Beliefs, Desires And Intentions

Transcription

1 Jordy Oldenkamp Erwin Scholtens Jesse van den Kieboom Pieter de Bie Michiel Holtkamp March 27, 2007

2 1 The BDI System 2 Agents within BDI-Architecture 3 Collective Intentions 4 Formalization 5 Problems with intentions

3 Overview Based on the article Modelling Rational Agents within a BDI-Architecture by Anand S. Rao and Michael P. Georgeff 1 History of Intention 2 Informal Semantics 3 Syntax

4 History of Intention Intention From the Cambridge Online Dictionary: Intention noun [C or U] something that you want and plan to do It wasn t my intention to exclude her from the list - I just forgot her. I ve no intention of changing my plans just to fit in with his.

5 History of Intention Intention by Bratman Philosophy professor who created foundations for further research regarding Intentions. Definition: Intention by Bratman Intentions are partial plans of action that the agent is committed tot execute to fulfill her goals.

6 History of Intention Formalized by Cohen and Levesque Intentions as temporal sequences of an agent s beliefs and goals. Definition: Fanatically committed Will maintain her goals until they are believed to be achieved or believed to be unachievable Definition: Relativized commitment Similar as Fanatically committed, but may also drop goals based on specified belief-conditions

7 History of Intention Alternative Formalism Rao defines an alternative formalism based on the following properties: Focus on Intentions Choice and Possibilities Interrelationship between beliefs, goals and intentions

8 Informal Semantics Informal Semantics The model uses the following new modal operators: optional inevitable The standard temporal operators are used: (eventually) (always)

9 Informal Semantics Informal - Time Tree s p s q Optionally eventually r r s r s r s Optionally always r q Inevitably eventually q s s q inevitably always s Figure: An example of a time tree

10 Informal Semantics Belief and Goal-accessible For every belief accessible world there is a subworld with Goals For every goal accessible world there is a subworld with Intentions However the converse relation between belief and goals does not need to hold

11 Informal Semantics Dentist Example Belief worlds b1 p Goal worlds g1 p Intention worlds i1 p -p -f d1 b d2 f -p -f p -p -f d1 d2 f p -p -f d1 f f f g2 i1 -p -p -p d1 f -p d1 f -f d2 -p -f f Figure: The dentist s example

12 Syntax Types of Formulas State Formulas Path Formulas Events

13 Syntax State Formulas Any first-order formula is a state formula If ϕ 1 and ϕ 2 are state formulas and x is an individual or event variable, then ϕ 1,ϕ 1 ϕ 2, and xϕ 1 (x) are state formulas. If ϕ is a state formula then BEL(ϕ), GOAL(ϕ) and INTENT (ϕ) are state formulas.

14 Syntax Example of State Formulas p and q are state formulas, therefore p q, p, q and GOAL(p) are state formulas.

15 Syntax Path Formulas any state formula is also a path formula If ψ 1 and ψ 2 are path formulas, then ψ 1, ψ 1 ψ 2, ψ 1 ψ 2, ψ 1, ψ 1 are path formulas. If ψ is a path formula, then optional(ψ) is a state formula.

16 Syntax Events If e is an event type, then succeeds(e), fails(e), does(e), succeeded(e), failed(e) and done(e) are state formulas.

17 Agents within BDI-Architecture 1 Possible-Worlds Semantics 2 Commitments as Axioms of Change

18 Possible-Worlds Semantics Formal - Interpretation M Definition: Interpretation M An interpretation M is a tuple, M = W, E, T,, U, B, G, I, Φ W A set of worlds w 1, w 2, E A set of events e T A set of time points A binary relation on time points

19 Possible-Worlds Semantics Formal - Interpretation M Definition: Interpretation M An interpretation M is a tuple, M = W, E, T,, U, B, G, I, Φ U B G I Φ Universe of discourse Mapping of current situation to belief-accessible worlds Mapping of current situation to goal-accessible worlds Mapping of current situation to intention-accessible worlds Mapping of first-order entities to elements in U for any given world and time point

20 Possible-Worlds Semantics Formal - Time Tree Definition: Time Tree A time tree is defined as a tuple, T w, A w, S w, F w T w A w S w F w Set of time points in the world w, where T w T A binary relation on time points in T w Mapping of adjacent time points to successful events e Mapping of adjacent time points to failed events e

21 Possible-Worlds Semantics Formal - Subworld Definition: Subworld A subworld is defined to be a sub-tree of a world with the same truth assignment of formulas.

