Intention Interleaving Via Classical Replanning Mengwei Xu , Kim - PowerPoint PPT Presentation

Intention Interleaving Via Classical Replanning Mengwei Xu , Kim Bauters, Kevin McAreavey, Weiru Liu

Extending Belief-Desire-Intention (BDI) Agents to Managing Intention Interleaving Intention Resolution: to avoid negative interference Guarantee the achievability of intentions when interleaving the steps in different intentions Intention Merging: to facilitate positive interference Perform one task once for at least two goals, i.e. “kill two birds with one stone”

Motivation to Manage Intention Interleaving Intention Resolution Careless interleaving could result in that neither of its intention can be completed.

Motivation to Manage Intention Interleaving Intention Merging 𝐻 ! TransmitSoilResults 𝑏 " 𝑏 ! 𝑏 $ EstablishConnection BreakConnection SendSoilResults execute them once for both intentions 𝑏 # 𝑏 ! 𝑏 $ EstablishConnection SendImageResults BreakConnection 𝐻 " TransmitImageResults

Belief-Desire-Intention: Literature Software Platforms Jason [Bordini et al., 2007] Logics Jack [Winikoff, 2005] [Cohen & Levesque, 1990] Jadex [Pokahr et al., 2013] [Rao & Georgeff, 1991] [Shoham, 2009] Programming Languages AgentSpeak [Rao, 1996] CAN [Winikoff et al., 2002] CANPLAN [Sardina et al., 2011]

BDI Agent ℬ, Λ, Π Plan library Initial belief base Set of plan rules Belief base specifying agent’s initial beliefs Action library Set of STRIPS-style action descriptions

BDI Agent ℬ, Λ, Π Initial belief base Belief base specifying agent’s initial beliefs Belief base ℬ ⊆ ℒ Set of formulas from logical language ℒ ℬ must support: • ℬ ⊨ 𝜒 (Entailment) • ℬ ∪ 𝜒 (Addition) • ℬ ∖ 𝜒 (Deletion) Assume ℬ is a set of atoms

CAN: Agent ℬ, Λ, Π Action library Set of STRIPS-style action descriptions Action description act ∶ 𝜒 ← ℬ # ; ℬ $ Set of “add” atoms ℬ " ⊆ ℒ Primitive action symbol Set of “delete” atoms ℬ ! ⊆ ℒ Precondition 𝜒 ∈ ℒ

BDI Agent ℬ, Λ, Π Plan library Set of plan rules 𝑫𝒑𝒐𝒖𝒇𝒚𝒖 𝑸 : 𝜒 ∈ ℒ body 𝑸 : ℎ ! ; ⋯ ; ℎ % 𝑰𝒇𝒃𝒆 𝑸 : 𝐻 Formula from ℒ e.g. a sequence of actions or goals e.g. new goal Plan rule P = 𝐻: 𝜒 ← ℎ % ; ⋯ ; ℎ &

BDI Operational Mechanism Sketch 𝐻 ∶ 𝜒 !! ← 𝑄 𝐻 ∶ 𝜒 ! ← 𝑄 !! ! 𝐻 ∶ 𝜒 "! ← 𝑄 𝐻 ∶ 𝜒 " ← 𝑄 "! select " select Goal 𝐻 𝐻 ∶ 𝜒 #! ← 𝑄 Relevant Plans 𝐻 ∶ 𝜒 # ← 𝑄 Applicable Plans #! # ⋮ ⋮ 𝐻 ∶ 𝜒 %! ← 𝑄 𝐻 ∶ 𝜒 % ← 𝑄 %! % ⊆ Π where 𝓒 ⊨ φ 𝒌𝟐 , 𝑘 ∈ 1, ⋯ , 𝑜 repeat for the subgoals A tree structure representing all possible ways of achieving a goal 𝐻

