Logics for multi-agent systems: an overview

Transcription

1 Logics for multi-agent systems: an overview Andreas Herzig University of Toulouse and CNRS, IRIT, France EASSS 2014, Chania, 17th July / 40

2 Introduction course based on an overview paper to appear in J. AAMAS 2 / 40

3 Introduction Multi-Agent Systems (MAS): agents with imperfect knowledge perform actions in order to achieve goals philosophical logic/kr view: what are the main concepts? what properties do they have? how do they relate? formal, logical analysis logics of action and knowledge extensions of propositional logic by modal operators 3 / 40

4 Introduction: modal operators of knowledge knowledge of individual i Agt : K i ϕ = agent i knows that ϕ knowledge of group J Agt : EK J ϕ = it is shared knowledge in J that ϕ = every agent in J knows that ϕ CK J ϕ = it is common knowledge in J that ϕ = EK J ϕ EK J EK J ϕ EK J EK J EK J ϕ DK J ϕ = it is distributed knowledge in J that ϕ if each agent in J tells all he knows to J then EK J ϕ 4 / 40

5 Introduction: modal operators of action and ability nonstrategic (ceteris paribus) π ϕ = there is an execution of program π after which ϕ J ϕ = coalition J can achieve ϕ (while opponents don t act) strategic ( ceteris agentis, ceteris mutandis ) J ϕ = coalition J can achieve ϕ (whatever opponents do) 5 / 40

6 Introduction: modal operators of action and ability nonstrategic (ceteris paribus) π ϕ = there is an execution of program π after which ϕ J ϕ = coalition J can achieve ϕ (while opponents don t act) strategic ( ceteris agentis, ceteris mutandis ) J ϕ = coalition J can achieve ϕ (whatever opponents do) 5 / 40

7 Introduction: modal operators of action and ability nonstrategic (ceteris paribus) π ϕ = there is an execution of program π after which ϕ J ϕ = coalition J can achieve ϕ (while opponents don t act) strategic ( ceteris agentis, ceteris mutandis ) J ϕ = coalition J can achieve ϕ (whatever opponents do) 5 / 40

8 Introduction: the grid of MAS logics aim: overview main MAS logics & highlight problematic points KR point of view which logical language? focus on deduction (vs. model checking) almost semantic-free the grid of MAS logics: S5 CK PAL CK ATEL CK S5 PAL ATEL no uncertainty PDL, CL-PC ATL, STIT knowledge action no actions nonstrategic strategic 6 / 40

9 Outline 1 No uncertainty, nonstrategic actions 2 No uncertainty, strategic actions 3 Individual knowledge, no actions 4 Individual knowledge, nonstrategic actions 5 Individual knowledge, strategic actions 6 Group knowledge, no actions 7 Group knowledge, nonstrategic actions 8 Group knowledge, strategic actions 7 / 40

10 No uncertainty, nonstrategic actions: PDL language of Propositional Dynamic Logic PDL: π ϕ = there exists a possible execution of π after which ϕ [π]ϕ = for every possible execution of π... where π is a program (alias complex action): π a π; π π π π ϕ? express: if ϕ then π 1 else π 2 and while ϕ do π 8 / 40

11 No uncertainty, nonstrategic actions: PDL semantics: transition systems (graphs with action-labelled edges) paintcard 1 movecard L1,L 2 Card@L 2 M, w Card@L1 = movecard L1,L 2 Card@L 1 because M, w Card@L2 = Card@L 2 model M = W, R, V W nonempty set R : Act 2 W W ( accessibility relation ) V : W 2 Prp M, w = a ϕ if M, v = ϕ for some v such that wr a v M, w = [a]ϕ if M, v = ϕ for every v such that wr a v complexity of satisfiability: EXPTIME 9 / 40

