Updating Agents

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A logic Based Asynchronous Multi-Agent System

• Luís Moniz Pereira
• Centro de Inteligência Artificial - CENTRIA
• Universidade Nova de Lisboa
• lmp_at_di.fct.unl.pt

• Pierangelo DellAcqua
• Ulf Nilsson
• Dept. of Science and Technology - ITN
• Linköping University
• pier_at_itn.liu.se
• ulfni_at_ida.liu.se

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Contribution
The paper presents an asynchronous multi-agent
system for logic based agents, and provides its
semantics. The interaction among agents is
expressed via a transition rule system that
characterizes the global behaviour of the system.
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Our agents

• We proposed a LP approach to agents that can
• Reason and React to other agents
• Prefer among possible choices
• Intend to reason and to act
• Update their own knowledge, reactions, and goals
• Interact by updating the theory of another agent
• Decide whether to accept an update depending on
  the requesting agent
• Abduce hypotheses to explain observations

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Framework

• This agent framework builds on the works
• Dynamic Logic Program - J. J. Alferes et al.
• KR98
• Updating Agents - P. DellAcqua L. M. Pereira
  MAS99
• Updates plus Preferences - J. J. Alferes L.
  M. Pereira JELIA00

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Enabling agents to update their KB

• Updating agent a rational, reactive agent that
  can dynamically change its own knowledge and
  goals.

• makes observations
• reciprocally updates other agents with goals and
  rules
• thinks (rational)
• selects and executes an action (reactive)

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Agents language

• Atomic formulae

A objective atoms not A default atoms
?C projects updates
??C

• Formulae

generalized rules
Li is an atom, an update or a negated update
A L1 Ù...Ù Ln not A L1 Ù...Ù Ln
Zj is a project
integrity constraint
false L1 Ù...Ù Ln Ù Z1 Ù...Ù Zm
active rule
L1 Ù...Ù Ln ? Z
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Projects and updates

• A project ?2C denotes the intention of some
  agent ?1 of proposing the updating the theory of
  agent ?2 with C.

• denotes an update proposed by ?1 of the
  current theory of some agent ?2 with C.

?1?C
fred?C
wilmaC
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Example active rules
Consider the following active rules in the theory
of an agent ?1.
A ? ?2 not B B ? ?1 C
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Agents language

• A project ?C can take one of the forms

? ( A L1 Ù...Ù Ln )
? ( not A L1 Ù...Ù Ln )
? ( false L1 Ù...Ù Ln Ù Z1 Ù...Ù Zm )
? ( L1 Ù...Ù Ln ? Z )
? ( ?- L1 Ù...Ù Ln )

• Note that a program can be updated with another
  program, i.e., any rule can be updated.

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Agents knowledge states

• Knowledge states represent dynamically evolving
  states of agents knowledge. They undergo change
  due to updates.

• 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 only
  affect the successor state the precondition of
  the action is evaluated in the current state and
  the postcondition updates the successor state.

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Abductive agents

• The initial theory of an agent ? is a tuple
  (P,A,R)
• - P is a set of generalized rules and integrity
  constraints.
• - A is a set of abducibles.
• - R is a set of active rules.

• An updating program is a finite set of updates.

• Let 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 ?.
• - UU1,, Us is a sequence of updating programs.

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Semantics of abductive agents

• Let ??s (T,U) and ? be the hypotheses assumed
• by ? at state s.
• An abductive stable model of ? at state s with
  hypotheses ? is a stable model of the program
  that extends T to contain
• - the updates in U,
• - the rules whose updates (in U) are neither
  distrusted nor rejected,
• - the projects of active rules with true body,
  and
• - the hypotheses in ?.

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Example abductive agent
Consider the following theory of an agent ?2.
A B A
T (P,?,R) (P,,) and P
??20 (T,)
M A, B
M is the unique abductive stable model of ? at
state s with hypotheses ?.
??21 (T,U1) with U1 ?1?not B
M A, not B, ?1?not B
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Multi-agent systems
A MAS consists of a number of agents acting
concurrently and transition rules that
characterize the global behaviour of the system.

