Section 9: Planning CPSC Artificial Intelligence Michael M. Richter

Transcription

1 Section 9: Planning

2 Actions (1) An action changes a situation and their description has to describe this change. A situation description (or a state) sit is a set of ground atomic formulas (sometimes literals are allowed). The application part of an action A consists of two lists of ground atomic formulas: The delete list DEL The add list ADD The new situation sit from applying A to sit is sit = (sit DEL) ADD This means: We describe what is discarded by the action and what is newly generated. A set PRE of formulas describres when the action can be performed..

3 Actions (2) For each action therefore a triple set (PRE, ADD, DELETE) of atomic formulas (sometimes literals) is associated which represents the action. The action can be applied if the formulas from a list PRE of preconditions are satisfied. A situation sit satisfies the preconditions if it contains the list. Each action is syntactically described by some operator. The operator description can contain variables, actions will then be obtained as instances.

4 Operator Description An operator is of the form O(x 1,...,x n ) where O is the operator symbol the x i are variables which range over constants describing the situations Operator description: Described by precondition list PRE, ADD and DEL list which now can contain variables Matching: The variables are matched against the constants in the situation description Application: After the match an action is obtained as an instance of the operator and its description which is applied to the situation.

5 Plan A plan is a sequence of instantiated operators, i.e. each parameter x i in an operator has a ground term assigned. Plans are written as follows: Plan = ( o 1 (t 11,...,t 1n1 ), o 2 (t 21,...,t 2n2 ),..., o m (t m1,...,t mnm ) ) Here, all terms t ij must be ground. The plan consists of m operators, or we say this is a plan of size m. A plan can be applied to an initial situation sit 0. Then, the operators are applied from left to right. Please note, that each operator is only applicable if its precondition is true in the situation it is applied. o 1 (...) o 2 (...) o 3 (...) o m (...) sit 0 sit 1 sit 2... sit m

6 Plan Description A plan is described by The situations in which the plan is informed The description of operators for the actions A sequence of operator applications A plan is correct if all operator applications in the sequence can be performed, i.e. the preconditions are always satisfied. This can also be expressed in specific correctness conditions. A plan problem is a pair of situations (Initial, Goal). A plan is a solution to a planning problem if it transforms stepwise Initial to Goal. These concepts will later on be slightly revised and extended.

7 Properties of Plans A plan as a solution for a problem can have, besides the correctness, various other properties associated with it, e.g.: a length (number of steps) costs (often depending on the number of steps) a quality (this has many different interpretations) a consume of resources etc. Such properties give rise to optimality problems in planning. We will discuss the in the chapter of Planning with Incomplete Information.

8 Operators: Example PICKUP (x) Takes block x from the table Initial state: A B PUTDOWN(x) Puts block x on the table STACK(x,y) Puts block x on block y UNSTACK(x, y) Takes block x from block y Goal state: B A

9 Operators with Preconditions PICKUP (x) Takes block x from the table Cond.: x on T, clear(x), clear(hand) PUTDOWN(x) Puts block x on the table Cond.: x in hand Initial state: A B STACK(x,y) Puts block x on block y Cond.: clear(y), x in hand UNSTACK(x,y) Takes block x from block y Cond.: clear(x), on(x,y), clear(hand) Goal state: B A

10 Space of Situations (State Space) A B PICKUP(A) PICKUP(B) A B B PUTDOWN(A) STACK(A, B) STACK(B, A) A PUTDOWN(B) A B A B B A A B UNSTACK(A, B) A B Each actions leads from one possible situation to another one.

11 Means-End-Analysis (1) General heuristics to control search in backwards planning Idea : (a) Determine difference between initial state and goal state (b) Select an operator which makes this difference smaller (c) Apply the operator backwards and determine a new goal state (d) IF initial state = goal state THEN STOP otherwise GOTO (a)

12 Means-End-Analysis (2) Initial Goal Difference Applicable operators A B B not on A STACK(B, A) B A A B B A B not in hand PICKUP(B) A B A B None

13 An Unsolvable Problem Exchanging two variables: Initial.: X=A, Y=B, Z=undefined Goals: X=B, Y=A Operator: Precondition: Post conditions: ADD-List: DELETE-List: ASSIGN(u, a, v, b) u=a, v=b u=b u=a 1. Goal X=B ASSIGN(X, A, Y, B) actual state: X=B, Y=B, Z=undefined 2.Goal: Y=A no operator applicable

14 Two Types of Linearity Representation of plans as graphs: Partially ordered plans : Actions not ordered can be performed in any order or in parallel. Insertion of parts of plans at any place of the plan: non-linear planning. In contrast: Linear plans have first to achieve the first goal, then the second goal etc. These two types of non-linearity are often not carefully distinguished in the literature.

