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Compositional Verification of Multi-Agent Systems a Formal Analysis of Pro-activeness and R

Compositional Verification of Multi-Agent Systems a Formal Analysis of Pro-activeness and R
Compositional Verification of Multi-Agent Systems a Formal Analysis of Pro-activeness and R

Compositional Verification

of Multi-Agent Systems:

a Formal Analysis of

Pro-activeness and Reactiveness

Catholijn M. Jonker, Jan Treur

Vrije Universiteit Amsterdam

Department of Mathematics and Computer Science, Artificial Intelligence Group De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands

URL: http://www.cs.vu.nl, Email: {jonker,treur}@cs.vu.nl

Abstract

A compositional method is presented for the verification of multi-agent

systems. The advantages of the method are the well-structuredness of the

proofs and the reusability of parts of these proofs in relation to reuse of

components. The method is illustrated for an example multi-agent system,

consisting of co-operative information gathering agents. This application

of the verification method results in a formal analysis of pro-activeness and

reactiveness of agents.

1 Introduction

When designing multi-agent systems, it is often hard to guarantee that the specification of a system that has been designed actually fulfils the needs, i.e., whether it satisfies the design requirements. Especially for critical applications, for example in real-time domains, there is a need to prove that the designed system will have certain properties under certain conditions (assumptions). While developing a proof of such properties, the assumptions that define the bounds within which the system will function properly are generated. For nontrivial examples, verification can be a very complex process, both in the conceptual and computational sense. For these reasons, it is a recent trend in the literature on verification in general to study the use of compositionality and abstraction to structure the process of verification; for example, see (Abadi and Lamport, 1993; Hooman, 1994; Dams, Gerth and Kelb, 1996).

The development of structured modelling frameworks and principled design methods tuned to the specific area of multi-agent systems is currently underway; e.g., (Brazier, Dunin-Keplicz, Jennings and Treur, 1995; Fisher and Wooldridge, 1997; Kinny, Georgeff and Rao, 1996). As part of any mature multi-agent system design method, a verification approach is required. For example, in (Fisher and Wooldridge, 1997) verification is addressed within a temporal belief logic. This verification method does not exploit compositionality within the agents. In the current paper, in Section 3, a compositional verification method for multi-agent systems is introduced. Roughly spoken, the requirements of the whole system are formally verified by deriving them from assumptions that themselves are properties of agents, which in their turn may be derived from assumptions on sub-components of agents, and so on.

The compositional verification method introduced here is illustrated for an example multi-agent system, consisting of two cooperative information gathering agents and the world. For this example multi-agent system, requirements are formulated (both the required static and dynamic properties), including variants of pro-activeness and reactiveness. These requirements are formalised in terms of temporal semantics. It is shown how they can be derived from properties of agents and how these agent properties in turn can be derived from properties of the agent components. A compositional system specification is introduced in Section 4. The system specification defines how the system is composed of the two agents and the world and how each agent is composed of four agent components: for own process control, world interaction management, agent interaction management, and an agent specific task (which in this case is classification of objects in the world). The compositional specification itself is expressed in the modelling framework DESIRE, shortly introduced in Section 2. The application of the compositional verification method to the example multi-agent system is presented in Section 5 for the top level of the composition. More details on the lower levels can be found in Sections 6 and 7.

2 Compositional Modelling of Multi-Agent Systems

The example task model described in this paper is specified within the compositional modelling framework DESIRE for multi-agent systems (framework for DEsign and Specification of Interacting REasoning components; cf. (Langevelde, Philipsen and Treur, 1992; Brazier, Dunin-Keplicz, Jennings, Treur, 1995)). In DESIRE, a design consist of knowledge of the following three types:

? process composition,

? knowledge composition,

? the relation between process composition and knowledge composition. These three types of knowledge are discussed in more detail below.

2.1 Process Composition

Process composition identifies the relevant processes at different levels of (process) abstraction, and describes how a process can be defined in terms of lower level processes.

2.1.1 Processes at Different Levels of Abstraction

Processes can be described at different levels of abstraction; for example, the process of the multi-agent system as a whole, processes defined by individual agents and the external world, and processes defined by task-related components of individual agents.