12 No uncertainty, nonstrategic actions: PDL semantics: transition systems (graphs with action-labelled edges) paintcard 1 movecard L1,L 2 Card@L 2 M, w Card@L1 = movecard L1,L 2 Card@L 1 because M, w Card@L2 = Card@L 2 model M = W, R, V W nonempty set R : Act 2 W W ( accessibility relation ) V : W 2 Prp M, w = a ϕ if M, v = ϕ for some v such that wr a v M, w = [a]ϕ if M, v = ϕ for every v such that wr a v complexity of satisfiability: EXPTIME 9 / 40

13 No uncertainty, nonstrategic actions: PDL in focus: reasoning about action/program effects? (ActionTheory Init) a 1 ; ; a n Goal PDL action theories must be augmented by frame axioms CardRed [movecard L1,L 2 ]CardRed PDL doesn t solve the frame problem [McCarthy & Hayes 1969] unsatisfactory from a KR point of view a lot of dedicated logical formalisms to solve the frame problem SitCalc, EventCalc, FluentCalc, A, B, C, C+, BC,... separation logic, logic of bunched implications,... SitCalc basic action theories [Reiter 1991]: x ([x]cardred ( x = paintred (CardRed x paintblue) ) ) general schema ( successor state axioms ): x ( [x]p γ p (x) ) 10 / 40

14 No uncertainty, nonstrategic actions: PDL in focus: reasoning about action/program effects? (ActionTheory Init) a 1 ; ; a n Goal PDL action theories must be augmented by frame axioms CardRed [movecard L1,L 2 ]CardRed PDL doesn t solve the frame problem [McCarthy & Hayes 1969] unsatisfactory from a KR point of view a lot of dedicated logical formalisms to solve the frame problem SitCalc, EventCalc, FluentCalc, A, B, C, C+, BC,... separation logic, logic of bunched implications,... SitCalc basic action theories [Reiter 1991]: x ([x]cardred ( x = paintred (CardRed x paintblue) ) ) general schema ( successor state axioms ): x ( [x]p γ p (x) ) 10 / 40

15 No uncertainty, nonstrategic actions: PDL in focus: reasoning about action/program effects? (ActionTheory Init) a 1 ; ; a n Goal PDL action theories must be augmented by frame axioms CardRed [movecard L1,L 2 ]CardRed PDL doesn t solve the frame problem [McCarthy & Hayes 1969] unsatisfactory from a KR point of view a lot of dedicated logical formalisms to solve the frame problem SitCalc, EventCalc, FluentCalc, A, B, C, C+, BC,... separation logic, logic of bunched implications,... SitCalc basic action theories [Reiter 1991]: x ([x]cardred ( x = paintred (CardRed x paintblue) ) ) general schema ( successor state axioms ): x ( [x]p γ p (x) ) 10 / 40

16 DL-PA: a dialect of PDL solving the frame problem Reiter s basic action theories can be expressed in Dynamic Logic of Propositional Assignments DL-PA [van Ditmarsch et al., JLC 2011] atomic programs: assign propositional variables to formulas CardAt L1 successor state axioms become DL-PA programs: moveblock L1,L 2 = (Free?; CardAt L1 ; CardAt L2 ) ( hyp.: in x [x]p γ p (x) ), if a γ p (x) then γ p (a) p better than PDL [Balbiani et al., LICS 2013; submitted] Kleene star eliminable every formula reducible to a boolean formula compact, interpolation property model checking as complex as validity checking complexity of satisfiability: PSPACE claim: DL-PA = Assembler language for logics of change embeds planning [H et al., ECAI 2014], update and revision operations [H, KR 2014], Dung argumentation frameworks and their modification [Doutre et al. KR 2014], / 40

17 No uncertainty, nonstrategic actions: CL-PC language of Coalition Logic of Propositional Control CL-PC: J ϕ = coalition J can achieve ϕ by modifying its variables (while opponents don t act) each propositional variable controlled by some agent; action of i = change of some of i s variables (cf. bool. games) [van der Hoek & Wooldridge, AIJ 2005; JAIR 2010] in focus: reasoning about nonstrategic (ceteris paribus) ability? (AbilityTheory Init) {i 1,..., i n } Goal 12 / 40

