Explicit Implicit Belief Atoms Explicit Belief Atoms of
Explicit / Implicit Belief Atoms ê Explicit Belief Atoms of view a ç Expl(BX, a ) BA(a) for each a Bn BX ç if a B* Bn then Expl(BX, a ) = for each BX
Explicit / Implicit Belief Atoms ê Explicit Belief Atoms of view a ç Expl(BX, a ) BA(a) for each a Bn BX ç ê if a B* Bn then Expl(BX, a ) = for each BX Implicit Belief Atoms of view a Bn ç )BX ç Impl(BX, a ) = BA(a) Expl(BX, a BX if a B* Bn then Impl(BX, a ) = for each BX
Multi. Agent 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: ê ç ç Pa and BX Expl(BX, a) for each a Bn ( B* )
Multi. Agent 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: ê ç ç Pa and BX ê Expl(BX, a) F e for each a Bn ( B* )
Multi. Agent 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: ê ç ç Pa and Expl(BX, a) for each a Bn ( B* ) BX ê F e ê if a B* Bn then Fa=
Satisfiability in a MAFSM Definition: Let {La } be a family of MATL languages on {Pa } and F = {Fa } a MAFSM and f a formula of La : ê F, a, f, s BX reachable from J F, a. BX, f , s y iff f’ Fa. BX and s f Argexpl(BX, a, s) y where Argexpl(BX, a, s)= {f | BXf L(s) and BXf Expl(BX, a)}
Satisfiability in a MAFSM Definition: Let {La } be a family of MATL languages on {Pa } and F = {Fa } a MAFSM and f a formula of La : ê F, a, f, s BX reachable from J F, a. BX, f , s y iff f’ Fa. BX and s f Argexpl(BX, a, s) y where Argexpl(BX, a, s)= {f | BXf L(s) and BXf Expl(BX, a)}
Satisfiability in a MAFSM Definition: Let {La } be a family of MATL languages on {Pa } and F = {Fa } a MAFSM and f a formula of La : ê F, a, f, s BX reachable from J F, a. BX, f , s y iff f’ Fa. BX and s f Argexpl(BX, a, s) y where Argexpl(BX, a, s)= {f | BXf L(s) and BXf Expl(BX, a)} ê F, a, f, s y as for FSMs satisfiability
MAFSM and Consistency e B Af BA( f) f f BA
MAFSM and Consistency e B Af BA( f) f f BA
Consistent MAFSM Definition: A MAFSM F is a consistent MAFSM if and only if for every view a and every reachable state s f ( Fa): ê if BX f Expl(BX, a) and BX f L(s), then for some f Fa. BX and reachable state s of f F, a. BX, f , s Argexpl(BX, a, s) f
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