Specification of a Process

The identified processes are modelled as components. For each process the types of information required as input and resulting as output are identified as well. This is modelled as input and output interfaces of the components.

Specification of Process Abstraction Levels

The identified levels of process abstraction are modelled as abstraction/specialisation relations between components at adjacent levels of abstraction: components may be

composed of other components or they may be primitive. Primitive components may be either reasoning components (for example based on a knowledge base), or, alternatively, components capable of performing tasks such as calculation, information retrieval, optimisation, et cetera.

The identification of processes at different abstraction levels results in specification of components that can be used as building blocks, and of a specification of the sub-component relation, defining which components are a sub-component of a which other component. The distinction of different process abstraction levels results in process hiding.

2.1.2 Composition of Processes

The way in which processes at one level of abstraction are composed of processes at the adjacent lower abstraction level is called composition. This composition of processes is described by the possibilities for information exchange between processes (static view on the composition), and task control knowledge used to control processes and information exchange (dynamic view on the composition). Information Exchange

Knowledge of information exchange defines which types of information can be transferred between components and the information links by which this can be achieved. Two types of information links are distinguished: private information links and mediating information links. For a given parent component, a private information link relates output of one of its components to input of another, by specifying which truth value of a specific output atom is linked with which truth value of a specific input atom. Atoms can be renamed: each component can be specified in its own language, independent of other components. In a similar manner mediating information links transfer information from the input interface of the parent component to the input interface of one of its components, or from the output interface of one of its components to the output interface of the parent component itself. Mediating links specify the relation between the information at two adjacent abstraction levels in the process composition.

Task Control Knowledge

Components may be activated sequentially or they may be continually capable of processing new input as soon as it arrives (awake). The same holds for information links: information links may be explicitly activated or they may be awake. Task control knowledge specifies under which conditions which components and information links are active (or made awake). Evaluation criteria, expressed in terms of the evaluation of the results (success or failure), provide a means to guide further processing.

2.2 Knowledge Composition

Knowledge composition identifies the knowledge structures at different levels of (knowledge) abstraction, and describes how a knowledge structure can be defined in terms of lower level knowledge structures. The knowledge abstraction levels may correspond to the process abstraction levels, but this is often not the case.

2.2.1 Knowledge Structures at Different Abstraction Levels

The two main structures used as building blocks to model knowledge are: information types and knowledge bases. Knowledge structures can be identified and described at different levels of abstraction. The resulting levels of knowledge abstraction can be distinguished for both information types and knowledge bases.

Information Types

An information type defines an ontology (lexicon, vocabulary) to describe objects or terms, their sorts, and the relations or functions that can be defined on these objects. Information types can logically be represented as signatures in order-sorted predicate logic.

Knowledge Bases

A knowledge base defines a part of the knowledge that is used in one or more of the processes. Knowledge is represented logically by rules in order-sorted predicate logic. Knowledge bases use ontologies defined in information types. Which information types are used in a knowledge base defines a relation between information types and knowledge bases.

2.2.2 Composition of Knowledge Structures

Information types can be composed of more specific information types, following the principle of compositionality discussed above. Similarly, knowledge bases can be composed of more specific knowledge bases. The compositional structure is based on the different levels of knowledge abstraction that are distinguished, and results in information and knowledge hiding.

2.3 Relation Between Process and Knowledge Composition

Each process in a process composition uses knowledge structures. Which knowledge structures are used for which processes is defined by the relation between process composition and knowledge composition.

The semantics of the modelling language are based on temporal logic (cf., Brazier, Treur, Wijngaards and Willems, 1996). Design is supported by graphical tools within the DESIRE software environment. Translation into an operational system is straightforward; the software environment includes implementation generators with which specifications can be translated into executable code. DESIRE has been successfully applied to design both single agent and multi-agent systems.

3 Compositional Verification

The purpose of verification is to prove that, under a certain set of assumptions, a system will adhere to a certain set of properties, for example the design requirements. In our approach, this is done by a mathematical proof (i.e., a proof in the form mathematicians are accustomed to do) that the specification of the system together with the assumptions implies the properties that it needs to fulfil. In this sense verification leads to a formal analysis of relations between properties and assumptions.