18 No uncertainty, nonstrategic actions: CL-PC captures strategic ability J [ J]ϕ = J can achieve ϕ whatever the opponents in J do can be embedded into DL-PA: i ϕ = π i,ϕ ϕ with π i,ϕ polynomial in ϕ [H et al., IJCAI 2011] program π i,ϕ uses propositional variables C i,p i controls p to be axiomatised: agents exclusive and exhaustive control over the variables occurring in ϕ 13 / 40

19 Outline 1 No uncertainty, nonstrategic actions 2 No uncertainty, strategic actions 3 Individual knowledge, no actions 4 Individual knowledge, nonstrategic actions 5 Individual knowledge, strategic actions 6 Group knowledge, no actions 7 Group knowledge, nonstrategic actions 8 Group knowledge, strategic actions 14 / 40

20 No uncertainty, strategic actions: ATL language of Alternating-time Temporal Logic ATL: J Xϕ = the agents in J have a strategy such that whatever the other agents do, next ϕ J Gϕ =..., henceforth ϕ J ϕ U ψ =..., ϕ until ψ Coalition Logic CL [Pauly, JLC 2002]: no G, no U 15 / 40

21 No uncertainty, strategic actions: ATL semantics: effectivity functions / concurrent game structures / alternating-time transition systems basically: transition systems labelled by profiles (action vectors, one action per agent) (1:paintCard,2:nop) Card@L 1 (1:moveCard L1,L 2,1:moveCard L1,L 3 ) Card@L 1 complexity of satisfiability: EXPTIME (CL fragment: PSPACE) in focus: reasoning about the existence of strategies? (AbilityTheory Init) {i 1,..., i n } Goal 16 / 40

22 ATL: the problem of strategy revocability problem: strategies can be canceled i G ( married i X married ) is consistent in ATL reason: strategies are unsung heroes [van Benthem] solution: commit to a strategy ATL with irrevocable strategies [Ågotnes et al., TARK 2007] ATL with strategy contexts [Brihaye et al., LFCS 2009] make adoption and canceling of strategies explicit undecidable [Troquard & Walther, JELIA 2012] Strategy Logic (SL) [Mogavero et al., FSTTCS 2010] uses strategy variables; undecidable ATL with explicit strategies [Walther et al., TARK 2007] {i} i:σ G(married {i} i:σ X married) more principled: commit to an action/program ATLEA = ATL + Explicit Actions [H et al., LORI 2013; LAMAS 2014] {i} i:staymarried G(married {i} i:staymarried X married) same complexity as ATL 17 / 40

23 ATL: the problem of strategy revocability problem: strategies can be canceled i G ( married i X married ) is consistent in ATL reason: strategies are unsung heroes [van Benthem] solution: commit to a strategy ATL with irrevocable strategies [Ågotnes et al., TARK 2007] ATL with strategy contexts [Brihaye et al., LFCS 2009] make adoption and canceling of strategies explicit undecidable [Troquard & Walther, JELIA 2012] Strategy Logic (SL) [Mogavero et al., FSTTCS 2010] uses strategy variables; undecidable ATL with explicit strategies [Walther et al., TARK 2007] {i} i:σ G(married {i} i:σ X married) more principled: commit to an action/program ATLEA = ATL + Explicit Actions [H et al., LORI 2013; LAMAS 2014] {i} i:staymarried G(married {i} i:staymarried X married) same complexity as ATL 17 / 40

24 No uncertainty, strategic actions: STIT language of Seeing-To-It-That Logic STIT [Belnap et al. 2001; Horty 2001] Stit J ϕ = by following their current strategy the agents in J guarantee that ϕ is true, whatever the other agents do ϕ = it is historically possible that ϕ = Stit Agt ϕ F ϕ =... (temporal operators) in focus: reasoning about causality ( agency )? Cond Stit {i1,...,i n } Fact reasoning about strategic ability à la ATL: J Xψ = Stit J Xψ satisfiability undecidable [H & Schwarzentruber, AiML 2008] 18 / 40