Our Intention Interleaving Framework in BDI 1. Intention Formalisation • Model an intention as an AND/OR graph • Define the execution trace for multiple intentions • Define the conflict-free and maximal-merged execution trace for multiple intentions 2. Intention Interleaving Planning Preparation • Indexing nodes • Defined terminal, initial node sets, and progression links of intentions • Computing overlapping programs between multiple intentions 3. Intention Interleaving Planning Formalism • Formalise FPP problem of interleaving intentions • Correctness Proof 4. Implementation 5. Evaluation

AND/OR Graphs for Intentions 𝑄 ! = 𝐻 ! : 𝜒 ! ← 𝑏 ! ; 𝑏 " ; 𝑏 $ 𝑄 " = 𝐻 " : 𝜒 " ← 𝑏 ! ; 𝑏 # ; 𝑏 $ OR-nodes OR-edges AND-nodes AND-edges OR-nodes

Execution Trace for An Intention To identifies every unique way in which a given intention can be achieved 𝜐 ! 𝑈 " = 𝐻 " ; 𝑄 " ; 𝑏 # ; 𝑏 $ Execution trace for 𝑈 ! : 𝜐 𝑈 ! = 𝐻 ! ; 𝑄 ! ; 𝑏 ! ; 𝑏 " ; 𝑏 $ Execution trace for 𝑈 # : 𝜐 % 𝑈 " = 𝐻 " ; 𝑄 # ; 𝑐 # ; 𝑐 $ ; 𝑐 &

Execution Trace for Multiple Intentions The construction of an execution trace of a set of intentions is to interleave elements in the execution traces of different intentions Potential execution trace for 𝑈 % and 𝑈 H : 𝜏 = 𝑯 𝟐 ; 𝑸 𝟐 ; 𝐻 H ; 𝑄 H ; 𝒃 𝟐 ; 𝑏 J ; 𝒃 𝟑 ; 𝒃 𝟓 ; 𝑏 M by interleaving 𝜐 𝑈 ! = 𝑯 𝟐 ; 𝑸 𝟐 ; 𝒃 𝟐 ; 𝒃 𝟑 ; 𝒃 𝟓 and 𝜐 ! 𝑈 # = 𝐻 # ; 𝑄 # ; 𝑏 $ ; 𝑏 *

Execution Trace for Intentions (Cont.) Conflict-free Execution Trace: To model the successful interleaving which achieves all intentions 𝜏 1 𝜏 2 ⋯ 𝜏 𝑘 − 1 𝜏 𝑘 𝜏 𝑘 + 1 𝜏 𝑜 ⋯ ℬ ! ℬ " ℬ ℬ ℬ % ℬ +,! +-! + + is the belief base before the execution of the 𝑘 ./ element of an execution trace (i.e. 𝜏 𝑘 ) where ℬ An execution trace 𝜏 is conflict-free if and only if the following hold: 1. if 𝜏 𝑘 = 𝑄 ∈ Π , then ℬ ' ⊨ 𝑑𝑝𝑜𝑢𝑓𝑦𝑢(𝑄) , i.e. the context of plan 𝑄 must be met before selection 2. if 𝜏 𝑘 = 𝑏 ∈ Λ , then ℬ ' ⊨ 𝜔(𝑏) , i.e. the pre-condition of action `𝑏′ must be met before selection