3.1 The Compositional Verification Method

A compositional multi-agent system can be viewed at different levels of abstraction. Viewed from the top level, denoted by L0, the complete system is one component S, with interfaces, whereas internal information and processes are hidden (information and process hiding). At the next lower level of abstraction, the system component S can be viewed as a composition of agents and the world, information links between them, and task control. Each agent A is composed of its sub-components, and so on. The compositional verification method takes this compositional structure into account. For composed components two types of properties are recognised: behavioural and environmental properties. A behavioural property is a property on the output of the component. Behavioural properties can be conditional, or unconditional. A behavioural property is conditional if the statements about the output of the component hold under the assumption that some specific conditions hold for its input. For example, a conditional behavioural property of a diagnostic agent could be conditional conclusion correctness of an agent(i.e., if the observation information needed for diagnosis, which is input of the agent, is correct, then all diagnostic output of the agent is correct), whereas the corresponding unconditional property would be conclusion correctness of an agent (i.e., all diagnostic output of the agent is correct). An environmental property is a property on the input of the component (possibly referring to certain conditions on the output).

The primitive components can be verified using more traditional verification methods such as described in (Treur and Willems, 1994; Leemans, Treur and Willems, 1995). Verification of a composed component is done using properties of the sub-components it embeds and the task control knowledge, and environmental properties of the component (depending on the rest of the system, including the world). This introduces a form of compositionality in the verification process: given a set of environmental properties the proof that a certain component adheres to a set of behavioural properties depends on the (assumed) properties of its sub-components, properties of the interactions between those sub-components, and the manner in which they are controlled. The assumptions under which the component functions properly, are the properties to be proven for its sub-components. This implies that properties at different levels of abstraction are involved in the verification process.

Often these properties are not given at the start of the verification process. Actually, the process of verification has two main aims:

? to find the properties

? given the properties, to prove the properties

The verification proofs that connect one abstraction level with the other are compositional in the following manner: any proof relating level i to level i+1 can be combined with any proof relating level i-1 to level i, as long as the same properties at level i are involved. This means, for example, that the whole compositional structure beneath level i can be replaced by a completely different design as long as the same properties at level i are achieved. After such a modification the proof from level i to level i+1 can be reused; only the proof from level i-1 to level i has to be adapted. In this sense the verification method supports reuse of verification proofs.

The compositional verification method can be formulated in more detail as follows:

A. Verifying one Abstraction Level Against the Other

For each abstraction level the following procedure for verification is followed:

1.Determine which properties are of interest (for the higher level).

2.Determine which assumptions (at the lower level) are needed to guarantee these

properties, and which environment properties.

3.Prove the properties on the basis of these assumptions, and the environment

properties.

B. Verifying a Primitive Component

For primitive knowledge-based components a number of techniques exist in literature, see for example (Treur, Willems 1994; Leemans, Treur, Willems 1995). For primitive non-knowledge-based components, such as databases, or neural networks, or optimisation algorithms, verification techniques can be used that are especially tuned for that type of component.

C. The Overall Verification Process

To verify the complete system

1.Determine the properties that are desired for the whole system.

2.Apply the above procedure A iteratively until primitive components are reached.

In the iteration the desired properties of abstraction level L i are either:

? those determined in step A1, if i = 0, or

? the assumptions made for the higher level L i-1, if i > 0

3.Verify the primitive components according to B.

The results of verification are:

? Properties and assumptions at the different abstraction levels.

? The logical relations between the properties of different abstraction levels.

Notes:

? both static and dynamic properties and connections between them are covered.

? reuse of verification results is supported (refining an existed verified compositional model by further decomposition, leads to a verification of the

refined system in which the verification structure of the original system can

be reused).

? process and information hiding limits the complexity of the verification per abstraction level.

? a requirement to apply the compositional verification method described above is the availability of an explicit specification of how the system description

at an abstraction level L i is composed from the descriptions at the lower

abstraction level L i+1; the compositional modelling framework DESIRE is an

instance of a modelling framework that fulfils this requirement.

? in principle alternative (e.g., bottom-up or mixed) procedures can be formulated as well.

3.2 Semantics Behind the Compositional Verification Method

In principle, verification is always relative to semantics of the system descriptions that are verified. For the compositional verification method, these semantics are based on compositional information states which evolve over time. In this subsection a brief overview of these assumed semantics is given.