25 Outline 1 No uncertainty, nonstrategic actions 2 No uncertainty, strategic actions 3 Individual knowledge, no actions 4 Individual knowledge, nonstrategic actions 5 Individual knowledge, strategic actions 6 Group knowledge, no actions 7 Group knowledge, nonstrategic actions 8 Group knowledge, strategic actions 19 / 40

26 Individual knowledge, no actions language of epistemic logic S5: K i ϕ = agent i knows that ϕ is true principles K i (omniscience) (K i ϕ K i (ϕ ψ)) K i ψ (omniscience) K i ϕ ϕ (knowledge implies truth) K i ϕ K i K i ϕ (positive introspection) K i ϕ K i K i ϕ (negative introspection) example: the famous muddy children puzzle 1 K 1 ( m1 K 2 m1) 2 K 1 K 2 (m1 m2) 3 K 1 K 2 m2 consequence: child 1 knows it is muddy ( (1) (2) (3) ) K1 m1 20 / 40

27 Individual knowledge, no actions semantics: indistinguishability relations, one per agent {m1} R 2 R 1 R 2 {m1, m2} R 1 {m2} (refl. arrows omitted) M, w m1m2 = K 1 m2 because M, w m1m2 = m2 and M, w m2 = m2 model M = W, R, V W nonempty set R : Agt 2 W W ; R i equivalence relation V : W 2 Prp M, w = K i ϕ if M, v = ϕ for every v R i (w) complexity of satisfiability: PSPACE (single agent: NP) the logic of knowledge? generally adopted in AI but: omniscience may be problematic but: / 40

28 Individual knowledge, no actions semantics: indistinguishability relations, one per agent {m1} R 2 R 1 R 2 {m1, m2} R 1 {m2} (refl. arrows omitted) M, w m1m2 = K 1 m2 because M, w m1m2 = m2 and M, w m2 = m2 model M = W, R, V W nonempty set R : Agt 2 W W ; R i equivalence relation V : W 2 Prp M, w = K i ϕ if M, v = ϕ for every v R i (w) complexity of satisfiability: PSPACE (single agent: NP) the logic of knowledge? generally adopted in AI but: omniscience may be problematic but: / 40

29 Individual knowledge, no actions negative introspection axiom K i ϕ K i K i ϕ too strong [Lenzen 1978, Voorbraak 1993] 1 suppose B i K i p 2 suppose p i strongly believes to know p should not imply K i p 3 then K i p (knowledge implies truth) 4 then K i K i p (neg. introspection) 5 then B i K i p (knowledge implies belief) (belief consistent) 6 ( p B i K i p)?!? logic of knowledge should be weaker S4.2 [Lenzen 1978] (replace K i ϕ K i K i ϕ by K i K i ϕ K i K i ϕ) S4.3 [van der Hoek & Meyer] dynamic epistemic logics get more involved / 40

30 Individual knowledge, no actions negative introspection axiom K i ϕ K i K i ϕ too strong [Lenzen 1978, Voorbraak 1993] 1 suppose B i K i p 2 suppose p i strongly believes to know p should not imply K i p 3 then K i p (knowledge implies truth) 4 then K i K i p (neg. introspection) 5 then B i K i p (knowledge implies belief) (belief consistent) 6 ( p B i K i p)?!? logic of knowledge should be weaker S4.2 [Lenzen 1978] (replace K i ϕ K i K i ϕ by K i K i ϕ K i K i ϕ) S4.3 [van der Hoek & Meyer] dynamic epistemic logics get more involved / 40

31 Individual knowledge, no actions negative introspection axiom K i ϕ K i K i ϕ too strong [Lenzen 1978, Voorbraak 1993] 1 suppose B i K i p 2 suppose p i strongly believes to know p should not imply K i p 3 then K i p (knowledge implies truth) 4 then K i K i p (neg. introspection) 5 then B i K i p (knowledge implies belief) (belief consistent) 6 ( p B i K i p)?!? logic of knowledge should be weaker S4.2 [Lenzen 1978] (replace K i ϕ K i K i ϕ by K i K i ϕ K i K i ϕ) S4.3 [van der Hoek & Meyer] dynamic epistemic logics get more involved / 40

