Explicit Belief Atoms of view a

1
Explicit / Implicit Belief Atoms

• Explicit Belief Atoms of view a
• ? Expl(BX,a ) ? BA(a) for each a ?Bn
• if a ? B \Bn then Expl(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 then Expl(BX,a ) ? for each BX
• Implicit Belief Atoms of view a ? Bn
• ? Impl(BX,a ) BA(a) \ ? Expl(BX,a )
• if a ? B \Bn then Impl(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
• Pa and
• ? Expl(BX,a) for each a ? 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
• Pa and
• ? Expl(BX,a) for each a ? 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
• Pa and
• ? Expl(BX,a) for each a ? Bn ( ? B )
• Fe? ?
• if a ? B \Bn then Fa ?

BX
6
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
• F,a, f, s ? BX y iff ?f ? FaBX and s??f?
  reachable from J?
• F,aBX, f?, s? ? Argexpl(BX, a, s) ? y
• where
• Argexpl(BX,a,s) f BXf ? L(s) and BXf ?
  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 f a
  formula of La
• F,a, f, s ? BX y iff ?f ? FaBX and s??f?
  reachable from J?
• F,aBX, f?, s? ? Argexpl(BX, a, s) ? y
• where
• Argexpl(BX,a,s) f BXf ? L(s) and BXf ?
  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 f a
  formula of La
• F,a, f, s ? BX y iff ?f ? FaBX and s??f?
  reachable from J?
• F,aBX, f?, s? ? Argexpl(BX, a, s) ? y
• where
• Argexpl(BX,a,s) f BXf ? L(s) and BXf ?
  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 F is a consistent MAFSM if
  and
• only if for every view a and
  every reachable state
• s?f (?Fa)
• if BX f ? Expl(BX,a) and BX f ?L(s),
• then for some f? ?FaBX and reachable state s?
  of f?
• F,aBX, f?, s? ? Argexpl(BX, a, s) ? ?f