22 Possible-Worlds Semantics Semantics of some first order formulas Definition: (not) M, v, w t = ϕ iff M, v, w t = ϕ p ~p

23 Possible-Worlds Semantics Semantics of some first order formulas Definition: (next) M, v, (w t0, w t1, ) = ϕ iff M, v, (w tk, ) = ϕ p next(p)

24 Possible-Worlds Semantics Semantics of some first order formulas Definition: (eventually) M, v, (w t0, w t1, ) = ϕ iff k, k 0 such that M, v, (w tk, ) = ϕ p eventually(p)

25 Possible-Worlds Semantics Semantics of some first order formulas Definition: (until) M, v, (w t0, w t1, ) = φ 1 φ 2 iff 1 k, k 0 such that M, v, (w tk, ) = ϕ 2 and for all 0 j < k, M, v, (w tk, ) = ϕ 1 or 2 for all j 0, M, v, (w tk, ) = ϕ 1

26 Possible-Worlds Semantics Semantics of some first order formulas q p p U q q p p U q

27 Possible-Worlds Semantics Semantics of some first order formulas Definition: optional M, v, w t0 = optional(ϕ) iff there exists a path (w t0, w t1, ) such that M, v, (w t0, w t1, ) = ϕ

28 Possible-Worlds Semantics Formal - Events M, v, w t1 = succeeded(e) iff there exists t 0 such that S w (t 0, t 1 ) = e

29 Possible-Worlds Semantics Formal - Events M, v, w t1 = succeeded(e) iff there exists t 0 such that S w (t 0, t 1 ) = e M, v, w t1 = failed(e) iff there exists t 0 such that F w (t 0, t 1 ) = e

30 Possible-Worlds Semantics Formal - Events M, v, w t1 = succeeded(e) iff there exists t 0 such that S w (t 0, t 1 ) = e M, v, w t1 = failed(e) iff there exists t 0 such that F w (t 0, t 1 ) = e done(e) is defined as succeeded(e) failed(e)

31 Possible-Worlds Semantics Belief Desire and Intention M, v, w t = BEL(ϕ) iff w ɛb w t M, v, w t = ϕ

32 Possible-Worlds Semantics Belief Desire and Intention M, v, w t = BEL(ϕ) iff w ɛb w t M, v, w t = ϕ M, v, w t = GOAL(ϕ) iff w ɛg w t M, v, w t = ϕ

33 Possible-Worlds Semantics Belief Desire and Intention M, v, w t = BEL(ϕ) iff w ɛb w t M, v, w t = ϕ M, v, w t = GOAL(ϕ) iff w ɛg w t M, v, w t = ϕ M, v, w t = INTEND(ϕ) iff w ɛi w t M, v, w t = ϕ

34 Possible-Worlds Semantics An Example Belief worlds b1 p Goal worlds g1 p Intention worlds i1 p -p -f d1 b d2 f -p -f p -p -f d1 d2 f p -p -f d1 f f f g2 i1 -p -p -p d1 f -p d1 f -f d2 -p -f f In all goal accessible worlds inevitable( f ), in beliefs this is BEL(optional( f )).

35 Possible-Worlds Semantics Another Example b1 w0 t0 e0 e1 t2 t1 e2 B t3 t0 e0 e1 t2 t1 e2 t3 B b2 e0 e1 t2 t0 t1 e2 t3

36 Commitments The basic agent and commitment strategies The basic I-system : AI1 - AI8 The basic agent: The basic I-system + AI9a OR AI9b OR AI9c

37 Commitments Blind Commitment A blindly committed agent maintains her intentions until she believes that she has achieved them. Axiom: AI 9a INTEND(inevitable ϕ) inevitable(intend(inevitable ϕ) BEL(ϕ))

38 Commitments Single-minded Commitment A single-minded agent maintains her intentions as long as she believes that they are still options. Axiom: AI 9b INTEND(inevitable ϕ) inevitable(intend(inevitable ϕ) (BEL(ϕ) BEL(optional ϕ))

39 Commitments Open-minded Commitment An open-minded agent maintains her intentions as long as these intentions are still her goals. Axiom: AI 9c INTEND(inevitable ϕ) inevitable(intend(inevitable ϕ) (BEL(ϕ) GOAL(optional ϕ)))

