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Explicit / Implicit Belief Atoms

Explicit / Implicit Belief Atoms. Explicit Belief Atoms of view a  Expl (B X , a )  BA ( a) for each a  B n if a  B * B n then Expl (B X , a ) =  for each B X. B X. Explicit / Implicit Belief Atoms. Explicit Belief Atoms of view a

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Explicit / Implicit Belief Atoms

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  1. Explicit/Implicit Belief Atoms • Explicit Belief Atoms of view a • Expl(BX,a ) BA(a)for each a Bn • if a  B* \Bn thenExpl(BX,a ) =  for each BX BX

  2. Explicit/Implicit Belief Atoms • Explicit Belief Atoms of view a • Expl(BX,a ) BA(a) for each a Bn • if a  B* \Bn thenExpl(BX,a ) =  for each BX • Implicit Belief Atomsof view a  Bn •  Impl(BX,a ) = BA(a) \Expl(BX,a ) • if a  B* \Bn thenImpl(BX,a ) =  for each BX BX BX BX

  3. MultiAgent Finite State Machine Definition: Let {La } be a family of MATL languages on {Pa }. A MAFSM F= {Fa } is a total recursive function such that: • Fa is a (set of ) Finite State Machines on the MATL language on: • Paand •  Expl(BX,a) for eacha Bn ( B* ) BX

  4. MultiAgent Finite State Machine Definition: Let {La } be a family of MATL languages on {Pa }. A MAFSM F= {Fa } is a total recursive function such that: • Fa is a (set of ) Finite State Machines on the MATL language on: • Paand •  Expl(BX,a) for eacha Bn ( B* ) • Fe BX

  5. MultiAgent Finite State Machine Definition: Let {La } be a family of MATL languages on {Pa }. A MAFSM F= {Fa } is a total recursive function such that: • Fa is a (set of ) Finite State Machines on the MATL language on: • Paand •  Expl(BX,a) for eacha Bn ( B* ) • Fe • ifaB* \BnthenFa=  BX

  6. Satisfiability in a MAFSM Definition: Let {La }be a family of MATL languages on {Pa } and F= {Fa} a MAFSM and fa formula of La: • F,a, f, s BXy ifff’ FaBXand sfreachable from J F,aBX, f, s Argexpl(BX, a, s)  y where Argexpl(BX,a,s)= {f| BXf L(s)andBXf Expl(BX,a)}

  7. Satisfiability in a MAFSM Definition: Let {La }be a family of MATL languages on {Pa } and F= {Fa} a MAFSM and fa formula of La: • F,a, f, s BXy ifff’ FaBXand sfreachable from J F,aBX, f, s Argexpl(BX, a, s)  y where Argexpl(BX,a,s)= {f| BXf L(s)andBXf Expl(BX,a)}

  8. Satisfiability in a MAFSM Definition: Let {La }be a family of MATL languages on {Pa } and F= {Fa} a MAFSM and fa formula of La: • F,a, f, s BXy ifff’ FaBXand sf reachable from J F,aBX, f, s Argexpl(BX, a, s)  y where Argexpl(BX,a,s)= {f| BXf L(s)andBXf Expl(BX,a)} • F,a, f, s y as for FSMs satisfiability

  9. MAFSM and Consistency e BAf BA(f) BA f f

  10. MAFSM and Consistency e BAf BA(f) BA f f

  11. Consistent MAFSM Definition:A MAFSM Fis aconsistent MAFSM if and only if for every view a and every reachable state sf(Fa): • ifBXf  Expl(BX,a) andBXf L(s), then for some f FaBX and reachablestate s of f F,aBX, f, s Argexpl(BX, a, s)  f

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