Formal Model of Joint Achievement Intention Mao Xinjun MOCA’02, Aarhus University, Aug 26-27, 2002 National Lab. for Parallel and Distributed Processing

1. Background(1/2) Joint Intention is an important concept model to investigate multi-agent system – Agent and multi-agent system provide more natural and effective method to develop complex software, and is a promising software development paradigm – As dependencies among agent ’ s actions, limitation of agents ’ capability, and distribution of resources, cooperation among agent is necessary in multi-agent – Joint intention is an important concept model to examine cooperation in multi-agent system – Joint intention is not just the sum of individual agent ’ s actions

1. Background(2/2) Evaluation of existing works on joint intention – Representative works Cohen, Levesque, Jenning, Nunes, Raimo …. – The semantics of joint intention is based on possible world model, and can not well capture the characteristics of action choice of agents – Model is complicated, as the semantics definition incorporates the modification strategy

2. What is joint Achievement Intention?(1/2) There are two kinds of joint intentions – joint achievement intention: achieve task jointly – joint maintenance intention: maintain condition jointly What is joint achievement intention? – Agents work together to achieve some preposition by joint behaviors – Representation of common tasks of agents

2. What is joint Achievement Intention?(2/2) Properties of joint achievement intention – Action choice rational choice for future joint behaviors of agents – Relativity mutual belief and cooperation – Satisfiable: achievable – Persistent Agents will not abandon joint intention at random – Consistent – Non-conflict one will not hinder another from achieving – Consistent with belief

3. Logical Model(1/2) Multi-agent system logical framework is composed of three parts: – Syntax – Model – Semantics Formal language is the extension of branch temporal logic CTL*

3. Logical Model(2/2)

4. Semantics Model(1/3) Individual Intention – M|  t AI(x,  ) iff M|  t Bel(x,  ) and (  S: S  C(x, t)  M |  s,t FBel(x,  )) Common Achievement Choice – MAI(x, y,  ) = AI(x,  )  AI(y,  )

4. Semantics Model(2/3) Mutual Achievement Belief – MAB(x, y,  )= MB(x, y, AI(x,  )  AI(y,  )) Weak Achievement Cooperation – WAC(x, y,  ) = (Bel(x,  )   Bel(x, Bel (y,  ))  AI(x, MB(x, y,  )))  (Bel(x, AG  )  Bel(x, Bel(y, AG  ))  AI(x, MB(x, y, AG  )))

4. Semantics Model(3/3) Mutual Achievement Cooperation – M |  t MAC(x, y,  ) iff (  S: S  C(x,t)  M |  s,t (MB(x, y, WAC(x, y,  )  WAC(y, x,  ))) Until  AI(x,  )) and (  S: S  C(y,t)  M |  s,t (MB(x, y, WAC(x, y,  )  WAC(y, x,  ))) Until  AI(y,  )) Joint Achievement Intention – JAI(x, y,  ) = MAI(x, y,  )  MAB(x, y,  )  MAC(x, y,  )

5. Model Properties(1/1) Specify and validate a number of important properties of joint achievement intention – Relativity – Satisfiable – Persistent – Consistent – Non-conflict – Consistent with belief

6. Conclusion and Future Work(1/2) Two kinds of joint intention are distinguished – Joint achievement intention – Joint maintenance intention, will appear in MALCEB'2002, 3rd International Symposium on Multi-Agent Systems, Large Complex Systems, and E- Businesses held in Germany – Present complete joint intention theory

6. Conclusion and Future Work(2) Investigate the interaction semantics and cooperation model based on the theory of joint intention Investigate the behaviors decision model of agent in multi-agent system

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