Multiagent planning and epistemic logic

Transcription

1 Multiagent planning and epistemic logic Andreas Herzig IRIT, CNRS, Univ. Toulouse, France Journée plénière, prégdr sur les Aspects Formels et Algorithmiques de l IA July 5, / 25

2 Outline 1 Planning: KR vs. ICAPS 2 What s in a planning problem? 3 States and goals: Epistemic Logic 4 Actions and plans: Dynamic Epistemic Logic 2 / 25

3 KR vs. ICAPS: two diverging communities ICAPS KR 2002 France 2004 Canada 2006 UK 2008 Australia 2010 Canada 2012 Brazil Italy 2014 USA Austria 2016 UK South Africa 2018 NL USA where should I publish my paper on action and planning? case when (complex concepts complex models) then submit(kr); when (implemented fast) then submit(icaps) esac 3 / 25

4 KR vs. ICAPS: reasons for the divergence 1 KR: focus on representation which language? which concepts? (action, initial state, goal,... ) which logical form? (arguments,... ) has truth values? (facts do, actions don t) which models? theoretical properties of reasoning problems? plan existence decidable? complexity of decision problems? logic is like a toothbrush 2 ICAPS: focus on fast reasoning methods standardised representation languages (PDDL, PDDL+++,... ) performance on benchmarks? 4 / 25

5 KR vs. ICAPS: soon back together? since 2013: planning goes multiagent workshop Distributed and Multi-Agent ICAPS [Petrick, Geffner, Domshlak, Brafman, Kambhampati, Nebel,... ] since 2011: Dynamic Epistemic Logic goes planning [Bolander, van der Hoek, Wooldridge, Aucher, Schwarzentruber,... ] Dagstuhl workshops on multiagent epistemic planning (2008, 2014, 2017) many new representation problems in particular: reasoning about other agents mental states fundamental in any kind of interaction people who are unable to attribute mental states to others have a lot of difficulties to interact with them counts as a disorder, cf. autism, schizophrenia,... 5 / 25

6 The need for epistemic reasoning in planning 1 single-agent planning uncertainty about initial situation uncertainty about action effects sensing actions (alias knowledge producing actions) contingent/conformant planning 2 multiagent planning initial situation: first-order: I don t know whether p. second-order: I don t know whether you know that p. second-order: I know that you don t know whether p.... goal: first-order: I want to know whether p. second-order: I want to know whether you know that p. second-order: I want you to believe that q.... actions with epistemic effects sensing actions communication actions how to model the agents perception of actions and events? 6 / 25

7 KR vs. ICAPS What s in a planning problem? States and goals: EL Actions and plans: DEL Challenge: robots with theory of mind [Milliez et al. 2014] at step 3, agent Green s beliefs become false colored arrows = beliefs about white book position (red = robot) colored spheres = reachability of an object for an agent / 25

8 representation problems: Problems, problems simple integrations of epistemic and spatial reasoning? model expiry date for knowledge/belief? light in room x is on at T j is in room x (so j believes that the light is on at T) j leaves the room at T+1 at T > T, does j still believe that the light in x is on? higher-order belief revision? to be solved in any application! reasoning problems: epistemic reasoning is difficult at least PSPACE EXPTIME complete if common knowledge/belief involved what are good benchmarks? what is epistemic planning s blocksworld? centralised or decentralised planning? 8 / 25

9 Outline 1 Planning: KR vs. ICAPS 2 What s in a planning problem? 3 States and goals: Epistemic Logic 4 Actions and plans: Dynamic Epistemic Logic 9 / 25

10 What s in a planning problem? planning problem = init, goal, actionlaws 1 logical form of init: proposition proposition = set of possible worlds (states) can be described in various logical languages: propositional logic epistemic logic... classical planning: initial state = complete proposition = a single possible world = a valuation of propositional logic 2 logical form of goal: proposition 3 logical form of actionlaws: action type action type: arm-raising action token: Bruno s raising of his right arm in room 7 of building 007 of Caen IUT on July 5, 2017 at 10:55:55 10 / 25

11 What s in an action? event brought about by an agent [Davidson] proposition that can be phrased agent i sees to it that proposition ϕ is true [Belnap s stit thesis] something that has precondition and effects [AI folklore] precond = proposition effect =? action = precond, effect 11 / 25

12 What s in an action effect? STRIPS actions: effect = conjunction of literals however: an action type is instantiated in different circumstances effects typically depend on these circumstances conditional effects: effect = { condition 1, L 1,1 L 1,m1,..., condition n, L n,1 L n,m1 } example: agent i s action of flipping a switch precond(flip i ) = AtSwitch i effect(flip i ) = { On, On, On, On } 12 / 25