An information state M of a component D is an assignment of truth values {true, false, unknown} to the set of ground atoms that play a role within D. The compositional

structure of D is reflected in the structure of the information state. A formal definition can be found in (Brazier, Treur, Wijngaards and Willems, 1996; Brazier, Eck and Treur, 1996). The set of all possible information states of D is denoted by IS(D).

A trace M of a component D is a sequence of information states (M t)t N in IS(D). The set of all traces is denoted by IS(D)N, or Traces(D). Given a trace M of component D, the information state of the input interface of component C at time point t of the component D is denoted by state D(M , t, input(C)), where C is either D or a sub-component of D. Analogously, state D(M ,t, output(C)), denotes the information state of the output interface of component C at time point t of the component D. Given a trace M of component D, the task control information state of component C at time point t of the component D is denoted by state C(M , t, tc(C)), where C is either D or a sub-component of D.

To connect neighbouring levels of abstraction in a verification proof for a DESIRE specification, the following elements can be used:

? the assumptions of the sub-components specified within component D

? the interactions between the sub-components of D and/or the interfaces of D ? the input / output information states of the sub-components of D

? the task control information states of the sub-components of D

? the information states of component D

? the task control information states of component D

4 The Example Multi-Agent Model

The example multi-agent model is composed of three components: two agents A and B and a component W representing the external world, see Figure 1. Each of the agents is able to acquire partial information about the external world (by observation). Each agent’s own observations are insufficient to draw conclusions of a desired type, but the combined information of both agents is sufficient. Therefore communication is required to be able to draw conclusions. The agents can communicate their own observation results and requests for observation information of the other agent. This by itself not unrealistic situation is simplified to the following materialised form. The world situation consists of an object that has to be classified. One agent can only observe the bottom view of the object, the other agent the side view. By exchanging and combining observation information they are able to classify the object.

Fig. 1. The example Multi-Agent System Communication from the agent A to B takes place in the following manner:? the agent A generates at its output interface a statement of the form:

to_be_communicated_to(, , , B)

? the information is transferred to B; thereby it translated into

communicated_by(, , , A)

In the example can be filled with a label request or world_info, is an atom expressing information on the world, and , is one of pos or neg, to indicate truth or falsity.

Interaction between an agent A and the world takes place as follows:

? the agent A generates at its output interface a statement of the form:

to_be_observed()

? the information is transferred to W; thereby it is translated into

to_be_observed_by(, A)

? the world W generates at its output interface a statement of the form:

observation_result_for(, , A)

? the information is transferred to A; thereby it is translated into

observation_result(, )

Part of the output of an agent are conclusions about the classification of the object of the form object_type(s); these are transferred to the output of the system.

To be able to perform its tasks, each agent is composed of four components, see Figure 2: three for generic agent tasks (world interaction management, agent interaction management, own proces control), and one for an agent specific task (object classification).

Fig. 2. Composition of an agent

object classification(agent specific task)

This component is able to draw a conclusion if it has input on the two views on the object. The component can reason on the basis of the world knowledge represented in the table depicted in Table 1:

Table 1. World knowledge

world interaction management

This component reasons about the manner in which the agent interacts with the world. Here it is decided under which conditions which observations are to be performed in the world.

agent interaction management

This component reasons about the agent’s communication with other agents. In this component it is determined when to request which information from the other agent. Another task is to determine when to provide which observation information to the other agent and what to do with the world information received from the other agent. own process control

This component defines the agent’s own characteristics or attitudes. Information on these attitudes can be transferred to other components, to influence the reasoning that takes place there. The agents can differ in their attitudes towards observation and communication: an agent may or may not be pro-active, in the sense that it takes the initiative with respect to one or more of:

? performing observations

? communicate its own observation results to the other agent

? ask the other agent for its observation results

? draw conclusions about the classification of the object

Moreover, it may be reactive to the other agent in the sense that it responds to a request for observation information:

? by communicating its observation result as soon as they are available

? by starting to observe for the other agent

These agent attitudes are represented explicitly as (meta-)facts in the agent’s component own process control. By varying these attitude facts, different variants of agents can be defined. The impact of these explicitly specified characteristics has been specified in the model. For example, if an agent has the attitude that it will always take the initiative to communicate its observation results as soon as they are acquired, then the agent’s behaviour should show this, but if the characteristic is not there, then this behaviour should not be present. This requires an adequate interplay between the component own process control and the component agent interaction management within the agent, and adequate knowledge within agent interaction management.

