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adaptive by hedongchenchen

VIEWS: 6 PAGES: 34

									       Adaptive Reasoning for
        Cooperative Agents
      Luís Moniz Pereira Alexandre Pinto

      Centre for Artificial Intelligence – CENTRIA
            Universidade Nova de Lisboa

INAP’09, 5-7 November                     Évora, Portugal
                  Summary - 1
• Explicit affirmation and negation plus a 3rd logic value
  of undefined, is useful in situations where decisions
  must be taken based of scarce, ambiguous, or
  contradictory information

• In a 3-valued setting, we consider agents that learn
  definitions for a target concept and its opposite,
  taking both positive and negative examples as
  instances of the two classes
                 Summary - 2
• A single agent exploring an environment can gather
  only so much information, which may not suffice to
  find good explanations
• A cooperative multi-agent strategy, where each agent
  explores part of the environment and shares its
  findings, provides better results
• We employ a distributed genetic algorithm framework,
  enhanced by a Lamarckian belief revision operator
• Agents communicate explanations—coded as belief
  chromosomes—by sharing them in a common pool
                  Summary - 3
• Another way of interpreting this communication is via
  agent argumentation
• When taking in all arguments to find a common
  ground or consensus, we may have to revise
  assumptions in each argument
• A collaborative viewpoint results: Arguments are put
  together to find 2-valued consensus on conflicting
  learnt concepts, within an evolving genetic pool, so as
  to identify “best” joint explanations to observations
Learning Positive and Negative Knowledge

– Autonomous agent: acquisition of information by
  means of experiments
– Experiment:
   • execution of an action
   • evaluation of the results with respect to the
     achievement of a goal
   • positive and negative results
– Learning general rules on actions:
   • distinction among actions with a positive, negative or
     unknown or undefined outcome
      2-valued vs. 3-valued Learning

– Two values:
   • bottom-up generalization from instances
   • top-down refinement from general classes
– Three values:
   • learning a definition both for the concept and its
     opposite

         - -                - -               - -
    -- - - - -         -- - - - -        -- - - - -


   + ++ + +           + ++ + +          + ++ + +
     + ++               + ++              + ++
                 a                  b                 c
     Learning in a 3-valued Setting

– Extended Logic Programs (ELP):
   with explicit negation “ A”
– Clauses of the form
   L0  L1, ... , Lm, not Lm+1, ... , not Lm+n
   where Li can be either A or A
– Explicit representation of negative information
    fly(X)  penguin(X).
– Three logical values: true, false, unknown or
  undefined
                Problem definition

Given
   •   a set P of possible ELP programs (bias)
   •   a set E+ of positive examples
   •   a set E- of negative examples
   •   a consistent extended logic program 
       (background knowledge)

Use learning to find an ELP, P  P such that
   P   | E+ P   | E- (completeness)
   P   | L- P   | L+ L  E+  E- (consistency)
                 Intersection of definitions

                 p                             p




            E+                            E-




Exceptions to the       Unseen atoms
negative concept:                        Exceptions to the
positive examples                        positive concept:
                                         negative examples
               Unseen atoms

– Unseen atoms which are both true and false
  are classified as unknown or undefined:
     p(X)  p+(X), not p(X).
    p(X)  p-(X), not p(X).

– If the concept is true and its opposite
  undefined, then it is classified as true:
     p(X)  p+(X), undefined( p(X) ).
    p(X)  p-(X), undefined( p(X) ).
             Training set atoms


– They must be classified according to the
  training set

– Default literals, representing non-abnormality
  conditions, are added to rules:

    p(X)  p+(X), not abp (X), not p(X).
   p(X)  p-(X), not abp (X), not p(X).
                    Example: knowledge

B: bird(a).              has_wings(a).
   jet(b).               has_wings(b).
   angel(c).             has_wings(c).          has_limbs(c).
   penguin(d).           has_wings(d).          has_limbs(d).
   dog(e).                                      has_limbs(e).
   cat(f).                                      has_limbs(f).
E+ = { flies(a) }        E- = { flies(d), flies(e) }

           flies+   E+                                  E-          flies-



                          a        b        c     d    e        f
            Example: learned theory

     flies+(X)  has_wings(X).
     flies-(X)  has_limbs(X).
     flies(X)  flies+(X), not abflies+(X), not flies(X).
    flies(X)  flies-(X), not flies(X).
     abflies+(d).
     flies(X)  flies+(X), undefined( flies(X) ).
    flies(X)  flies-(X), undefined( flies(X) ).

Generalizing exceptions we obtain:
     abflies+(X)  penguin(X).
Least General vs. Most General Solutions

– Bottom-up methods:
  • Search from specific to general:
       Least General Solution (LGS)
  • GOLEM (RLGG), CIGOL (Inverse Resolution)

– Top-down methods:
  • Search from general to specific:
       Most General Solution (MGS)
  • FOIL, Progol
    Criteria for chosing the generality

– Risk that can derive from a classification error
   high risk              LGS
   low risk               MGS


– Confidence in the set of negative examples
   high confidence           MGS
   low confidence            LGS
                    Generality of Solutions
B:       bird(X)  sparrow(X).
         mammal(X)  cat(X).
         sparrow(a).          cat(b).      bird(c).   mammal(d).

E+ = { flies(a) }      E– = { flies(b) }

       fliesMGS(X)  bird(X).
       fliesLGS(X)  sparrow(X).
     fliesMGS(X)  cat(X).
     fliesLGS(X)  mammal(X).
                Of Beggars and Attackers


beggar2   beggar1                     attacker2
                                                  attacker1
   Example: Mixing LGS and MGS (1)

– Concept of attacker  maximize the concept and
  minimize its opposite:
    attacker1(X)  attacker +MGS(X), not attacker1(X).
   attacker1(X)  attacker –LGS(X), not attacker1(X).