13 Outline 1 Planning: KR vs. ICAPS 2 What s in a planning problem? 3 States and goals: Epistemic Logic 4 Actions and plans: Dynamic Epistemic Logic 13 / 25

14 Epistemic logic: language knowledge explained in terms of possible worlds [Hintikka]: K i ϕ = agent i knows that ϕ = ϕ true in every world that is possible for i BNF: ϕ ::= p ϕ ϕ ϕ K i ϕ where p ranges over Prp and i over Agt 3 possible epistemic attitudes w.r.t. a formula ϕ: K i ϕ K i ϕ K i ϕ K i ϕ 14 / 25

15 Epistemic logic: possible worlds semantics model M = (W, {R i } i Agt, V) with W non-empty set of possible worlds R i W W accessibility relations V : W 2 Prp valuation R i is an equivalence relation (indistinguishability) R i (w) = set of worlds i cannot distinguish from w = set of worlds compatible with i s knowledge truth conditions: M, w p iff... M, w ϕ iff... M, w ϕ ψ iff... M, w K i ϕ iff M, w ϕ for all w R i (w) 15 / 25

16 Epistemic logic: possible worlds semantics muddy children puzzle, initial situation R R R2 12 R 1 (reflexive arrows omitted) M, 12 m 1 m 2 K 1 m 2 K 1 m 1 K 1 m 1 16 / 25

17 Epistemic logic for epistemic planning? can be modeled: init = formula of epistemic logic goal = formula of epistemic logic cannot be expressed: actionlaws 17 / 25

18 Outline 1 Planning: KR vs. ICAPS 2 What s in a planning problem? 3 States and goals: Epistemic Logic 4 Actions and plans: Dynamic Epistemic Logic 18 / 25

19 Muddy children: Episode 1 1 initially, common knowledge that nobody is muddy 2 1 gets muddy but isn t sure; 2 watches 3 2 gets muddy but isn t sure; 1 watches R 2 12 R 1 R 1 R gets muddy = gets muddy = 1 2 R / 25

20 Dynamic epistemic logic DEL idea: model uncertainty about current event by introducing possible events uncertainty about world possible worlds indistinguishability of worlds uncertainty about event possible events indistinguishability of events possible event models distinguish agents who observe from agents who don t N.B.: an agent typically observes only very few events muddy children: event model where 1 plays, 2 watches skip 1 R 1 getsmuddy 1 (reflexive arrows omitted) 20 / 25

21 DEL: event models EM = (E, {S i } i Agt, precond, effect) event model, where E is a nonempty set of events S i E E every S i is an equivalence relation es i f = i perceives occurrence of e as occurrence of f precond : E Fmls effect : E Fmls s.t. effect(e) conjunction of literals (just as in STRIPS) 21 / 25

22 DEL: product construction update world model WM = (W, R, V) by event model EM where WM EM = WM W = {(w, e) W E : M, w precond(e)} (w, e)r i (v, f) iff wr iv and es i f V ((w, e)) = (V(w) \ {p : p negative in effect(e)}) {p : p positive in effect(e)} 22 / 25

23 DEL for epistemic planning? explored since >5 years [Bolander & Anderson 2011]; [Löwe, Pacuit & Witzel 2011]; [Aucher, Maubert & Pinchinat 2014]; [Yu, Li & Wang 2015],... init = formula of multiagent epistemic logic goal = formula of multiagent epistemic logic action type = agent + event model reasoning: not so easy plan existence undecidable in general [Bolander & Anderson 2011]; [Aucher & Bolander 2013]; [Charrier, Maubert & Schwarzentruber 2016] decidable fragments: heavily restricted [Yu, Wen & Liu 2013]; [Bolander et al. 2015],... representation: some problems that seemingly went unnoticed / 25

24 DEL for epistemic planning: problems event models rather describe action tokens actionlaws describe types, not tokens how to describe conditional effects? list all possible cases of perception of the actual event infinitely many conditional effects needed conditional effects of getmuddy(i): (ingarden i, m i ) (ingarden j, K j m i ) (K i ingarden j, K i (K j m i K j m i )) (K j K i ingarden j,... ). (CK i,j ingarden j, CK i,j (K j m i K j m i )) event models with an infinite number of points! even when finite, event models have to be big world models typically grow exponentially when updated 24 / 25

25 Conclusion knowledge representation with DEL event models: art rather than craft practical problems conceptual problems (type vs. token) the other agents observation should be based on information from the possible worlds model, not from the event model edge-conditioned event models [Bolander, 2015] special propositional variable agent i is watching [Bolander et al., JoLLI 2016] part of the state, not part of the action! special propositional variable agent j is watching agent i [Bolander et al., ongoing] j changes her beliefs when j watches i s action j does not change her beliefs when j does not watch i s action 25 / 25