Complexity Results in Epistemic Planning

Transcription

1 Comlexity Results in Eistemic Planning Thomas Bolander, DTU Comute, Tech Univ of Denmark Joint work with: Martin Holm Jensen and Francois Schwarzentruer Comlexity Results in Eistemic Planning. 1/9

2 Automated lanning Automated lanning (or, simly, lanning): Given is a lanning task consisting of: 1) initial state; 2) finite set of actions; 3) goal formula. The aim is to comute a lan: a sequence of actions that leads from the initial state to a state satisfying the goal formula. Examle. Goal: On(A,B) On(B,C). C A B initial state Put(,tale) Put(,c) goal C B A Put(c,tale) C B A Put(,c) B C A Put(a,) A B C Comlexity Results in Eistemic Planning. 2/9

3 Eistemic lanning Eistemic lanning: Planning where agents can reason aout their own and other agents eliefs as art of the lanning rocess. Eistemic lanning alication examles: Games with strong eistemic comonents (Cluedo, Hanai, etc.). What will the other agents know if I choose to announce that I have this card? Roots or intelligent software assistants taking and giving instructions. Fetch a cu of coffee. The eans are in the cuoard. Crytograhic rotocols. How can agent a get to know ϕ without agent knowing? Comlexity Results in Eistemic Planning. 3/9

4 Our framework for Eistemic Planning Eistemic lanning: Our framework for lanning with eistemic reasoning ased on Dynamic Eistemic Logic (DEL). From classical lanning to eistemic lanning: Relace the roositional logic underlying classical lanning y DEL. Classical lanning Eistemic lanning States models of ro. logic models of MA eist. logic Goal formula formula of ro. logic formula of MA eist. logic Actions induced y action schemas action models of DEL Eistemic lanning can deal with: non-determinism, artial oservaility, sensing actions, multile agents, aritrary nestings of eliefs aout eliefs. Comlexity Results in Eistemic Planning. 4/9

5 Eistemic lanning tasks and lan existence rolem Eistemic lanning task: Planning task in eistemic lanning. Plan existence rolem for class of eistemic lanning tasks X : Given an lanning task in X, does there exist a lan for it?. Our aer: Comlexity results for the lan existence rolem for various classes of eistemic lanning tasks. Comlexity Results in Eistemic Planning. 5/9

6 Examle Consider the eistemic lanning task with 1) Initial state: w 1 : 2) Actions: w 2 a α 1 = e1 : e 2 : α 2 = e1 : a α 3 = e 2 : e 1 : (α 1 : rivately announcing to a; α 2 : rivately announcing to ; α 3 : ulicly announcing to oth agents) 3) Goal formula: K a K K a K K K a A lan for this task is α 1, α 2. Another lan is α 2, α 1. Also α 1, α 2, α 1 and α 1, α 1, α 2 are lans, etc. Comlexity Results in Eistemic Planning. 6/9

7 Comlexity of lan existence in eistemic lanning The ad news: The lan existence rolem in eistemic lanning is undecidale. [Bolander and Andersen, 2011] The even worse news: The lan existence rolem of non-factual eistemic lanning (changing only eliefs, no ontic effects) is undecidale. [Aucher and Bolander, 2013] Some slightly good news: The lan existence rolem in eistemic lanning with roositional reconditions is decidale (in NON-ELEMENTARY). [Yu et al., 2013] This aer: Getting lower comlexities for further restricted (ut still ractically relevant) classes of lanning tasks. Comlexity Results in Eistemic Planning. 7/9

8 Actions are grahs q a a a a ulic announcement rivate announcement semi-rivate announcement Different grah structures allow different actions to e formed (e.g. ulic announcements like in Cluedo = singletons ). We study how the underlying grah structure imact comlexity of lan existence. Comlexity Results in Eistemic Planning. 8/9 a q

9 Summary of comlexity results for lan existence Underlying grahs of actions Singletons Chains Trees Grahs Tyes of eistemic actions Non-factual, Factual, Factual, roositional roositional eistemic reconditions reconditions reconditions NP-comlete NP-comlete PSPACE-comlete in EXPSPACE in this aer PSPACE-hard [Jensen, 2014]? (oen question)? (oen question) in NON- ELEMENTARY [Yu et al., 2013] PSPACE-hard [Jensen, 2014]? (oen question)? (oen question) Undecidale [Bolander and Andersen, 2011] Comlexity Results in Eistemic Planning. 9/9

10 APPENDIX Why study very exressively restricted fragments? Motivation for studying comlexity of very restrictive fragments of eistemic lanning: Still relevant for many interesting alications (e.g. Cluedo only involves ulic announcements = singleton action models). Where does the comlexity come from? Constructing search heuristics for lanning engines (relaxed rolems). Comlexity Results in Eistemic Planning Aendix. 1

11 Aendix: References I Aucher, G. and Bolander, T. (2013). Undecidaility in Eistemic Planning. In Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence (IJCAI) ,. Aucher, G., Mauert, B. and Pinchinat, S. (2014). Automata Techniques for Eistemic Protocol Synthesis. In Proceedings 2nd International Worksho on Strategic Reasoning, (Mogavero, F., Murano, A. and Vardi, M. Y., eds), vol. 146, of Electronic Proceedings in Theoretical Comuter Science ,. Aucher, G. and Schwarzentruer, F. (2013). On the Comlexity of Dynamic Eistemic Logic. In TARK. Bolander, T. and Andersen, M. B. (2011). Eistemic Planning for Single- and Multi-Agent Systems. Journal of Alied Non-Classical Logics 21, Jensen, M. (2014). Eistemic and Doxastic Planning. PhD thesis, Technical University of Denmark. DTU Comute PHD Löwe, B., Pacuit, E. and Witzel, A. (2011). DEL lanning and some tractale cases. In LORI 2011, (van Ditmarsch, H., Lang, J. and Ju, S., eds), vol. 6953, of Lecture Notes in Artificial Intelligence , Sringer. Comlexity Results in Eistemic Planning Aendix. 2

12 Sadzik, T. (2006). Exloring the Iterated Udate Universe. ILLC Pulications PP Aendix: References II Yu, Q., Wen, X. and Liu, Y. (2013). Multi-Agent Eistemic Exlanatory Diagnosis via Reasoning aout Actions. In IJCAI, (Rossi, F., ed.), IJCAI/AAAI. Comlexity Results in Eistemic Planning Aendix. 3