40 Conclusion Comparison and Conclusion Comparison with Cohen and Levesque Number of commitments

41 Collective Intentions Based on the article Collective Intentions by Rineke Verbrugge and Barbara Dunin-Kȩplicz 1 Introduction and definitions 2 Role of intentions in practical reasoning 3 Formal theory definition

42 Introduction and definitions Multi Agent Systems Agents need to communicate, cooperate, coordinate and negotiate Type of interaction depends on circumstances Paradigmatic example: Cooperative Problem Solving

43 Introduction and definitions Intentional systems Agents are represented as maintaining an intentional stance towards their environment

44 Introduction and definitions Intentional systems Agents are represented as maintaining an intentional stance towards their environment System realizes the practical reasoning paradigm

45 Introduction and definitions Intentional systems Agents are represented as maintaining an intentional stance towards their environment System realizes the practical reasoning paradigm Belief-desires-intentions systems

46 Introduction and definitions Intentional systems Agents are represented as maintaining an intentional stance towards their environment System realizes the practical reasoning paradigm Belief-desires-intentions systems Intentions are an inspiration for a goal-directed activity

47 Introduction and definitions Intentional systems Agents are represented as maintaining an intentional stance towards their environment System realizes the practical reasoning paradigm Belief-desires-intentions systems Intentions are an inspiration for a goal-directed activity Beliefs are the agent s informational attitudes

48 Introduction and definitions Intentional systems Agents are represented as maintaining an intentional stance towards their environment System realizes the practical reasoning paradigm Belief-desires-intentions systems Intentions are an inspiration for a goal-directed activity Beliefs are the agent s informational attitudes Desires/goals, intentions and commitments are the agent s motivational attitudes

49 Introduction and definitions Teams Collective notion implies groups of agents Definition: Team A group in which the agents are restricted to having a common goal of some sort. Definition: Teamwork Collective intention of a team to achieve a goal by simultaneous and coordinated individual actions and a team must be aware of the group effort as a whole

50 Introduction and definitions Collective intentions Intentions are first class citizens Intentions are a subset of the agent s goals Intentions are goal-directed activity reflected in social and collective commitments

51 Role of intentions in practical reasoning Reasoning Practical reasoning is aimed at conduct rather than knowledge Cycle of reasoning 1 Repeatedly updating beliefs about the environment 2 Deciding what options are available 3 Filtering these options to determine new intentions 4 Creating commitments on the basis of intentions 5 Performing actions in accordance with commitments

52 Role of intentions in practical reasoning Processes Practical reasoning involves two important processes 1 Deliberation: Deciding what goals to achieve 2 Means-end-reasoning: Deciding how to achieve these goals

53 Role of intentions in practical reasoning Intentions Not interested in drives and desires (human behaviour) Rather, interested in rational decision making Thus: agents are considered logical reasoners

54 Role of intentions in practical reasoning Role of intentions There is common agreement that intentions play important roles in practical reasoning 1 Intentions drive means-end-reasoning 2 Intentions constrain future deliberation 3 Intentions persist 4 Intentions influence beliefs upon which future practical reasoning is based

55 Role of intentions in practical reasoning Problems with BDI-agents How to achieve a good balance between previously mentioned roles? The need to drop intentions (intention strategies) Balancing pro-active and reactive behaviour

56 Formal theory definition System As defined by Rineke Verbrugge and Barbara Dunin-Kȩplicz Formally characterize what it means for a team to have a collective intention towards a common goal Using a multi-modal logical framework Two different definitions will be presented No temporal considerations

57 Formal theory definition Formulas and their meanings The following formulas are defined bel(a, ϕ) e-bel G (ϕ) c-bel G (ϕ) goal(a, ϕ) int(a, ϕ) agent a has the belief that ϕ every agent in group G has the belief that ϕ group G has the collective belief that ϕ agent a has as a goal that ϕ be true agent a has the intention to make ϕ true

58 Formalization 1 Collective Intentions 2 The Standard Case Informal Definition Formal Definition Example Nested Intentions

59 Collective Intentions How do teams acquire collective intentions? Each agent has its own abilities So, collective intentions arise by communication Opportunities and social structures generally influence group intentions However, we only try to find a minimal condition

60 Collective Intentions Informal Definition of Collective Intentions Intuitively, we might think: Collective intentions arise when all agents have the associated individual intention INT(i, ϕ) However, what if there are different agents all wanting exactly the same world state ϕ, but want it exclusively?