15 Sussman-Anomaly (1) C A B A B C B is on C A is on B Optimal Plan: Clear A - Put B on C - put A on B : UNSTACK(C, A), PUTDOWN(C) PICKUP(B), STACK(B, C) PICKUP(A), STACK(A, B)

16 Sussman-Anomaly (2) C A Two possible sequences for achieving subgoals: ON(A, B) A ON B before B ON C UNSTACK(C,A), PUTDOWN(C), PICKUP(A), STACK(A,B), UNSTACK(A,B), PUTDOWN(A), PICKUP(B), STACK(B,C), PICKUP(A), STACK(A,B) again: ON(A, B) B ON C before A ON B ON(B, C) PICKUP(B), STACK(B,C), UNSTACK(B,C), PUTDOWN(B), UNSTACK(C,A), PUTDOWN(C), ON(A; B) PICKUP(A), STACK(A,B), UNSTACK(A,B), PUTDOWN(A), PICKUP(B), STACK(B,C), PICKUP(A), STACK(A,B) again: ON(B,C) B A B C ON(B, C)

17 Sussman-Anomalie (3): Subgoal Interaction There are two goals to achieve. If either goal is achieved in an optimal way the second goal forces to destroy the first goal. There there is no linear plan for this problem available: Linearity assumption not valid. The optimal plan has to interleave the plans for the two individual goals: All goals have to be respected during planning. If linear plans are available this does not necessarily mean that they are easy to find (although the general search space is reduced). Sussman anomaly: Negative interaction. Positive interaction means: Another goal is achieved too.

18 (a) Independent goals G 1 Examples S1 S2 S 0 S 00 S 3 S 4 (b) Trivial serializable goals (c) difficult serializable goals S 2 G 1 G 2 G 1 S 0 S S 1 00 S 0 S 1 S 2 S 3 S 00 S 3 G 2 (d) Non-serializable goals G 2 S 0 S 1 S 2 S 3 S00 G 2 G 1

19 Partially Ordered Plans Idea: Parallel solution of several partial goals Restrict sequence of goals because of interactions Assumption: Plans with few interactions Partially ordered plan : Directed graph Convention: Directed from left to right And-Branches: Alle all successors or predecessors resp. have to be solved Actions not ordered can be executed in any order or in parallel

20 Example: Partially Ordered Plan H1 A B C D H2 A B C D S A ON B C ON D F S PICKUP(A, H1) PICKUP(C, H2) STACK(A, B, H1) STACK(C, D, H2) F

21 Definition: Partially Ordered Plan The concept of a plan will now be extended. A plan is an ordered pair P= (O,<) O: A set of nodes (operators), <: a strict partial ordering on O with a unique smallest element Start(P) and a unique largest element Finish(P). Strict ordering = transitive, antisymmetric and irreflexive Special case: Totally (linearly) ordered plan The concepts of planning problem, application of plans, solution of a problem and correctness of a plan remain as introduced earlier. A linearization of a partially ordered plan extens the partial ordering to a toatal ordering.

22 Plan Space & State Space The planning steps can be performed in two possible spaces: The state space: It deals with the underlying situations. When using e.g. means end analysis the state consists of the set of open goals. If no open goals exist the plan is found. The plan space: It deals with partially ordered plans and the state consists of a set of such plans. If the set contains a complete plan the plan is found. Both views have lead to different types of algorithms.

23 Systematic -Non-Linear Planning (SNLP) Domain independent plan-state planning algorithms Complete, correct plannings algorithms Systematic = each possible plan state is at most once generated Operators have an extended description. They are now represented by: Preconditions, Effects = Add-/Delete-List, Variables, Constraints on variables :

24 Relations between Actions (1) Def. (i) A causal link between g 1 and g 2 denotes that the post conditions of g 1 contain a precondition p of g 2 on the ADD-list. Notation: g 1 c g 2. (ii) g 1 is a threat for g 2 if g 1 destroys some precondition of g 1 (i.e. it has it on the DEL-list). Notation: g 1 t g 2. (iii) g 3 is a threat for a causal link between g 1 and g 2 g 2 p g 1 p g 3 Such a threat is also called negative interaction. A positive interaction has p again in the ADD-list

25 Relations between Actions (2) The interfering interaction g 3 may also p again in the ADD-list. This is called a positive interaction. Such interactions occur usually as side effects of actions and are also called phantomizations. They are often unwanted because of their unsystematic character ( similar to the use of side effects in ordinary programming).