The successfulness of the system depends on the attitudes of the agents. For example, if both agents are pro-active and reactive in all respects, then they can easily come to a conclusion. However, it is also possible that one of the agents is only reactive, and still the other agent comes to a conclusion. Or, an agent that is only pro-active in reasoning and reactive in information acquisition may come to a conclusion due to pro-activeness of the other agent. So, successfulness can be achieved in many ways and depends on subtle interactions between pro-activeness and reactiveness attitudes of both agents. The formal analysis of the example in the following sections provides a detailed picture of these possibilities.

5 Formal Analysis of the Example System: Top Level

In this section the properties of the system as a whole (defined in Section 5.1) are related to properties of the agents and the world (defined in Section 5.2 and 5.3), and their interaction.

5.1 Properties for the Top Level of the System

First, it is determined which properties the system as a whole should satisfy. Considering that the system S is a classification system, it is expected that S produces output of the form object_type(s) for some s. A first requirement is that output generated by the system is correct, i.e., if the system derives object_type(s) for some s, it is true in the world situation. Let the world state (which is assumed static) be denoted by M. In Figure 4 the successfulness property of S is related to other properties of S and assumed properties of the next level. In Figure 3 the correctness property of S is similarly related to other properties. The following property relates the output of the system to the current world state.

Correctness of S

The system S is called correct if:

M Traces(S) t s

[ state S(M , t, output(S)) object_type(s) M object_type(s) ]

∧ [ state S(M , t, output(S)) ?object_type(s) M ?object_type(s) ]

Output information of S is only provided by agents

As can be seen in Figure 1 the only information links connected to the output of S are the information link from agent A to S and the information link from agent B to S. Furthermore, the output interface of S cannot spontaneously change its contents. Therefore, the output information of the system is only provided by agents.

correctness of S

conclusion correctness of all agents

output

information of

S is only

provided by

the agents &

Fig. 3. Correctness of S

Next, the system is required to be successful in generating conclusions: during the process, for each s, at some time point it should either have derived positive output, or negative output:

Successfulness of S

The system S is called successful if:

M Traces(S) s t state S(M , t, output(S)) object_type(s))

∨t state S(M , t, output(S)) ?object_type(s))

To guarantee the adequate information exchange between the different components, the following properties are needed:

Interaction effectiveness

The interaction from agent X to the output interface of system S is called effective if, for φ either object_type(s) or?object_type(s):

M Traces(S) t s [state S(M , t, output(X)) φ

t’>t state S(M , t’, output(S)) φ]

The interaction from the external world W to agent X is called effective if: M Traces(S) t r,sign

[ state S(M , t, output(W)) observation_result_for(view(X,r), sign, X)

t’>t state S(M , t’, input(X)) observation_result(view(X,r),sign)]

The interaction from the agent X to the external world W is called effective if: M Traces(S) t r,sign

[ state S(M , t, output(X)) to_be_observed (view(X,r))

t’>t state S(M , t’, input(W)) to_be_observed_by (view(X,r), X)]

Interaction effectiveness can be proven from the detailed specification of the information links involved and the timely functioning of those information links as specified in the task control of the component containing the information link given in the detailed specification. This property is needed to prove several environment properties of the agents and also to prove successfulness of S. Sometimes it will not be stated explicitly.

Agent provides output information of S

An agent X provides output information of system S if X is conclusion successful and the interaction from X to S is effective.

S is successful

or

conclusion successfulness, A effective interaction

from A to S

conclusion

successfulness, B

effective interaction

from B to S

A provides output information of S

B provides output information of S

& def& def

Fig. 4. Successfulness of S

It is undesirable (for a static world situation) that the system changes its mind during the process. Therefore the requirement is chosen that once a conclusion has been derived, this is never revised:

Conservativity of S

The system S is called conservative if:

M Traces(S) t s

[ state S(M , t, output(S)) object_type(s)

t’>t state S(M , t’, output(S)) object_type(s) ]

∧ [ state S(M , t, output(S)) ? object_type(s)

t’>t state S(M , t’, output(S)) ? object_type(s) ] )

The property of conservativity of S can be proven in a similar way as the other properties of S. The proof has been omitted from this paper.

