Unawareness In Multi-Agent Systems with Partial Valuations Line van - PowerPoint PPT Presentation

Unawareness In Multi-Agent Systems with Partial Valuations Line van den Berg, Manuel Atencia and J´ erˆ ome Euzenat { line.van-den-berg,manuel.atencia,jerome.euzenat } @inria.fr https://moex.inria.fr Line van den Berg (UGA & Inria) Unawareness with Partial Valuations 1 / 10

Summary Introduction: why awareness? Line van den Berg (UGA & Inria) Unawareness with Partial Valuations 2 / 10

Summary Introduction: why awareness? Related work Line van den Berg (UGA & Inria) Unawareness with Partial Valuations 2 / 10

Summary Introduction: why awareness? Related work Agent awareness using partial valuations Line van den Berg (UGA & Inria) Unawareness with Partial Valuations 2 / 10

Summary Introduction: why awareness? Related work Agent awareness using partial valuations Raising awareness Line van den Berg (UGA & Inria) Unawareness with Partial Valuations 2 / 10

ñ Introduction: why awareness? Agents represent their knowledge in different ways Line van den Berg (UGA & Inria) Unawareness with Partial Valuations 3 / 10

ñ Introduction: why awareness? Agents represent their knowledge in different ways Communication Line van den Berg (UGA & Inria) Unawareness with Partial Valuations 3 / 10

ñ Introduction: why awareness? Agents represent their knowledge in different ways Communication via alignments Line van den Berg (UGA & Inria) Unawareness with Partial Valuations 3 / 10

ñ Introduction: why awareness? Agents represent their knowledge in different ways Communication via alignments Dynamic Epistemic Logic: announcements and conservative upgrades Line van den Berg (UGA & Inria) Unawareness with Partial Valuations 3 / 10

ñ Introduction: why awareness? Agents represent their knowledge in different ways Communication via alignments Dynamic Epistemic Logic: announcements and conservative upgrades But agents need to have access to what is announced Line van den Berg (UGA & Inria) Unawareness with Partial Valuations 3 / 10

ñ Introduction: why awareness? Agents represent their knowledge in different ways Communication via alignments Dynamic Epistemic Logic: announcements and conservative upgrades But agents need to have access to what is announced This prevents agents to acquire new vocabulary or adapt the meaning of the words they use Line van den Berg (UGA & Inria) Unawareness with Partial Valuations 3 / 10

ñ Introduction: why awareness? Agents represent their knowledge in different ways Communication via alignments Dynamic Epistemic Logic: announcements and conservative upgrades But agents need to have access to what is announced This prevents agents to acquire new vocabulary or adapt the meaning of the words they use Undesirable for open multi-agent systems Line van den Berg (UGA & Inria) Unawareness with Partial Valuations 3 / 10

Introduction: why awareness? Agents represent their knowledge in different ways Communication via alignments Dynamic Epistemic Logic: announcements and conservative upgrades But agents need to have access to what is announced This prevents agents to acquire new vocabulary or adapt the meaning of the words they use Undesirable for open multi-agent systems ñ Awareness Line van den Berg (UGA & Inria) Unawareness with Partial Valuations 3 / 10

ñ Related Work Partial valuations for DEL [Jaspars and Thijsse, 1996] Line van den Berg (UGA & Inria) Unawareness with Partial Valuations 4 / 10

ñ Related Work Partial Awareness valuations logic for DEL [Fagin and Halpern, 1987] [Jaspars and Thijsse, 1996] Line van den Berg (UGA & Inria) Unawareness with Partial Valuations 4 / 10

ñ Related Work Raise aware- ness [Van Ditmarsch et al.,2009] Partial Awareness valuations logic for DEL [Fagin and Halpern, 1987] [Jaspars and Thijsse, 1996] Line van den Berg (UGA & Inria) Unawareness with Partial Valuations 4 / 10

Related Work Raise aware- ness [Van Ditmarsch et raise al.,2009] awareness without Partial truth Awareness valuations logic for DEL [Fagin and Halpern, 1987] [Jaspars and Thijsse, 1996] ñ Becoming aware of a proposition and learning its truth value are two different acts Line van den Berg (UGA & Inria) Unawareness with Partial Valuations 4 / 10

✥ Unawareness with Partial Valuations Partial valuations allow propositions to be true, false or undefined Line van den Berg (UGA & Inria) Unawareness with Partial Valuations 5 / 10

✥ Unawareness with Partial Valuations Partial valuations allow propositions to be true, false or undefined ✥ p p w v u Line van den Berg (UGA & Inria) Unawareness with Partial Valuations 5 / 10