26 Relations between Actions (3) g3 is a threat for a causal link between g1 and g2 if g3 destroys the precondition of g2 established by g1. Consequence: in order to include g3 into the plan it has to be included either before g1 or after g3. In the terminology used for resource oriented configuration g1 is the producer and g2 is the consumer (see chapter on configuration). The consumer g2 needs a result of g1 which is destroyed by g3. A question remains: Where to include g3 Which other plan changes have to be made The corresponding changings are called protections

27 Protection against Threats There are two ways of protection: (i) By ordering: g 1 p g 2 g 3 g 3 Either - Or (ii) By introducing constraints on the actions that the threat no longer occurs. Warning: Removing a threat is a local operation which may create another threat.

28 Start Step-1 Effekte: +P, +R Step-2 Effekte: +P, +Q +R +P +Q Finish Complete Plans The notion of a partially ordered plan is now extended to P=(S,O,C) where C are the binding constraints for the variables. P is complete if: p s t For each precondition p of an action t there is a causal link of the form s p t. Each causal link s p t is protected against all threats. Each linearization of a complete plan is correct.

29 SNLP ( (S,O,F), Goals, Links, Threats) 1. Termination if G = Ø and T = Ø 2. Threat treatment: (if T Ø) (a) Threat selection: thr T threat between u and p t (b) Threat solution: (backtracking point) ResolveThreat(thr): Promotion, Demotion, Separation (c) Threat-update: T = { active threats from T } (d) Recursive call: SNLP ((S,O,B ), G, L, T ) 3. Goal-treatment (if G Ø) ResolveThreat(thr): Promotion:O = O {t < u} Demotion: O = O {u < s} Separation:introduce new binding constraint c which Avoids all threats; B = B {c} (a) Goal treatment: (p, s need ) G (b) Operator selection : (backtracking point) select step s add (from S or new step) with effect p; (S,O,B ) yield by operator application (c) Threat recognition: T = { active threats for plan (S,O,B ) } (d) Recursive call: SNLP ((S,O,B ), G, L, T ) Operator application: p s need L = L { s add } S = S {s add } B = B {Constraints for s } G = (G - {(p,, s need )}) {precond.for S }

30 Partial Goal Hierarchy Goal Partial Goals obtained by applications of operators

31 D 21 G1 G2 D 22 Chronological Backtracking D 3 G3 G4 D 41 D42 G5 G6 G8 (...) G7 Dij Gi Goal Operator Application (Decision)

32 culprit D 21 G1 G2 D 22 Dependency Directed Backtracking D 3 G3 G4 D 41 D42 G5 G6 G7 G8 (...) gain

33 The New View on Planning (1) Planning so far was considered as a clearly stated problem. Once it was formulated it as well as the environment remained unchanged. All problem details as e.g. the result and the consequence of actions were assumed to be known. with incomplete and changing information is most important for planning complex tasks. This means we deal with knowledge and information which may be Incomplete (asks for completion) Changing (asks for changemanagement) Partially incorrect or vague (asks for precision) In addition we tolerate that the execution of a plan can be started before planning is finished.

34 Traditional View: Sequential Classical AI-Planning: Specification Planning Execution Collect requirements and information Make plan, design Interface Interface All three phases are independent of each other

35 Concurrent View Concurrent, parallel: Collecting Information Planning Execution All three arrows represent complex concurrent activities. Concurrency creates communication problems!

36 Models, External World and Executions Planning as considered so far took place in a model. There is also an external world. In this world actions are executed; executions can never be retracted, they are done. In contrast to planning, an execution can fail. costs apply ( in reality ) additional information may be available. The external world is partially mapped into a model world but it exists independent of the model. It can be influenced by the user but not completely controlled. The external world will play a major role in this chapter.