• The interaction among the agents is asynchronous
  and modelled via buffers.

• A buffer U1,,Ui is a sequence of updating
  programs U1,,Ui (i ? 0).

• Each agent ? is equipped with a buffer ??s
  U1,,Ui

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Multi-agent systems

• A multi-agent system ? consists of a number of
  abductive agents ?1,,?n acting concurrently
• ? ??1s1 U1,,Ui ??nsn V1,,Vj
• together with the transition rules
• EXTP, INTP, and INCUP.

• ? characterizes a fixed society of evolving
  agents.

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Transition rules - EXTP
Let P?i be the set of executable projects of an
agent ?i
EXTP to execute external projects of ?1 if ?
(?2C) ? P?1 where ?1??2 and Vj1 ?1?C
for every ?2C ? P?1
??1s1 U1,,Ui ??2s2 V1,,Vj ?
??1s1 U1,,Ui ??2s2 V1,,Vj, Vj1
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Transition rules - INTP
INTP to execute internal projects of ? if ?
(?C) ? P? where Vi1 ??C for every ?C
? P?
??s V1,,Vi ? ??s V1,,Vi, Vi1
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Transition rules - INCUP
INCUP to incorporate updates into ? from its
buffer Let ??s (T,U1,,Us) where i?1
and ??s1 (T,U1,,Us,Us1) with Us1V1
??s V1,,Vi ? ??s1 V2,,Vi
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Multi-agent system at state s
A multi-agent system ? at state 0 (initial
configuration) ? 0 ??10 ??n0
A multi-agent system ? at state s ?s ??1s1
U1,, Ui ??nsn V1,, Vj where s
s1sn
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Multi-agent system at state s

• The MAS remains at the same state when the
  transition rule INTP or EXTP is applied.

• If INCUP is employed by agent ?i then the MAS
• ?s ??1s1 U1,, Ui ??isi T1, T2,,
  Tk ??nsn V1,, Vj
• moves to the next state

? s1 ??1s1 U1,, Ui ??isi1 T2,,
Tk ??nsn V1,, Vj
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Semantics of multi-agent systems

• The declarative semantics S? of MAS ?
  characterizes the relationship among the agents
  in ? and how the system evolves.

• The declarative semantics S?s of ? at state s is
  the set of all the sets of abductive stable
  models M?isi of every agent ?i in ? at state si
  with hypotheses ?i
• S?s M?1s1 ,, M?nsn

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Executable projects

• The set P? of executable projects of an agent ?
  contains the projects that occur in every
  abductive stable model of ? at state s with
  hypotheses ?.

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Example MAS
Consider the following two agents ?1 and ?2.
A A ? ?2 not B B ? ?1 C
T?1
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Example MAS
? 0 ??10 ??20
by EXTP
? 0 ??10 ??20 U1 with U1
?1?not B
by INCUP
? 1 ??10 ??21
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Example MAS
? 0 ??10 ??20
S?0 M?10, M?20
M?10 A, ?2 not B
P?1 ?2 not B
M?20 A, B
P?2
EXTP is applicable
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Example MAS
? 0 ??10 ??20 U1 with U1
?1?not B
S?0 M?10, M?20
INCUP is applicable
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Example MAS
? 1 ??10 ??21
M?10 A, ?2 not B
M?21 A, not B, ?1?not B
S?1 M?10, M?21
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Future work

• Investigate whether there are invariants and
  other properties of the MAS that can guarantee
  the behaviour of the entire system.

• How to represent organisational structures, and
  how to animate them with agents in a way that
  each agent will have a view of the organisational
  structure and the externally visible events.

• Ongoing implementation of our agent framework
• - its logical parts (logical reasoning,
  updating, preferring, etc.) are
• implemented in XSB Prolog, and
• - its non-logical parts are implemented in Java.
• - InterProlog is then used to interface XSB and
  Java.