61 Collective Intentions Informal Definition of Mutual Intentions Having the same individual intentions is not enough All agents need to have the intention that all other agents have the same intention And all agents should intend all other agents to intend all agents to have the intentions... We call this Mutual intentions Definition: Mututal Intentions Mutual intentions exist when all agents intend ϕ, all agents intend all agents to intend ϕ, and so on.

62 Collective Intentions Formal Definition of Mutual Intentions First, we define Every agent intends : Definition: Everyone Intends In a group G, model M and world s: E-INT G (ϕ) iff for all i G, (M, s) =INT(i, ϕ).

63 Collective Intentions Formal Definition of Mutual Intentions Mutual Intentions 1 Let E-INT 1 G (ϕ) be an abbrevation for E-INT G (ϕ) 2 Let E-INT n G (ϕ)(n > 1) be an abbrevation for E-INT G (E-INT n 1 G (ϕ)) 3 then, (M, s) = M-INT G (ϕ) iff (M, s) =E-INT n G (ϕ) for all n > 1

64 Collective Intentions Formal Definition of Mutual Intentions II Or, alternatively: Definition: Mutual Intentions (M, s) = M-INT G (ϕ) iff (M, t) = ϕ for all t that are G I reachable from s Definition: G I reachability A world t W is G I reachable from s W iff there are I accessibility arrows for all agents i G from world s, w 1,, t.

65 Defining the system KD C-INT G n Extending KD n Now, we can add the previous definitions to KD n, creating the new system KD M-INT G n The system KD M-INT G n M1 E-INT G (ϕ) i G INT(i, ϕ) M2 M-INT G (ϕ) E-INT G (ϕ M-INT G (ϕ)) RM1 ϕ E-INT G (ψ ϕ) infer ϕ M-INT G (ψ)

66 Defining the system KD C-INT G n Soundness of KD M-INT G n KD M-INT G n is complete and sound with respect to all Kripke-models where all n accessibility relations are serial We will not give a completeness proof here We WILL give a soundness proof of RM1 Soundness of RM1 Suppose that = ϕ E-INT G (ψ ϕ). We need to show that = ϕ M-INT G (ψ)

67 Defining the system KD C-INT G n Soundness of RM1 Soundness of RM1 Suppose that = ϕ E-INT G (ψ ϕ). We need to show that = ϕ M-INT G (ψ) 1. Take any Kripke model M = (W, B, G, I, Val) with serial I -accessibility for agents and any world s W with (M, s) = ϕ ϕ s I G w 1 I G I G t

68 Defining the system KD C-INT G n Soundness of RM1 Soundness of RM1 Suppose that = ϕ E-INT G (ψ ϕ). We need to show that = ϕ M-INT G (ψ) 1. Take any Kripke model M = (W, B, G, I, Val) and s W, (M, s) = ϕ 2. Suppose that t is G I reachable from s with k steps along the path w 0,, w k (= t) ϕ s I G w 1 I G I G t

69 Defining the system KD C-INT G n Soundness of RM1 Soundness of RM1 Suppose that = ϕ E-INT G (ψ ϕ). We need to show that = ϕ M-INT G (ψ) 1+2. Take any Kripke model M = (W, B, G, I, Val), s W, (M, s) = ϕ, t G I reachable from s 3. We know that (M, s) = ϕ E-INT G (ψ ϕ), (M, s) = ϕ and thus (M, s) = E-INT ( ψ ϕ), and thus (M, w 1 ) = ψ ϕ ϕ I G s E-INT(ϕ ψ) ϕ ψ w 1 I G I G t

70 Defining the system KD C-INT G n Soundness of RM1 Soundness of RM1 Suppose that = ϕ E-INT G (ψ ϕ). We need to show that = ϕ M-INT G (ψ) 4. Since in w 1, ϕ is true, we can continue along the same route for w 2, and so on to t. ϕ E-INT(ϕ ψ) ϕ ψ I w G 1 I G I G s E-INT(ϕ ψ) ϕ ψ t

71 Defining the system KD C-INT G n Soundness of RM1 Soundness of RM1 Suppose that = ϕ E-INT G (ψ ϕ). We need to show that = ϕ M-INT G (ψ) 4. Since in w 1, ϕ is true, we can continue along the same route for w 2, and so on to t. 5. Since (M, t) = ψ, for every t reachable from s, we conclude that (M, s) = ϕ M-INT G (ψ) ϕ I G s E-INT(ϕ ψ) M-INT(ψ) E-INT(ϕ ψ) E-INT(ϕ ψ) ϕ ψ ϕ ψ I w G 1 t I G