37 Execution and Backtracking There are two views on actions: 1) Planning view: Here actions are elements of a planning model, they are ideas and not elements of the reality. Backtracking means to revise some ideas and is always at no costs possible (if one neglects the planning effort of the planner). 2) Execution view: Here actions are executed in reality. This changes the (external) world and the results cannot be simply withdrawn at no costs and sometimes they cannot be withdrawn at all (e.g. costs apply and resources may be consumed). Instead of backtracking one has to apply other actions for reversal, if possible. In order to model execution of actions this aspect has to be modeled too.

38 Costs (1) Utility (see chapter on Partial Orders): Utility distinguishes costs and benefits. They are multi-dimensional and the different dimensions cannot always be compared in an easy way. Simplified assumptions: 1) Everything is reduced to costs (positive as well as negative ones). 2) Only one type of costs is considered which is represented in real numbers. Costs are associated with Executed actions (self or externally generated) Actions which are not or could not be executed Solutions (correct, incorrect, good ones, bad ones).

39 Costs (2) Difference: 1) Costs exe(g) of the execution an action g. This applies also for actions which cannot be executed. 2) Costs cons(g) of the consequences of an action g: Costs which arise necessarily after the action is executed Examples: -- Costs after some sales decision -- Costs as consequences of a contract -- Costs of an unprofessional repair -- Costs of lost resources etc.

40 Resources (1) Resources are prerequisites for actions like energy, storage space, money, persons, in particular information, etc. The existence of resources is demanded in the precondition list. What happens with the resources is described in the ADD and DELETE lists. If actions are executed these effects cannot be made undone. The management for resources is a planning task in itself. In order to describe this systematically we define an abstract terminology and framework for this.

41 Resources (2) We consider:the following sets which have to be specified in individual situations: A set S of states A finite set R of resources A set A of actions Actions g: The needed resources are listed in the preconditions of g. Each action undertakes acquisition steps for Resources: At each time there is a subset V R, the available resources; all other resources are blocked. acquiring the needed resources. At each time there is some set AR(g) of acquired resources associated to g.

42 Resources (3) The acquisition (request) is itself some action which may have preconditions and costs; they can also fail. The acquisition of a resource R R is successful if the preconditions of the acquisition action are satisfied and if R V (this may also be counted under the preconditions). Effects: (a) AR(A) = AR(A) {R}; (b) V = V - {R} (blockade of R); (c) V is unchanged if the acquisition fails; (c) Mixed forms of actions can share resources.

43 Resources (4) There are different types of resources: Usable resources: They can be used by other actions when they are released after a blockade. Consumable resources: They cannot be reused because they are consumed during the execution of an action. Resources which can be shared: They are not blocked by acquisition actions. Here we can distinguish two kinds: Resources which can be shared by an arbitrary number of actions (e.g. information units) Resources which can be shared by a limited number of actions only (e.g. a parking lot). In this case again blockade takes place.

44 Resources (5) Effects of the execution of g with respect to resources: (a) Consumable resources: These resources are consumed by action g and no longer available. A variation is that part of the resources is consumed, e.g. some amount of gasoline. (b) Usable resources: These resources are released after the action is executed, i.e. AR(A) = and V = V AR(A) (the temporary blockade is over) (c) Shared resources: May be released. Again there are mixed forms. The acquisition of resources and the execution of actions can be interleaved.

45 Resources (6) There can be different possible resources for some action; this is represented as a disjunction. Such different resources may have different costs different influence on the quality of the action, i.e. they may lead to different situations with different costs cons(g). The cost structure can be partially unknown. The availability of resources can be partially unknown. This gives arise to actions which obtain additional information.

46 Resources (7) Resources may be the subject of planning. There are special resource providing actions; a special case is information providing actions. This leads to a special form of goals: Resource goals (see also knowledge goals below). Restricted resources can lead to new constraints. Planning with respect to resources has to respect constraints from restricted resources (which may result in goal orderings, see chapter on Planning) organize book keeping for partially consumed resources employ resource providing actions

47 First Example: Travel The task is to travel from A to B. We assume that we decide first to go from A to C and then from C to B. The information is that train is the most efficient way of transportation; this is an element of the solution space. We do not have information when the train goes from C to B. We execute the trip from A to C. After arrival we have the new task with the new problem to go from C to B. We also obtained the additional information that today there is no train from C to B. Therefore we decide on an another element of the solution space for the new problem: To take the bus from C to B.

