Reasoning About Beliefs, Observability, and Information Exchange in Teamwork

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Reasoning About Beliefs, Observability, and
Information Exchange in Teamwork
Thomas R. Ioerger Department of Computer
Science Texas AM University
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The Need for Reasoning about Beliefs of Others
in MAS
The traditional interpretation of BDI Beliefs,
Desires, and Intentions of self What about
beliefs of others? - important for agent
interactions
Decision-making depends on beliefs Does the
other driver see me? Does the other driver
seem to be in a hurry? Did the other
driver see who arrived at the intersection
first? Does the other driver see my turn
signal? Does other driver allow gap to open
for changing lanes?
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The Need for Reasoning about Beliefs of Others
in Teams

• Proactive Information Exchange
• automatically share info with others
• makes teamwork more efficient
• infer relevance from pre-conditions
• of others goals in team plan
• should try to avoid redundancy

A
B
Ideal conditions to send message Bel(A,I) ?
Bel(A,?Bel(B,I)) ?Bel(A,Goal(B,G)) ?
Precond(I,G) ??Bel(B,I) ???Done(B,G)
?Bel(B,I) ????Done(B,G)
team-plan catch-thief (do B (turn-on
light-switch)) (do A (enter-room)) (do A
(jump-on thief))
should B tell A the light is now on???
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Observability

• Obs(a,f,y) - agent a will observe f under
  conditions y (i.e. the context)
• example ?x Obs(A1,broken(x),holding(A1,x))
• Similarity to VSK logic (Wooldridge)
• V(f)accessible, S(f)perceives, K(f)knows
• Obs(a,f,y) ? y?Sa(f)
• Assumption agents believe what they see Sa(f)
  ? Ka(f)
• Small differences
• we use Belief instead of Knowledge Sa(f) ?
  Ba(f)
• B is weak-S5 modal logic (KD45, without T axiom,
  B(f) f)
• only believe whether f is true (or false)
• Obs(a,f,y) ? y?(f ? Sa(f)) ? (?f ? Sa(?f))

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Belief Database
tuples ltA,F,Vgt A?agents F?facts
(propositions) V?valuations valuations
true,false,unkown,whether unknown ?
?true??false whether ? true?false Update
Algorithm

• ltA1,in(gold,room1),truegt
• ltA1,lightOn(room1),falsegt
• ltA1,in(A1,room1),truegt
• ltA1,in(A1,room2),falsegt
• ltA1,in(A2,room1),falsegt
• ltA1,in(A2,room2),truegt
• ltA2,in(gold,room1),unknowngt
• ltA2,lightOn(room1),falsegt
• ltA2,in(A1,room1),truegt
• ltA2,in(A1,room2),falsegt
• ltA2,in(A2,room1),whethergt
• ltA2,in(A2,room2),whethergt
• ...
• ...

Di1Update(Di,P,J)
justification rules J
perceptions P
Di
Di
Di1
Update
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Justifications for Belief Updates

• Justification type Representation
  Priority Notes
• direct observation (sense s) ? y ? f 6 self
  only
• observability (obs a f y) 5 obs of others
• effects of actions (effect x q) 4 if aware of
  x
• inferences (infer f y) 3 y ? f
• memory (persist f) 2 f true OR false
• assumptions (default f) 1

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Belief Update Algorithm

• updating beliefs is not so simple...
• Prioritized logic programs
• Horn clauses annotated with strengths
• semantics based models in which facts are
  supported by strongest rule
• implementation
• (assuming rules are not cyclic...)
• create DAG of propositions
• topoligically sort P1..Pn
• determine true values in order
• Pi depends at most on truth
• values of P1..Pi-1

A?B?C (1) G??C (2) C??D?E (1) A?F??E (3)
E
C D
A B F G
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PIEX Algorithm

• PIEX Proactive Information EXchange
• given belief database D, perceptions P, and
• justification rules J
• D?BeliefUpdateAlg(D,P,J)
• for each agent Ai ? Agents and G ? Goals(Ai)
• for each C ? PreConditions(G)
• if C is a positive literal, let v?true
• if C is a negative literal, let v?false
• if ltAi,C,not(v)gt ? D or ltAi,C,unknowngt ?
  D
• Tell(Ai,C,v)
• Update(D,ltAi,C,vgt)

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Experiment Wumpus Roundup!
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Issues

• Current formalism does not allow for nested
  beliefs
• Bel(A1,Bel(A2,lightOn(room5)))
• Bel(A1,Bel(A2,Bel(A1,lightOn(room5))))
• see Isozaki and Katsuno (1996)
• We are working on an representation of modal
  logic in Prolog
• allows nested beliefs and rules
• backward-chaining rather than forward (e.g.
  UpdateAlg)
• of course, not complete
• Better reasoning about knowledge of actions
• assert pre-conds before effects? uncertainty of
  do-er/time?

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Conclusions

• 1. Modeling beliefs of others is important for
  multi-agent interactions
• 2. Observability is a key to modeling others
  beliefs
• 3. Must be integrated properly with other
  justifications, such as inference, persistence...
• 4. Different strengths can be managed using
  prioritized inference (Prioritized Logic
  Programs)
• 5. Proactive information exchange can improve
  performance of teams
• 6. Message traffic can be intelligently reduced
  by reasoning about beliefs