– Concept of beggar —give only to those appearing to
  need it  minimize the concept and maximize its
  opposite:
    beggar1(X)  beggar +LGS(X), not beggar1(X).
   beggar1(X)  beggar –MGS(X), not beggar1(X).
   Example: Mixing LGS and MGS (2)

– However, rejected beggars, may turn into attackers 
  maximize the concept and minimize its opposite:
    beggar2(X)  beggar +MGS(X), not beggar2(X).
   beggar2(X)  beggar –LGS(X), not beggar2(X).

– Concepts can be used to minimize the risk when
  carrying a lot of money:
     run  lot_of_money, attacker1(Y), not beggar2(Y).
    run  give_money.
     give_money  beggar1(Y).
     give_money  attacker1(Y), beggar2(Y).
    Example: Mixing LGS and MGS (3)
– When carrying little money, one may prefer to risk
  being beaten up.
  Therefore one wants to relax attacker1 but not so much
  as to use attacker –MGS :

   run  little_money, attacker2(Y).
     attacker2(X)  attacker +LGS(X), not attacker2(X).
   attacker2(X)  attacker –LGS(X), not attacker2(X).
                  Abduction
• Consider rule: a => b

• Deduction: from a conclude b

• Abduction: knowing or observing b, assume a as its
  hypothetical explanation

• From theory + observations find abductive models —
  the explanations for observations
        Distributing Observations
• Code observations as Integrity Constraints (ICs):
                <-- not some_observation
• Find abductive explanations for observations

• Create several agents, give each the same base theory
  and a subset of the observations
• Each agent comes up with alternative abductive
  explanations for its own ICs. These need not be
  minimal sets of hypotheses
    Choosing the Best Explanation
• “Brainstorming” is used for solving complex
  problems
• Each participant contributes by adding ideas
  (abducibles) to a common idea pool, shared by all
• Ideas are mixed, crossed, mutated, and selected
• Solutions arise from pool by iterating this
  evolutionary process
• Our work is inspired on the evolution of alternative
  ideas and arguments to find collaborative solutions
         Lamarckian Evolution - 1
• Lamarckian evolution = meme evolution

• “meme” is cognitive equivalent of gene

• In genetic programming Lamarckian evolution has
  proven a powerful concept

• There are GAs that include, additionally, a logic-based
  Lamarckian belief revision operator, where
  assumptions are coded as memes
        Lamarckian Evolution - 2
• Lamarckian operator (L-op)  Darwinian ones (D-ops)
• L-op modifies chromosomes coding beliefs to improve
  fitness with experience, rather than randomly
• L-op and D-ops play distinct roles
• L-op employed to bring chromosomes closer to a
  solution, by belief revision
• D-ops randomly produce alternative belief
  chromosomes to deal with unencountered situations,
  by interchanging memes
  Specific Belief Evolution Method
• In traditional multi-agent problem solving, agents
  benefit from others’ knowledge & experience by
  message-passing

• Our new method: knowledge & experience coded as
  memes, and exchanged by crossover

• Crucial: logic-based belief revision is used to modify
  belief assumptions (memes) based on individual agent
  experience
              Fitness Functions
• Various fitness functions can be used in belief
  revision. The simplest is:
             Fitness( ci ) = (ni /n) / (1 + NC )
  where
     - ni is number of ICs satisfied by chromosome ci
     - n is total number of ICs
     - NC is number of contradictions
              depending on chromosome ci
 Assumptions & Argumentation - 1
• Assumptions are coded as abducible literals in LPs

• Abducibles are packed together in chromosomes

• Evolutionary operators —crossover, mutation,
  revision, selection— are applied to chromosomes

• This setting provides means to search for
  evolutionary consensus from initial assumptions
 Assumptions & Argumentation - 2
• 3-valued contradiction removal presented before
  (with undefined value) is superficial

• Removes contradiction p(X) & ¬p(X) by forcing a
  3-valued semantics, not looking into reasons why
  both hold

• Improvement relies on principles of argumentation:
     find arguments supporting p(X) — or ¬p(X) —
     and change some of their assumptions
         Collaborative Opposition
• Challenging environment of Semantic Web is a ‘place’
  for future intelligent systems to float in
• Learning in 2- or in 3-values are open possibilities
• Knowledge & Reasoning shared and distributed
• Opposing arguments will surface from agents
• Need to know how to reconcile opposing arguments
• Find 2-valued consensus as much as possible
• Least commitment 3-valued consensus are not enough
  Argumentation & Consensus - 1
• The non-trivial problem we addressed was that of
  defining 2-valued complete models, consistent with
  the 3-valued preferred maximal scenarios of Dung

• The resulting semantics —Approved Models— is a
  conservative extension to the well-known Stable
  Models semantics, in that every SM is an Approved
  Model
   Argumentation & Consensus - 2
• Approved Models are guaranteed to exist for every
  Normal Logic Program (NLP), whereas SMs are not

• Examples show NLPs with no SMs can usefully model
  knowledge

• The guarantee is crucial in program composition of
  knowledge from diverse sources

• Model existence warrant also crucial after external-
  or self-updating NLPs
   Argumentation & Consensus - 3
• Start by merging all opposing abductive arguments
• Draw conclusions from program + single merged
  argument
• If contradictions arise: non-deterministically choose
  one assumption of single argument and revise its
  truth value
• Iteration finds the non-contradictory arguments
• Evolutionary method presented implements yet
  another mechanism to find consensual non-
  contradictory arguments
Thank you for your attention!

								
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