48 Second Example (1): Blocks world We use A,B, C,.. for blocks, X,Y,Z,... as variables for blocks, T is the table. We have the predicates ON(X,Y) resp. ON(X,T) and CLEAR(X). Actions are of the form PUT(A,B) and PUT(A,T). Information providing actions are queries of the form ON(A,B)? For both types of actions no variables are allowed. PUT-actions are executable if the usual preconditions are satisfied (what may not be known); queries are always executable. Besides the usual axioms for the blocksworld we assume that towers are of height at most 3. The cost structure is given by: cost(query) = 1 unit; cost(other action) = 4 units; cost(false solution) = 20 units. Costs will apply also to failed executions of actions.

49 Example (2) Initial situation (Complete information): ON(C,B), ON(B,A), ON(A,T), CLEAR(C), ON(E,D), ON(D,T), CLEAR(E). Goal situation: ON(C,D), ON(D,A), ON(A,T),, CLEAR(C), ON(B,E), ON(E,T), CLEAR(B). C C B E D B A D T A E T Initial Situation Goal Situation We observe that some information is redundant

50 Example (3) Given (incomplete) information about the initial situation: ON(X,B), ON(B,Y), ON(Z,D), ON(A,T), ON(E,U), ON(C,V), CLEAR(E), CLEAR(C). The variables are here understood as existentially quantified.? B???? D?? A E? C???? Inside of a block means that there is a block but it is unknown which one it is.? not in a block means there may be a block, otherwise there is no block.

51 Example (4) A first analysis of the situation using constraint propagation yields: X {E,C}, Y {A,D}, Z {B,E,C}, U {B,D,A}, V {B,D,A}. Now there is a choice between a put action and a query. A) PUT-actions: There are two actions which can surely be executed: PUT(C,T) and PUT(E,T). The latter has necessarily to be executed at some time. It prevents us, however, to rise queries of the form ON(E,.)?. Therefore it may make impossible to find out what U is (unless U =X) or what X and Z are (because E = X or E = Z may hold). All other PUT-actions will probably fail unless information about the probability distribution is given. B) Queries: One verifies that at least two queries are needed. It suffices to rise the queries ON(C,B)? And ON(B,A)? In order to get complete information. The order of the queries is irrelevant because both solutions lead to optimal costs.

52 Example (5) Although one knows that a complete information is achieved there are too many possibilities to continue planning on the concrete level. On an abstract level the following plan is possible: (i) ON(C,B)? (ii) ON(B,A)? (iii) Solve the remaining task. In order to make more detailed planning one needs to execute the first two steps: (i) execute(on(c,b)?) (ii) execute(on(b,a)?). This changes the task and one can proceed as usual

53 Example (6) We repeat the cost structure: cost(query) = 1 unit; cost(other action) = 4 units; cost(false solution) = 20 units. Costs do also apply if the execution fails. The cost structure influences the choice of actions. Because queries are cheap compared with failed actions they are preferred. If probabilities of failure of actions are known this may lead to a change in the choice of actions because then cost have to be replaced by expected costs.

54 Knowledge Goals (1) Knowledge goals are subgoals which are defined for information providing actions. Actions providing knowledge and information are not meaningful if they are not executed; the execution has, however, not to occur immediately (e.g. if we go to the airport we have to ask for the gate only if we are there). Knowledge goals compete with each other: An action providing one information may exclude to obtain some other information. There may not be enough resources to satisfy all knowledge goals of interest.

55 Knowledge Goals (2) A first overview over interesting knowledge goals is provided by influence diagrams. It has always to be observed in the overall cost structure that information providing actions have costs.

56 Quality of General Objects The quality of arbitrary objects depends on other objects and their properties. These relations can be described by an influence diagram (see chapter on General Properties). Examples: The quality of a software product depends on %code from universities, %code from research institutions, %industrial code used. The quality of some material X depends on %material A and %material B used. In addition to the influences it is often necessary to quantify the degree of the influence. For action planning this specializes to the influence diagram for actions or sequences of actions.

57 The Value of Information (1) The value of information is defined by the value of the actions which use the information. With an action g mainly two types of costs and benefits are connected : Costs of performing (executing) g. Costs and benefits of the new situation obtained by executing g. Here we subsume costs which arise when an action cannot be executed (e.g. if preconditions are not satisfied). From now on we consider only (positive or negative) costs, denoted by cost(g).

