Modeling Belief Reasoning in Multi-Agent Systems* Thomas R. Ioerger Department of Computer Science Texas A&M University *funding provided by a MURI grant through DoD/AFOSR

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

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))

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)

(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)(> ?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)))) BOA Syntax consequent antecedent assume believer is ‘self’ context function procedural attachment

Prioritized Inference What conclusions can be drawn from KB? Update cycle (hence forward chaining): –KB’=update(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

Queries in BOA You get back a Vector of JareEnv’s 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)))) Can’t use variable for agent name: –(query (bel ?a (has-weapon ?a))) does not work!

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 KB’s beliefs can’t be used as conds in IF, WHILE...; use bq-if –method 2: replace JARE completely efficiency? - assert/retract used for many things in CAST

(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)) ))))))))

Concluding Remarks Ryan’s experience –useful for implementing Proactive Information Exchange in CAST-PM (Master’s thesis online) –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...)