Communication effectiveness

The communication from agent X to agent Y is called effective if:

M Traces(S) t φ

[state S(M , t, output(X)) to_be_communicated_to(q, φ, sign, Y)

t’>t state S(M , t’, input(Y)) communicated_from(q, φ, sign, X) ]

Communication effectiveness can be proven in the same way as interaction effectiveness. This property is needed to prove environment properties of the agents.

5.2 Properties of the Agents

The required properties of the system have been proven from assumed properties of the components at one level lower. During this proof process these assumptions have been discovered. A number of assumptions are quite straightforward. For example, correctness inherits upward from the agents to the system:

Conclusion correctness of an agent

An agent X is called conclusion correct if:

M Traces(X) t s

[ state X(M , t, output(X)) object_type(s) M object_type(s) ]

∧ [ state X(M , t, output(X)) ?object_type(s) M ?object_type(s) ]

This property logically depends on other properties of the agent, input correctness and conditional conclusion correctness, as can be seen for agent A in Figure 5.

Input correctness of an agent

a) An agent X is called observation input correct if

M Traces(X) t r

[state X(M , t, input(X)) observation_result(view(X,r),pos) M view(X,r) ]∧M Traces(X) t r

[state X(M , t, input(X)) observation_result(view(X,r),neg) M ?view(X,r) ]

b) An agent X is called communication input correct if

M Traces(X) t r

[state X(M , t, input(X)) communicated_from(world_info,view(Y,r), pos,Y) M view(Y,r) ]∧ M Traces(X) t r

[state X(M , t, input(X)) communicated_from(world_info,view(Y,r), neg,Y) M ?view(Y,r) ]

c) An agent X is called input correct if X is observation input correct and

communication input correct.

Conditional conclusion correctness of an agent

An agent X is called conditionally conclusion correct if the following holds: if input correctness of X then conclusion correctness of X.

input correctness, A

conditional conclusion correctness, A

observation

input

correctness, A &

conclusion correctness, A

& def communication input correctness, A

Fig. 5. Conclusion correctness of A

The following property is needed to prove conservativity of S .

Conclusion conservativity of an agent

The agent X is called conclusion conservative if:M Traces(X) t s

[ state X (M , t, output(X)) object_type(s)

t’>t state X (M , t’, output(X)) object_type(s) ]

∧ [ state X (M , t, output(X)) ? object_type(s)

t’>t state X (M , t’, output(X)) ? object_type(s) ] )

Again, the proof has been omitted from this paper. Successfulness of the system (see Figure 4) depends on successfulness of at least one of the agents.

Conclusion successfulness of an agent

The agent X is called conclusion successful if:M Traces(X) t state X (M , t, output(X)) object_type(s))

∨ t state X (M , t, output(X)) ?object_type(s))

This property can be proven in a number of ways. However, in all proofs the properties information saturation of the agent and conclusion pro-activeness is required, see Figure 6 for the logical relations between properties of agent A that are needed to prove conclusion successfulness of agent A .

Information saturation of an agent

a) The agent X is called observation info saturating if:

M Traces(X) t r sign

state X(M , t, input(X)) observation_result(view(X,r), sign)

b) The agent X is called communicated info saturating if:

M Traces(X) t r sign

state X(M , t, input(X)) communicated_from(world_info, view(Y,r), sign, Y)

c) The agent X is called request saturating if for all agents Y different from X:

M Traces(X) t r

state X(M , t, input(X)) communicated_from(request, view(X,r), pos, Y)

d) The agent X is called information saturating if X is observation info saturating and communicated info saturating.