32 Outline 1 No uncertainty, nonstrategic actions 2 No uncertainty, strategic actions 3 Individual knowledge, no actions 4 Individual knowledge, nonstrategic actions 5 Individual knowledge, strategic actions 6 Group knowledge, no actions 7 Group knowledge, nonstrategic actions 8 Group knowledge, strategic actions 23 / 40

33 Individual knowledge, nonstrategic actions: PAL Public Announcement Logic PAL ψ! ϕ = the truthful public announcement of ψ can be made and ϕ will be true afterwards reduction axioms (aka regression): ψ! p ψ p ψ! K i ϕ ψ K i [ψ!]ϕ facts don t change (epistemic change only) semantics: S5 models announcements update Kripke models (relativization) M ψ = W ψ, R ψ, V ψ W ψ = ψ M = {w W : M, w = ψ} R ψ (i) = R(i) ( ψ M ψ M ) V ϕ (p) = V(p) ψ M M, w = ψ! ϕ iff M, w = ψ and M ψ, w = ϕ complexity of satisfiability: same as underlying epistemic logic [Lutz, AAMAS 2006] but more succinct [French et al., IJCAI 2011; AIJ 2013] 24 / 40

34 Individual knowledge, nonstrategic actions: the problem of closure under updates in PAL most papers choose S5 as the logic of knowledge others adopt K for generality S5-based PAL works because the set of S5 models is closed under updates by announcements holds also in modal logic K fails in logic of belief KD45 and in logic of knowledge S4.2 [Balbiani et al., AiML 2012] reason: confluence node may be eliminated by update {p} R i {p} R i {p} R i R i {p} R i p! = {p} similar problem with other modal logics R i {p} 25 / 40

35 Individual knowledge, nonstrategic actions: variants of PAL DEL = Dynamic Epistemic Logic [Baltag & Moss, Synthese 2004] agents perceive events only incompletely event models GAL = PAL plus Group announcements [Ågotnes et al., J. Applied Logic 2010] J ϕ = J can achieve ϕ by announcing some known formulas cf. ATL, CL APAL = PAL plus Arbitrary announcements! ϕ = there is a ψ such that ψ! ϕ [Balbiani et al., RSL 2008] 26 / 40

36 Individual knowledge, nonstrategic actions: the problem of uniform choices in APAL You don t see B s and C s cards, and they only see their cards. Among the ace of hearts and the ace of clubs, B has one and C has one, but You don t know who has which. You want agent B to know both Hearts and Clubs, but not C. Is there a public announcement doing the job? 27 / 40

37 Individual knowledge, nonstrategic actions: the problem of uniform choices in APAL B C or B C in S5: Init = K Y Hearts K Y Clubs K Y ( (KB Clubs K C Hearts) = K Y Hearts K Y Clubs K Y ( (KB Hearts K C Clubs) ) Goal = K B (Hearts Clubs) K C (Hearts Clubs) provable in PAL: (K B Hearts K C Hearts) Hearts Clubs! Goal (K B Clubs K C Clubs) Clubs Hearts! Goal so Init K Y! Goal,... but you don t know what to say! 28 / 40

38 Individual knowledge, nonstrategic actions: the problem of uniform choices in APAL B C or B C in S5: Init = K Y Hearts K Y Clubs K Y ( (KB Clubs K C Hearts) = K Y Hearts K Y Clubs K Y ( (KB Hearts K C Clubs) ) Goal = K B (Hearts Clubs) K C (Hearts Clubs) provable in PAL: (K B Hearts K C Hearts) Hearts Clubs! Goal (K B Clubs K C Clubs) Clubs Hearts! Goal so Init K Y! Goal,... but you don t know what to say! 28 / 40

