Modeling Belief Reasoning

1
Modeling Belief Reasoning in Multi-Agent Systems
Thomas R. Ioerger Department of Computer
Science Texas AM University
funding provided by a MURI grant through
DoD/AFOSR
2
Motivation

• Many interactions in collaborative MAS require
  reasoning about beliefs of others
• There are no efficient, complete inference
  procedures for modal logics of belief
• Need a practical way of maintaining models of
  other agents beliefs
• Want it to work much like JARE
• Correct representation of unknown is a must
• New Issue how do you know what others believe?
  various reasons of different strength

3
Approach

• Define hierarchy of justification types
• including rules, defaults, persistence
• also incorporate observability
• a major source of info about others beliefs
• represent truth-values explicitly (T,F,?)
• update cycle (given current beliefs, senses...)
• BOA - Beliefs of Other Agents
• like JARE syntax, binding envs, API, query,
  assert
• forward-chaining
• single-level of nesting (bel joe (open door))

4
Justifications

• Rule types (with strengths for resolving
  conflicts)
• 8 - assertions (e.g. from shell, perceptions,
  messages)
• 7 - facts (static, never change truth value)
• 6 - direct observation (self)
• 5 - effects of actions (for whoever is aware of
  it...)
• 4 - inferences (by any agent)
• 3 - observability (of others)
• 2 - persistence (memory, certain beliefs
  persist)
• 1 - default assumptions (given no other evidence)

5
BOA Syntax
consequent antecedent

• (infer (bel ?a (not (tank empty ?car)) (bel ?a
  (running ?car))
• (persist (bel ?a (light-on ?room)))
• (obs ?a (light-on ?r) (in ?a ?r) (light-on ?r))
• (effect (running ?c) (do ?a (start ?c)) (have
  ?a (keys ?c)))
• (default (unknown (wumpus alive)))
• (init (val (num-arrows) 3))
• (infer (can-shoot)(val (num-arrows) ?x)(gt ?x 0))
• (obs (bel ?a (whether (light-on ?rm)) (in ?a
  ?rm))
• (fact (bel archer (value-of (num-arrows))))
• (fact (bel archer (whether (can-shoot))))

assume believer is self
context
function
procedural attachment
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Prioritized Inference

• What conclusions can be drawn from KB?
• Update cycle (hence forward chaining)
• KBupdate(KB,senses,action?,justification rules)
• If multiple rules relevant to a predicate can
  fire, want strongest to determine truth-value
• Must control order of firing, avoid premature...
• Semantics based on prioritized logic programs
• Brewka Eiter, Sakama Inoue, Delegrande
  Schaub
• Sort predicates by antecedent dependencies
• fire all for rules for least-dependent predicate
  first

no circularities allowed
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Queries in BOA

• You get back a Vector of JareEnvs with variable
  bindings for alternative solutions (as usual)
• (query (threat enemy-unit-17))
• (query (val (target enemy-unit-17) ?target))
• (query (bel sam (light-on room-1)))
• (query (bel joe (light-on ?r)))
• (query (bel joe (not (light-on room-1))))
• (query (bel joe (whether (light-on room-1))))
• Cant use variable for agent name
• (query (bel ?a (has-weapon ?a))) does not work!

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Integration into CAST (?)

• Useful for writing plans that depend on what
  others believe
• Challenges
• interaction with JARE and variable binding in
  conditions
• Preliminary experiments
• method 1 separate JARE and BOA KBs
• beliefs cant be used as conds in IF, WHILE...
  use bq-if
• method 2 replace JARE completely
• efficiency? - assert/retract used for many things
  in CAST

9

• (task inform-others-of-loc (?enemy)
• (seq
• (bupdate)
• (foreach ((agent ?ag))
• (if (cond (gunner ?ag) (not
  (radio-silence)))
• (bq-if (bel ?ag (unknown (val (loc
  ?enemy)))
• (bq-if (val (loc ?enemy) ?loc)
• (seq
• (send ?ag (val (loc ?enemy) ?loc))
• (bassert (bel ?ag (val (loc ?enemy)
  ?loc))
• ))))))))

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Concluding Remarks

• Ryans experience
• useful for implementing Proactive Information
  Exchange in CAST-PM (Masters thesis online)
• http//faculty.cs.tamu.edu/ioerger/thesi/rozich-
  thesis.pdf
• awkward to have to say that everything persists!
• Reflection on Belief Reasoning...
• not as expressive as Modal Logic, but efficient
• no nested beliefs
• the real issue is managing the various reasons
  for beliefs about others beliefs (observability,
  actions, inference, defaults, persistence...)