72 Defining the system KD C-INT G n Formal Definition of Collective Intention Finally, we can come to the full definition of collective intention: Definition: Collective Intention M3 C-INT G (ϕ) M-INT G (ϕ) C-BEL G (M-INT G (ϕ)) This last axiom, added to KD M-INT G n KD C-INT G n defines the system

73 Examples Example (I) 1 Two assassins have the idea to assassinate someone together: ϕ = perform the assassination together INT(Balthasar, ϕ) INT(Gerard, ϕ) 2 They communicate about this, and start practising together. A mutual intention is now in place. There is also a collective belief C-BEL G (M-INT(ϕ)), and thus C-INT(ϕ)

74 Examples Example (II) 3 Now they are asked to murder Willem van Oranje (= ψ), and thus a more concrete plan forms: C-INT G (ψ) 4 They sign a contract together, declaring their intentions to assassinate together. 5 Because of this contract, we can speak of collective knowledge, not merely belief, thus: Figure: The murder of William the Silent by Balthasar Gérard. M-INT G (ψ) C-KNOW G (M-INT G (ψ))

75 Examples Nested Intentions How can nested intentions, which seem to be infinite, be established? Answer: Although the intentions are nested infinitely, this nesting is in real life established in a finite number of steps The amount of communication is expressed in M3 by C-BEL G (M-INT G (ϕ)). It depends on the circumstances For example, in a rescue situation where everybody has a predefined task in the case of an emergency, very little communication is necessary for collective intentions to exist

76 Problems with intentions 1 Inappropriate cases Joint-intention problem More-person coalition problem 2 Alternative definitions for time-critical situations

77 Inappropriate cases Going to New York Definition: Joint intention by Rao et al. C-INT Rao G (ϕ) E-INT G (ϕ) C-BEL G (E-INT G (ϕ))

78 Inappropriate cases Going to New York Definition: Joint intention by Rao et al. C-INT Rao G (ϕ) E-INT G (ϕ) C-BEL G (E-INT G (ϕ)) ϕ = a and b go to NY together

79 Inappropriate cases Going to New York Definition: Joint intention by Rao et al. C-INT Rao G (ϕ) E-INT G (ϕ) C-BEL G (E-INT G (ϕ)) ϕ = a and b go to NY together E-INT G (ϕ)

80 Inappropriate cases Going to New York Definition: Joint intention by Rao et al. C-INT Rao G (ϕ) E-INT G (ϕ) C-BEL G (E-INT G (ϕ)) ϕ = a and b go to NY together E-INT G (ϕ) Possibly C-BEL G (E-INT G (ϕ)) thus, C-INT Rao G (ϕ)

81 Inappropriate cases Going to New York Definition: Joint intention by Rao et al. C-INT Rao G (ϕ) E-INT G (ϕ) C-BEL G (E-INT G (ϕ)) ϕ = a and b go to NY together E-INT G (ϕ) Possibly C-BEL G (E-INT G (ϕ)) thus, C-INT Rao G (ϕ) but although INT(a, E-INT G (ϕ))

82 Inappropriate cases Going to New York Definition: Joint intention by Rao et al. C-INT Rao G (ϕ) E-INT G (ϕ) C-BEL G (E-INT G (ϕ)) ϕ = a and b go to NY together E-INT G (ϕ) Possibly C-BEL G (E-INT G (ϕ)) thus, C-INT Rao G (ϕ) but although INT(a, E-INT G (ϕ)) not INT(b, E-INT G (ϕ))

83 Inappropriate cases Going to New York Definition: Joint intention by Rao et al. C-INT Rao G (ϕ) E-INT G (ϕ) C-BEL G (E-INT G (ϕ)) ϕ = a and b go to NY together E-INT G (ϕ) Possibly C-BEL G (E-INT G (ϕ)) thus, C-INT Rao G (ϕ) but although INT(a, E-INT G (ϕ)) not INT(b, E-INT G (ϕ)) so not E-INT G (E-INT G (ϕ))

84 Inappropriate cases Going to New York Definition: Joint intention by Rao et al. C-INT Rao G (ϕ) E-INT G (ϕ) C-BEL G (E-INT G (ϕ)) ϕ = a and b go to NY together E-INT G (ϕ) Possibly C-BEL G (E-INT G (ϕ)) thus, C-INT Rao G (ϕ) but although INT(a, E-INT G (ϕ)) not INT(b, E-INT G (ϕ)) so not E-INT G (E-INT G (ϕ)) so not M-INT G (ϕ)