39 Outline 1 No uncertainty, nonstrategic actions 2 No uncertainty, strategic actions 3 Individual knowledge, no actions 4 Individual knowledge, nonstrategic actions 5 Individual knowledge, strategic actions 6 Group knowledge, no actions 7 Group knowledge, nonstrategic actions 8 Group knowledge, strategic actions 29 / 40

40 Individual knowledge, strategic actions Alternating-time Temporal Epistemic Logic ATEL [van der Hoek & Wooldridge, Studia Logica 2003] J ϕ = coalition J can achieve ϕ (whatever opponents do) K i ϕ = agent i Agt knows that ϕ problem of uniform strategies [Schobbens, ENTCS 2004] same as problem of uniform choice for APAL, v.s. K i i XsafeOpen solution in ATELEA = ATEL with Explicit Actions K i i i:dial1234 XsafeOpen 30 / 40

41 Individual knowledge, strategic actions Alternating-time Temporal Epistemic Logic ATEL [van der Hoek & Wooldridge, Studia Logica 2003] J ϕ = coalition J can achieve ϕ (whatever opponents do) K i ϕ = agent i Agt knows that ϕ problem of uniform strategies [Schobbens, ENTCS 2004] same as problem of uniform choice for APAL, v.s. K i i XsafeOpen solution in ATELEA = ATEL with Explicit Actions K i i i:dial1234 XsafeOpen 30 / 40

42 Individual knowledge, strategic actions Alternating-time Temporal Epistemic Logic ATEL [van der Hoek & Wooldridge, Studia Logica 2003] J ϕ = coalition J can achieve ϕ (whatever opponents do) K i ϕ = agent i Agt knows that ϕ problem of uniform strategies [Schobbens, ENTCS 2004] same as problem of uniform choice for APAL, v.s. K i i XsafeOpen solution in ATELEA = ATEL with Explicit Actions K i i i:dial1234 XsafeOpen 30 / 40

43 Outline 1 No uncertainty, nonstrategic actions 2 No uncertainty, strategic actions 3 Individual knowledge, no actions 4 Individual knowledge, nonstrategic actions 5 Individual knowledge, strategic actions 6 Group knowledge, no actions 7 Group knowledge, nonstrategic actions 8 Group knowledge, strategic actions 31 / 40

44 Group knowledge, no actions S5 CK = S5 plus Common knowledge CK J ϕ = it is common knowledge in J Agt that ϕ = EK J ϕ EK J EK J ϕ EK J EK J EK J ϕ useful concept: required for multi-agent coordination [Fagin et al., 1995] required for the existence of a convention [Lewis, 1996] common ground in a conversation [Clark & Marshall, 1981] fixpoint axiom: CK J ϕ EK J (ϕ CK J ϕ) induction axiom (greatest fixpoint axiom): ( ϕ CKJ (ϕ EK J ϕ) ) CK J ϕ will be criticized in the next section other forms of group knowledge/belief exist [Tuomela] group acceptance: does not imply individual belief Acc {lawyer} Guilty B lawyer Guilty consistent 32 / 40

45 Group knowledge, no actions S5 CK = S5 plus Common knowledge CK J ϕ = it is common knowledge in J Agt that ϕ = EK J ϕ EK J EK J ϕ EK J EK J EK J ϕ useful concept: required for multi-agent coordination [Fagin et al., 1995] required for the existence of a convention [Lewis, 1996] common ground in a conversation [Clark & Marshall, 1981] fixpoint axiom: CK J ϕ EK J (ϕ CK J ϕ) induction axiom (greatest fixpoint axiom): ( ϕ CKJ (ϕ EK J ϕ) ) CK J ϕ will be criticized in the next section other forms of group knowledge/belief exist [Tuomela] group acceptance: does not imply individual belief Acc {lawyer} Guilty B lawyer Guilty consistent 32 / 40

