • 2. if there exists a path b1 ? ai with vertices
    b1,,bm,ai and
  • w((ai-1,ai)) lt w((bm,ai)), then every vertex
    bj prevails a1 wrt. an.

1.
2.
a1 ? ai
a1 ? bj
an
an
34
Links
  • Def. Link
  • Given two WDAGs, D1 and D2, a link is an edge
    between a vertice of D1 and a vertice D2.

35
Joining WDAGs
  • Def. Link
  • Given two WDAGs D1 and D2, a link is an edge
    between vertices of D1 and D2.
  • Def. WDAGs joining
  • Given n WDAGs Di (Vi,Ei,wi), a set L of
    links, and a function
  • wL L ? R, the joining ?(D1,, Dn,L,wL) is
    the WDAG D(V,E,w) obtained by the union of all
    the vertices and edges, and
  • w(e)

wi(e) if e?Ei wL(e) if e?L
36
Joined MDLP
  • Def. Joined MDLP
  • Let F(A,L,wL) be a logical framework.
  • Assume that A?1,,?n and each ?i(?Di,Di).
  • The joined MDLP induced by F is the WDAG ?(?D,D)
    where
  • - D ?(D1,, Dn,L,wL) and
  • - ?D ?i ?Di

37
Stable models of MDLP
  • Def. Stable models of MDLP
  • Let ?(?D,D) be a MDLP, where D(V,E,w) and
    ?DPv v?V. Let s ?V.
  • An interpretation M is a stable model of ? at s
    iff

M least( X ? Default(X, M) ) where
Q ??v ? s Pv Reject(s,M) r ? Pv2 ?r?
Pv1, head(r)not head(r), M body(r),
X Q - Reject(s,M) Default(X,M) not
A ?? (ABody) in X and M Body
38
Stable models of F
  • Def. Stable models of F
  • Let F(A,L,wL) be a logical framework and? the
    joined MDLP induced by F.
  • M is a stable model of F at state s iff M is a
    stable model of ? at state s.
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