58 The Value of Information (2) Often costs are not exactly known but estimates exist: (1) Local view: With respect to the next step Let Unc(sit) be the set of actions with unknown costs in the situation sit. Def.: (i) Maxcost(sit) = min((max{cost(g) g Unc(sit)}), g Poss(sit) - Unc(sit)) (ii) Expcost(Unc(sit)) = (Prob(g) cost(g) g Unc(sit) (Expected value of unknown costs). (iii) Expcost(sit) = min((expcost(unc(sit)), g Poss(sit) - Unc(sit)) Here a probability distribution of the costs of actions is assumed..

59 The Value of Information (3) If I is the information gain when sit1 is changed to sit2 then worst-case-value(i) = Maxcost(sit1) - Maxcost(sit2) exp-value(i) = Expcost(sit1) - Expcost(sit2) This reflects that if costs are unknown then there is no choice if costs are known then the best alternative can be selected If costs are unknown then there are several possibilities: The possibilities for costs are known but the specific costs depend on the truth of certain statements Even for the possible costs there are only estimates

60 The Value of Information (4) : (2) Global view: More than one action (2a) Sequential view: Several sequentially ordered actions: Can be combined to one macro step and one can proceed as in (1). (3) Proper global view : The whole plan is considered. This view is parctically and often even theoretically only in a very restricted way possible. Often one proceeds empirically (experiments, experiences). An important point is that some cheap action may have an expensive action as a necessary consequence (look-ahead techniques are useful here).

61 The Value of Information (5) Example: In sit there are two possible action g(1) and g(2) which both achieve the same goal. There is furthermore a predicate P with unknown truth value. If P is true then cost(g(1)) = 50, cost(g(2)) = 100; If P then cost(g(1)) = 100, cost(g(2)) = 50. For the information I about the truth of P we have worst-case-value(i) = 50, exp-value(i) = 25 (if equally distributed) These costs have to be compared with the costs of the corresponding information providing actions.

62 The Quality of Information (1) From the viewpoint of classical logic data and information units are of 0-1 character. This is not always justified Data and information units have a certain quality Quality is defined and measured in several dimensions Correctness and completeness problem Quality has consequences for subsequent actions and decisions: The insights may be misleading or too general

63 The Quality of Information (2) Data may be noisy Incorrect data wrong values for the attributes incorrect classification duplicate data Incomplete data missing values for some attributes missing attributes missing objects Data not usable free text difficult to cope with terminology not understood not suitable for the intended goals

64 Quality and Value of Information The quality of an information unit I can be represented by a quality vector Q(I). This vector has three parts 1) Objective part: Components like completeness, probabilty of truth, degree of noise etc. 2) Subjective part: Components like understandability 3) Application oriented part: Components like correct format, goal orientation etc. To the vector Q(I) weights can be associated. They should reflect the importance of the components for the task. It can e.g. be the case that noisy information can be admitted to some degree because it does not matter. The quality of information and knowledge may decrease, see the comments on maintenance, chapter on assistant systems and knowledge management.

65 Quality of Information and Quality of Actions Actions can be better performed in the presence of certain information and units, e.g. which tools to use or which parameter values for the actions to choose. Here we present a simple linear computationally model where we assume that the quality of the action is measured by a real number. Given is: A task T, an action A, information units (l 1,...,l n ), vector (α 1,...,α n ) of relevances of information unit for the action A, quality aspects (Q 1,...,Q m ), vector of (β 1i,...,β mi ) of quality degrees for information unit l k,vector (q 1i,...,q mi ) of relevancies of the quality degrees for task T. All vectors are normalized: i (α i ) = i (β ik ) = i (q ik ) = 1 In the model the quality of action A for task T is computed as Q(A,T) = i α i ( k (q ki. β ki ))

66 Example In travel problem we want to cross next day the lake by boat. General knowledge is that boats can go in the morning and in the afternoon. There are two possible points of departure, A and B which are not very far from each other, one can walk from A to B. Two information units: Time of departure: relevance: high quality aspect preciness: low quality aspect of reliability: high Place of departure: relevance: high quality aspect preciness : low quality aspect reliability: low

67 Example Action: Translation of a document in one language into a second language. The quality of a translation is determined by the relation of the value of the information before and after the translation and the utilities of the receiver agent(s). Example a): A program for searching in a data base (a software document). High quality of accurate translation, low quality of understandability Example b): A recipe in a cooking book (a text document). Average quality of accurate translation, high quality of understandability.