46 Group knowledge, no actions S5 CK = S5 plus Common knowledge CK J ϕ = it is common knowledge in J Agt that ϕ = EK J ϕ EK J EK J ϕ EK J EK J EK J ϕ useful concept: required for multi-agent coordination [Fagin et al., 1995] required for the existence of a convention [Lewis, 1996] common ground in a conversation [Clark & Marshall, 1981] fixpoint axiom: CK J ϕ EK J (ϕ CK J ϕ) induction axiom (greatest fixpoint axiom): ( ϕ CKJ (ϕ EK J ϕ) ) CK J ϕ will be criticized in the next section other forms of group knowledge/belief exist [Tuomela] group acceptance: does not imply individual belief Acc {lawyer} Guilty B lawyer Guilty consistent 32 / 40

47 Group knowledge, no actions S5 CK = S5 plus Common knowledge CK J ϕ = it is common knowledge in J Agt that ϕ = EK J ϕ EK J EK J ϕ EK J EK J EK J ϕ useful concept: required for multi-agent coordination [Fagin et al., 1995] required for the existence of a convention [Lewis, 1996] common ground in a conversation [Clark & Marshall, 1981] fixpoint axiom: CK J ϕ EK J (ϕ CK J ϕ) induction axiom (greatest fixpoint axiom): ( ϕ CKJ (ϕ EK J ϕ) ) CK J ϕ will be criticized in the next section other forms of group knowledge/belief exist [Tuomela] group acceptance: does not imply individual belief Acc {lawyer} Guilty B lawyer Guilty consistent 32 / 40

48 Outline 1 No uncertainty, nonstrategic actions 2 No uncertainty, strategic actions 3 Individual knowledge, no actions 4 Individual knowledge, nonstrategic actions 5 Individual knowledge, strategic actions 6 Group knowledge, no actions 7 Group knowledge, nonstrategic actions 8 Group knowledge, strategic actions 33 / 40

49 Group knowledge, nonstrategic actions PAL CK = PAL plus Common knowledge semantics: same as PAL accessibility relation for CK J = greatest fixpoint of EK J relation rebuilt after each update no reduction axioms for CK J : = CK J [ψ!]ϕ [ψ!]ck J ϕ = [ψ!]ck J ϕ ( ψ CK J [ψ!]ϕ) common knowledge may pop up in an unforeseeable way! 34 / 40

50 Group knowledge, nonstrategic actions: the ignorant compatriots Agents B and C are both Italian and don t know each other. They meet during the coffee break and start to talk in English. Init = K B IT B CK {B,C} (IT B K B IT B ) ( IT B K B IT B ) K C IT C CK {B,C} (IT C K C IT C ) ( IT C K C IT C ) 1 first scenario: a third agent truthfully says: Hey, you are both Italian! Init IT B IT C! CK {B,C} (IT B IT C ) 2 second scenario: a third agent truthfully says: Hey, you are compatriots! Init IT B IT C! CK {B,C} (IT B IT C ) [Lorini & H, 2013] 35 / 40

51 Group knowledge, nonstrategic actions: the ignorant compatriots Agents B and C are both Italian and don t know each other. They meet during the coffee break and start to talk in English. Init = K B IT B CK {B,C} (IT B K B IT B ) ( IT B K B IT B ) K C IT C CK {B,C} (IT C K C IT C ) ( IT C K C IT C ) 1 first scenario: a third agent truthfully says: Hey, you are both Italian! Init IT B IT C! CK {B,C} (IT B IT C ) 2 second scenario: a third agent truthfully says: Hey, you are compatriots! Init IT B IT C! CK {B,C} (IT B IT C ) [Lorini & H, 2013] 35 / 40

52 Group knowledge, nonstrategic actions: the ignorant compatriots Agents B and C are both Italian and don t know each other. They meet during the coffee break and start to talk in English. Init = K B IT B CK {B,C} (IT B K B IT B ) ( IT B K B IT B ) K C IT C CK {B,C} (IT C K C IT C ) ( IT C K C IT C ) 1 first scenario: a third agent truthfully says: Hey, you are both Italian! Init IT B IT C! CK {B,C} (IT B IT C ) 2 second scenario: a third agent truthfully says: Hey, you are compatriots! Init IT B IT C! CK {B,C} (IT B IT C ) [Lorini & H, 2013] 35 / 40