Execution Trace for Intentions (Cont.) Mergeable Execution Trace of 𝑼 𝟐 , ⋯ , 𝑼 𝒏 To capture the overlapping programs of different intentions 𝝉: 𝜏 𝑜 𝜏 1 𝜏 2 𝜏 𝑘 𝜏 𝑘 + 1 ⋯ 𝜏 𝑘 + 𝑙 − 1 𝜏 𝑘 + 𝑙 ⋯ ⋯ 𝑙 consecutive same element from all difference intentions in 𝜏 𝝉 𝒏 : 𝜏 1 𝜏 𝑘 𝜏 𝑘 + 𝑙 + 1 𝜏 𝑜 ⋯ ⋯ 𝜏 2 An execution trace 𝜏 is a mergeable execution trace if and only if the following hold: 1. ∃𝑘 ∈ 1, ⋯ , 𝑜 such that 𝜏 𝑘 = 𝜏 𝑘 + 1 = ⋯ 𝜏 𝑘 + 𝑙 where 2 ≤ 𝑙 ≤ 𝑜 − 𝑘 ; 2. ∀𝑚 ∈ 1, ⋯ , 𝑛 , ∄𝑡, 𝑢 ∈ 𝑘, ⋯ , 𝑘 + 𝑙 where 𝑡 ≠ 𝑢 such that 𝜏 𝑡 ⊆ 𝜐 𝑈 * ⊆ 𝜏 and 𝜏 𝑢 ⊆ 𝜐 𝑈 * ⊆ 𝜏 ; 𝜏 + is a conflict-free execution trace where 𝜏 + is the merged execution trace of 𝜏 by reducing each 3. subsequence consisting of consecutive identical elements characterized by 1 and 2 in 𝜏 to only one element left.

Execution Trace for Intentions (Cont.) Maximal-merged Trace of 𝑼 𝟐 , ⋯ , 𝑼 𝒏 To capture the most merged execution trace of multiple intentions The merged execution trace 𝜏 + of a mergeable execution trace 𝜏 of 𝑈 ! , ⋯ , 𝑈 + is maximal-merged if there is no another mergeable execution trace 𝜏 , of 𝑈 + such that 𝜏 ,+ < 𝜏 + where ! , ⋯ , 𝑈 𝜏 stands for the length of 𝜏 . the potential maximal-merged trace of 𝑈 ! , 𝑈 " 𝜏 1 = 𝐻 ! ; 𝑄 ! ; 𝐻 " ; 𝑄 " ; 𝑏 ! ; 𝑏 " ; 𝑏 # ; 𝑏 $ Perform action a ! and a $ once for both two goals 𝑈 ! and 𝑈 "

Indexing Nodes To ensure that e.g. the same actions in distinct plans is seen as different 𝑈 W 𝑜 A node 𝑜 is a top-level goal of intention 𝑈 : 𝑜 2,+,4 to denote the 𝑘 ./ member of 𝑐𝑝𝑒𝑧(𝑄) in 𝑈 The nodes of actions and subgoals of intention 𝑈 : 𝑜 4 A plan node in intention 𝑈 : 𝑨 5 = 𝑈 ! W 𝑜 , ⋯ , 𝑈 1 W 𝑜 Initial node set for intentions 𝑈 ! , ⋯ , 𝑈 1 : a collection of the last element of each execution trace of a goal Terminal node set for a goal node: 𝑨 6 = 𝑢𝑜 ! , ⋯ , 𝑢𝑜 1 where 𝑢𝑜 7 is a terminal node of 𝑈 7 W 𝑜 Terminal node set for intentions I = 𝑈 ! , ⋯ , 𝑈 1 𝑨 6 ⊳ .% 𝐽 if 𝑨 6 is a terminal node set of 𝐽

Progression Links To visualise the progression order of execution elements in the context of indexes The progression links of execution trace 𝜐(𝑈 " ) The progression links of execution trace 𝜐(𝑈 ! ) 4 4 (𝑈 " (W 𝑜) → 𝑄 " ) (𝑈 ! (W 𝑜) → 𝑄 ! ) " ! " → 𝑏 !2 " ,!,4 ! → 𝑏 !2 ! ,!,4 4 4 (𝑄 " ) (𝑄 ! ) " ! They are also called primitive progression links " → 𝑏 #2 " ,",4 ! → 𝑏 "2 ! ,",4 (𝑏 !2 " ,!,4 " ) (𝑏 !2 ! ,!,4 ! ) " → 𝑏 $2 " ,#,4 ! → 𝑏 $2 ! ,#,4 (𝑏 #2 " ,",4 (𝑏 "2 ! ,",4 " ) ! )