✥ Unawareness with Partial Valuations Partial valuations allow propositions to be true, false or undefined Agents can be uncertain and unaware about p a a b a ✥ p p w v u Line van den Berg (UGA & Inria) Unawareness with Partial Valuations 5 / 10

✥ Unawareness with Partial Valuations Partial valuations allow propositions to be true, false or undefined Agents can be uncertain and unaware about p Allowing agents to have different knowledge representations about the world a , b a , b a b b a p q w v u t Line van den Berg (UGA & Inria) Unawareness with Partial Valuations 5 / 10

Properties of awareness Agent awareness is preserved over accessibility: Line van den Berg (UGA & Inria) Unawareness with Partial Valuations 6 / 10

Properties of awareness Agent awareness is preserved over accessibility: a a p w v Line van den Berg (UGA & Inria) Unawareness with Partial Valuations 6 / 10

Properties of awareness Agent awareness is preserved over accessibility: Weak reflexivity a a a p w v Line van den Berg (UGA & Inria) Unawareness with Partial Valuations 6 / 10

Properties of awareness Agent awareness is preserved over accessibility: Weak reflexivity Consideration consistency a a a p p w v Line van den Berg (UGA & Inria) Unawareness with Partial Valuations 6 / 10

Properties of awareness Agent awareness is preserved over accessibility: Weak reflexivity Consideration consistency Specification a a a p p w v b a , b u Line van den Berg (UGA & Inria) Unawareness with Partial Valuations 6 / 10

Semantics Verification and falsification M , w ✭ ✥ φ iff M , w ✮ φ M , w ✮ ✥ φ iff M , w ✭ φ Line van den Berg (UGA & Inria) Unawareness with Partial Valuations 7 / 10

Semantics Verification and falsification Conjunction false iff both conjuncts defined M , w ✮ φ ❫ ψ iff M , w ✮ φ and M , w ✭ ψ, or M , w ✭ φ and M , w ✮ ψ, or M , w ✮ φ and M , w ✮ ψ Line van den Berg (UGA & Inria) Unawareness with Partial Valuations 7 / 10

Semantics Verification and falsification Conjunction false iff both conjuncts defined Knowledge and belief M , w ✭ iff ❅ v s.t. w ✒ a v : M , v ✭ φ K a φ M , w ✭ B a φ iff ❅ v s.t. w Ñ a v : M , v ✭ φ M , w ✮ iff ❉ v s.t. w ✒ a v : M , v ✮ φ K a φ M , w ✮ iff ❉ v s.t. w Ñ a v : M , v ✮ φ B a φ Where ✒ a and Ñ a are defined as “all accessible worlds with reflexivity” and “most plausible worlds with reflexivity”. Line van den Berg (UGA & Inria) Unawareness with Partial Valuations 7 / 10

Semantics Verification and falsification Conjunction false iff both conjuncts defined Knowledge and belief Raise awareness iff M � p , w ✭ ψ M , w ✭ r� p s ψ iff M � p , w ✮ ψ M , w ✮ r� p s ψ Line van den Berg (UGA & Inria) Unawareness with Partial Valuations 7 / 10

� � � � ✥ ✥ Raising awareness Raise awareness of p : Line van den Berg (UGA & Inria) Unawareness with Partial Valuations 8 / 10

� � � � ✥ ✥ Raising awareness Raise awareness of p : a w Line van den Berg (UGA & Inria) Unawareness with Partial Valuations 8 / 10

� � ✥ Raising awareness Raise awareness of p : � p w 0 p a a � p a w ✥ p a w 1 Line van den Berg (UGA & Inria) Unawareness with Partial Valuations 8 / 10

� � � ✥ Raising awareness Raise awareness of p : � p w 0 p a a ✥ p a w 1 Line van den Berg (UGA & Inria) Unawareness with Partial Valuations 8 / 10

� � ✥ ✥ Raising awareness Raise awareness of p : � p a a � p p p w w Line van den Berg (UGA & Inria) Unawareness with Partial Valuations 8 / 10

� � ✥ Raising awareness Raise awareness of p : � p w 0 p , q a a q � p a w ✥ p , q a w 1 Line van den Berg (UGA & Inria) Unawareness with Partial Valuations 8 / 10

Discussion & Conclusion We introduced a new semantics for modeling agent unawareness, using partial valuations Line van den Berg (UGA & Inria) Unawareness with Partial Valuations 9 / 10

Discussion & Conclusion We introduced a new semantics for modeling agent unawareness, using partial valuations Agents raise their awareness when needed Line van den Berg (UGA & Inria) Unawareness with Partial Valuations 9 / 10