53 Group knowledge, nonstrategic actions: the ignorant compatriots, ctd. After the announcement of IT B IT C, is it part of the common ground of the conversation that IT B IT C??? can be viewed as common knowledge version of the omniscience problem: does a group know all the consequences of its knowledge? implicit vs. explicit common knowledge Init IT B IT C! ( ICK {A,B} (IT B IT C ) ECK {A,B} (IT B IT C ) ) implicit common knowledge = PAL CK common knowledge induction axiom: OK reduction axiom: KO explicit common knowledge: accessibility relation for ECK J is some fixpoint, but not necessarily the greatest induction axiom: KO reduction axiom: OK [ψ!]eck J ϕ (ψ ECK J [ψ!]ϕ) 36 / 40

54 Group knowledge, nonstrategic actions: the ignorant compatriots, ctd. After the announcement of IT B IT C, is it part of the common ground of the conversation that IT B IT C??? can be viewed as common knowledge version of the omniscience problem: does a group know all the consequences of its knowledge? implicit vs. explicit common knowledge Init IT B IT C! ( ICK {A,B} (IT B IT C ) ECK {A,B} (IT B IT C ) ) implicit common knowledge = PAL CK common knowledge induction axiom: OK reduction axiom: KO explicit common knowledge: accessibility relation for ECK J is some fixpoint, but not necessarily the greatest induction axiom: KO reduction axiom: OK [ψ!]eck J ϕ (ψ ECK J [ψ!]ϕ) 36 / 40

55 Outline 1 No uncertainty, nonstrategic actions 2 No uncertainty, strategic actions 3 Individual knowledge, no actions 4 Individual knowledge, nonstrategic actions 5 Individual knowledge, strategic actions 6 Group knowledge, no actions 7 Group knowledge, nonstrategic actions 8 Group knowledge, strategic actions 37 / 40

56 Group knowledge, strategic actions ATEL CK = ATEL plus common knowledge problem: uniform strategies K i {i} XSafeOpen ( knowing that ) does not mean that the agent knows which action to choose ( knowing how ) in STIT logic: K i Stit {i} X SafeOpen K i Stit {i} X SafeOpen problem: which form of group knowledge required for (uniform) group strategies? sometimes distributed knowledge DK J ϕ sometimes shared knowledge EK J ϕ sometimes common knowledge CK J ϕ 38 / 40

57 Conclusion S5 CK PAL CK ATEL CK S5 PAL ATEL no uncertainty PDL, CL-PC ATL, STIT knowledge action no actions nonstrategic strategic revisited logics for MAS and their problems S5: inadequate as a logic of knowledge S5 CK : questionable as the logic of common knowledge APAL and ATEL: can t talk about uniform strategies ATL: commitment to strategies missing 39 / 40

58 Conclusion S5 CK PAL CK ATEL CK S5 PAL ATEL no uncertainty PDL, CL-PC ATL, STIT knowledge action no actions nonstrategic strategic revisited logics for MAS and their problems S5: inadequate as a logic of knowledge S5 CK : questionable as the logic of common knowledge APAL and ATEL: can t talk about uniform strategies ATL: commitment to strategies missing 39 / 40

59 Thanks based on joint work with: Philippe Balbiani (U. Toulouse, CNRS) Hans van Ditmarsch (U. Nancy, CNRS) Tiago de Lima (U. Artois, CNRS) Emiliano Lorini (U. Toulouse, CNRS) Frédédric Moisan (U. Toulouse) François Schwarzentruber (U. Rennes, ENS) Nicolas Troquard (CNR, Trento) Dirk Walther (U. Dresden) Eur. Network for Social Intelligence action and agency (WG1) group attitudes (WG3) Eur. Conf. on Social Intelligence ECSI-2014 (deadline Sept. 3) latest version downloadable from 40 / 40