Exploring the relation between knowledge and belief in multi-agent epistemic planning. Number 3

Participants Guillaume Aucher (consultant on knowledge/belief) Chitta Baral Esra Erdem Andreas Herzig Mathias Justesen Yongmei Liu Richard Scherl (coordinator) Hans van Ditmarsh Jan van Eijck

Goals: Identify the theoretical and computational challenges in planning with knowledge vs planning with belief; when one or the other is appropriate, or both are needed. How are knowledge and beliefs represented and distinguished from representation of the actual world? How do we formally handle that knowledge may turn into false belief after a partially observable action has occurred? What are the relevant formalisms for planning with knowledge and/or belief and what are their theoretical and computational properties? How do we deal with revision in planning? Are there specific types of interesting goals for epistemic planning? In planning with beliefs, goals can be false beliefs with relevance to formalizing false-belief tasks such as lying and deception.

Discussion: Knowledge vs Belief There was complete agreement here. Some felt that in planning we want to achieve something with certainty and therefore knowledge is needed. Others felt that the certainty required for knowledge is not achievable and so we should work with belief. From an external perspective the planner has a goal involving knowledge, but from an internal perspective each agent executing it’s part of the plan only needs belief. We can define knowledge in terms of belief as true belief. There are also a variety of ways of defining belief in terms of knowledge.

Representation of Epistemic States Possible Worlds (including variants) Plausible Models (Baltag and Smets) Formulas

Motivating Example Initial State: C{1,2} ~f Goal: K1f ⋀ K1K2~f Plan: KD45 agent1 makes f true while agent2 is not looking

Possible Worlds: DEL (continued) Initial State: 1,2 S0 = ~f <T, f:=T> 1 2 <T,⦰> agent1 makes f true while agent2 is not looking Action model: a = f 1 2 ~f 1,2 Result: S0 ⊗ a = S1 =

x Possible Worlds: DEL Possible Worlds: DEL (continued) f f ~f f Action Model Now what if we have public announcement of f f 1 2 ~f f a2 1,2 S1 1 f x S1 ⊗ a = S2 =

Need Belief Revision Plausibility Orderings Syntactic Belief Revision Baltag, A. and S. Smets, 2008a, “Probabilistic dynamic belief revision”, Synthese, 165(2): 179–202. doi:10.1007/s11229-008-9369-8 Syntactic Belief Revision Xiao Hung, Biqing Fang, HaiWan, and Yongmei Liu. “A General Multi-agent Epistemic Planner Based on Higher-order Belief Change.” 2017 IJCAI Recovery Jan van Eijk. Talk Public Lies and How to Recover from them

Plausibility Ordering Initial state 1,2 S0 = ~f Action model: 1,2 1,2 x y 1 2 X >2 Y Y >1 X a = <T, f:=T> <T,⦰> 1,2 X >2 Y Y >1 X f ~f X y 2 1 S0 ⊗ a = S1 =

Plausibility Ordering f 1,2 Public Announcement a2 = 1,2 X >2 Y Y >1 X f ~f X y 2 1 S0 ⊗ a = S1 = f 1,2 x S1 ⊗ a2 = S2 =

Syntactic Revision Algorithm Formulas: Xiao Hung, Biqing Fang, HaiWan, and Yongmei Liu. “A General Multi- agent Epistemic Planner Based on Higher-order Belief Change.” 2017 IJCAI Normal Form: Alternating Cover Disjunctive Formula (ACDF) Algorithm for syntactically manipulating form for update and revision. The result is still in ACDF.

Syntactic a1 effect f ⋀ k1 f a2 effect k1 f ⋀ k2 f ~f ⋀ k1~f ⋀ k2~f a1 update f ⋀ k1 f ⋀ k2~f a2 revision f ⋀ k1 f ⋀ k2 f

Recovering Action Recovering Action before adding result of public announcement R ⋃ (R;Ru) ⋃ Ru Ru inverse R;Ru composition of relation and inverse. Jan van Eijk. talk Public Lies and How to Recover from them

DEL with Recovering f f ~f Public Announcement 1,2 1 Recovered links in red. S1 After recovery

DEL with Recovery (cont) Action Model Now we have public announcement of f f 1 2 ~f f a2 1,2 S1 1,2 f x S1 ⊗ a2 = S2 =

Modify the DEL product operator – work in progress (Baral, Son) For edges in the updated state reached after executing action model A in epistemic state S, add some edges from the action model (even if they are not in S, under certain conditions. These conditions need to be defined so that the modification occurs when appropriate – work in progress.

Formalisms for Planning Model based progression (state-based search) Formula based progression Compilation (translation into classical planning problem) Others

Examples Story Understanding As the many stories progress characters will obtain false beliefs. Sally/Anne Autism Test A short skit is enacted. Sally takes a marble and hides it in her basket. She then leaves the room and Anne takes the marble out of Sally’s basket and puts it in her own basket. The question of where sally will look for her marble is asked. The autistic children tend to reply in Anne’s basket. Inability of people on autism spectrum to distinguish between actual world and a person’s belief about the world.