85 Inappropriate cases Going to New York Definition: Joint intention by Rao et al. C-INT Rao G (ϕ) E-INT G (ϕ) C-BEL G (E-INT G (ϕ)) ϕ = a and b go to NY together E-INT G (ϕ) Possibly C-BEL G (E-INT G (ϕ)) thus, C-INT Rao G (ϕ) but although INT(a, E-INT G (ϕ)) not INT(b, E-INT G (ϕ)) so not E-INT G (E-INT G (ϕ)) so not M-INT G (ϕ) so not C-INT G (ϕ)

86 Inappropriate cases Comparison with the two-level definition One-level definition C-INT 1 G (ϕ) E-INT G (ϕ) C-BEL G (E-INT G (ϕ)) Two-level definition C-INT 2 G (ϕ) E-INT G (ϕ) C-BEL G (E-INT G (ϕ)) E-INT G (E-INT G (ϕ)) C-BEL G (E-INT G (E-INT G (ϕ)))

87 Inappropriate cases Comparison with the two-level definition Two-level definition C-INT 2 G (ϕ) E-INT G (ϕ) C-BEL G (E-INT G (ϕ)) E-INT G (E-INT G (ϕ)) C-BEL G (E-INT G (E-INT G (ϕ)))

88 Inappropriate cases Comparison with the two-level definition Two-level definition C-INT 2 G (ϕ) E-INT G (ϕ) C-BEL G (E-INT G (ϕ)) E-INT G (E-INT G (ϕ)) C-BEL G (E-INT G (E-INT G (ϕ))) Three assassins, Two-person coalition

89 Inappropriate cases Comparison with the two-level definition Two-level definition C-INT 2 G (ϕ) E-INT G (ϕ) C-BEL G (E-INT G (ϕ)) E-INT G (E-INT G (ϕ)) C-BEL G (E-INT G (E-INT G (ϕ))) Three assassins, Two-person coalition ϕ = two assissins assassinate a person

90 Inappropriate cases Comparison with the two-level definition Two-level definition C-INT 2 G (ϕ) E-INT G (ϕ) C-BEL G (E-INT G (ϕ)) E-INT G (E-INT G (ϕ)) C-BEL G (E-INT G (E-INT G (ϕ))) Three assassins, Two-person coalition ϕ = two assissins assassinate a person Exclude coalitions: INT(a, M-INT {a,b} (ϕ)) but not INT(a, M-INT {a,b,c} (ϕ))

91 Inappropriate cases N-level definition In general, a situation with coalitions of k agents from a total of k + 1 agents, can be correctly described with a k + 1 level definition of C-INT G. M3 is a recursive definition that is valid for all levels. In practice a definition with level k + 1 is sufficient. Reminder: M3 C-INT G (ϕ) M-INT G (ϕ) C-BEL G (M-INT G (ϕ))

92 Alternative definitions for time-critical situations Time-critical situations No (time for) communication No collective belief about mutual intention Start cooperating before C-INT G is established We need E-INT G (C-INT G (ϕ))

93 Alternative definitions for time-critical situations Trapped under the ice trapped under the ice: Seabert

94 Alternative definitions for time-critical situations Trapped under the ice trapped under the ice: Seabert potential helpers: Tommy, Aura

95 Alternative definitions for time-critical situations Trapped under the ice trapped under the ice: Seabert potential helpers: Tommy, Aura no communication, limited perception; only movement

96 Alternative definitions for time-critical situations Trapped under the ice trapped under the ice: Seabert potential helpers: Tommy, Aura no communication, limited perception; only movement ϕ = Seabert has been rescued

97 Alternative definitions for time-critical situations Trapped under the ice trapped under the ice: Seabert potential helpers: Tommy, Aura no communication, limited perception; only movement ϕ = Seabert has been rescued ψ = two persons are needed

98 Alternative definitions for time-critical situations Trapped under the ice trapped under the ice: Seabert potential helpers: Tommy, Aura no communication, limited perception; only movement ϕ = Seabert has been rescued ψ = two persons are needed INT(Tommy, ϕ), INT(Aura, ϕ), C-BEL G (ψ), so: M-INT G (ϕ)

99 Alternative definitions for time-critical situations Trapped under the ice trapped under the ice: Seabert potential helpers: Tommy, Aura no communication, limited perception; only movement ϕ = Seabert has been rescued ψ = two persons are needed INT(Tommy, ϕ), INT(Aura, ϕ), C-BEL G (ψ), so: M-INT G (ϕ) M-INT G (ϕ) E-BEL G (M-INT G (ϕ))

100 Alternative definitions for time-critical situations Trapped under the ice trapped under the ice: Seabert potential helpers: Tommy, Aura no communication, limited perception; only movement ϕ = Seabert has been rescued ψ = two persons are needed INT(Tommy, ϕ), INT(Aura, ϕ), C-BEL G (ψ), so: M-INT G (ϕ) M-INT G (ϕ) E-BEL G (M-INT G (ϕ)) but not: C-BEL G (M-INT G (ϕ)) so no C-INT G (ϕ)!

101 Alternative definitions for time-critical situations M2 Definition: M2 M-INT G (ϕ) E-INT G (ϕ M-INT G (ϕ)) Definition: M2 M-INT G (ϕ) E-INT G (ϕ C-INT G (ϕ))

102 Alternative definitions for time-critical situations M2 Definition: M2 M-INT G (ϕ) E-INT G (ϕ M-INT G (ϕ)) Definition: M2 M-INT G (ϕ) E-INT G (ϕ C-INT G (ϕ)) M-INT G (ϕ) is meant to be true if everyone in G intends ϕ, everyone in G intends that everyone in G intends ϕ, etc. and that there is collective belief about those intentions (and thus collective intentions)

103 Alternative definitions for time-critical situations M2 Definition: M2 M-INT G (ϕ) E-INT G (ϕ M-INT G (ϕ)) Definition: M2 M-INT G (ϕ) E-INT G (ϕ C-INT G (ϕ)) M-INT G (ϕ) is meant to be true if everyone in G intends ϕ, everyone in G intends that everyone in G intends ϕ, etc. and that there is collective belief about those intentions (and thus collective intentions) Resulting system: KD M INT G n

104 Alternative definitions for time-critical situations M3 Definition: M3 C-INT G (ϕ) M-INT G (ϕ) C-BEL G (M-INT G (ϕ)) Definition: M3 C-INT G (ϕ) M-INT G (ϕ) C-BEL G (M-INT G (ϕ))

105 Alternative definitions for time-critical situations M3 Definition: M3 C-INT G (ϕ) M-INT G (ϕ) C-BEL G (M-INT G (ϕ)) Definition: M3 C-INT G (ϕ) M-INT G (ϕ) C-BEL G (M-INT G (ϕ)) Resulting system: KD C INT G n

106 Alternative definitions for time-critical situations Trapped under the ice (cont.) INT(Tommy, ϕ), INT(Aura, ϕ), C-BEL G (ψ), so: M-INT G (ϕ)

107 Alternative definitions for time-critical situations Trapped under the ice (cont.) INT(Tommy, ϕ), INT(Aura, ϕ), C-BEL G (ψ), so: M-INT G (ϕ) E-INT G (ϕ C-INT G (ϕ)), so M-INT G (ϕ)

108 Alternative definitions for time-critical situations Trapped under the ice (cont.) INT(Tommy, ϕ), INT(Aura, ϕ), C-BEL G (ψ), so: M-INT G (ϕ) E-INT G (ϕ C-INT G (ϕ)), so M-INT G (ϕ) M-INT G (ϕ) C-BEL G (M-INT G (ϕ)), so C-INT G (ϕ)

109 Alternative definitions for time-critical situations Trapped under the ice (cont.) INT(Tommy, ϕ), INT(Aura, ϕ), C-BEL G (ψ), so: M-INT G (ϕ) E-INT G (ϕ C-INT G (ϕ)), so M-INT G (ϕ) M-INT G (ϕ) C-BEL G (M-INT G (ϕ)), so C-INT G (ϕ) Seabert is saved!

110 Alternative definitions for time-critical situations Diamond of implications M-INT' C-INT' X M-INT C-INT Figure: The diamond of implications

111 Alternative definitions for time-critical situations Discussion How to achieve a good balance between previously mentioned roles? The need to drop intentions (intention strategies) Balancing pro-active and reactive behaviour What is more useful and more realistic; M2 or M2, M3 or M3? Is BDI a complete system for real life situations?

112 Alternative definitions for time-critical situations Questions