Conclusion pro-activeness

The agent X is called conclusion pro-active if for all agents Y different from X: M Traces(X) t,t’

[r,r’ sign,sign’

state X(M , t, input(X)) observation_result(view(X,r), sign)

state X(M , t’, input(X)) communicated_from(world_info, view(Y,r’), sign’, Y) ] ]

t”>t, t”>t’ s [ state X(M , t”, output(X)) object_type(s) ∨

state X(M , t“, output(X)) ?object_type(s)]

conclusion successfulness, A

information saturation, A

communicated info

saturation, A

observation info saturation, A

pro-active observation info saturation, A reactive observation info saturation, A

observation pro-activeness, A

observation

effectiveness, A

request

saturation, A

conclusion pro-activeness, A or

&

&

strongly reactive

information provision, A

or

spontaneous observation

info saturation, A

observation

reactiveness, A

weakly

reactive

information

provision, A

& def

& def& def

Fig. 6. Conclusion successfulness of A

All properties occurring in Figure 6 are also properties of agent A. The leaves in the tree are either environmental properties of A or behavioural properties of A. To prove environmental properties of a component behavioural properties of other components of the same level (in this case other agents and/or the world) are needed as are properties about interactions between these components (in this case interactions

between agents and between the world and agents). For example, the property communicated information saturation of agent A (see Figure 6) can be proved from interaction effectiveness from agent B to agent A and the property successful information provision of agent B , see Figure 7.

Information provision successfulness

a) The agent X is called successful information providing if:M Traces(X) r, sign t

state X (M , t, output(X)) to_be_communicated_to(world_info, view(X,r), sign, Y)

b) The agent X is called successful information providing pro-active if

X is observation effective and strongly information providing pro-active.c) The agent X is called successful information providing reactive if

X is request saturating and reactive observation effective.

communicated info saturation, A &

communication effectiveness from B to A successful information provision, B

Fig. 7. Communicated info saturation of A

Similarly, the properties observation input correctness and communication input correctness of an agent depend on correct information coming from the other agent or from the world (see Section 5.3 for definitions of properties concerning the world), see Figure 8.

interaction effectiveness,from W to A correctness of W &&input observation

information of A is only

provided by W observation input correctness, A communication input correctness, A information provision correctness, B communication effectiveness,from B to A

&

&input communication information of A is only provided by B Fig. 8. Information correctness of A The property spontaneous observation info saturation of an agent as used in Figure 6 is defined by the property pro-activeness of the world (see Section 5.3) and interaction effectiveness from the world to that agent, see Figure 9.

spontaneous observation info saturation, A

pro-activeness, W effective interaction from W to A

& def

Fig. 9. Spontaneous observation info saturation of A

The property successful information provision of agent B, used in Figure 7, can be proven in several ways. The first division made in Figure 10 is between pro-active and reactive information provision. Also the notions strong and weak are used. Information provision correctness

The agent X is called information providing correct if:

M Traces(X) r t

[ state X(M , t, output(X)) to_be_communicated_to(world_info, view(X,r), pos, Y)

M view(X,r) ]

M Traces(X) r t

[ state X(M , t, output(X)) to_be_communicated_to(world_info, view(X,r), neg, Y)

M ?view(X,r) ]

Information providing pro-activeness

a) The agent X is called weakly information providing pro-active if:

M Traces(X) t, r, sign

[ state X(M , t, input(X)) observation_result(view(X,r), sign)

t’ state X(M , t’, output(X)) to_be_communicated_to(world_info, view(X,r), sign, Y) ]

b) The agent X is called strongly information providing pro-active if

X is weakly information providing pro-active and observation pro-active. Information providing reactiveness

a) The agent X is called weakly information providing reactive if:

M Traces(X) t, t’,r, sign

[state X(M , t, input(X)) observation_result(view(X,r), sign)

state X(M , t’, input(X)) communicated_from(request,view(X,r), pos,Y) ]

t”>t, t”>t’ state X(M , t”, output(X))

to_be_communicated_to(world_info, view(X,r), sign, Y)

b) The agent X is called strongly information providing reactive if

X is weakly information providing reactive and observation reactive.

c) The agent X is called reactive observation info saturating if

X is request saturating and strongly information providing reactive.

The tree in Figure 10 consists of logical relations between properties of the agent B. Some of them have been defined above, the others are defined as follows. Information acquisition pro-activeness of an agent

a) The agent X is called observation pro-active if:

M Traces(X) r t state X(M , t, output(X)) to_be_observed (view(X,r)) ]

b) The agent X is called request pro-active if for all agents Y different from X:

M Traces(X) r t state X(M , t, output(X))

to_be_communicated_to(request, view(Y,r), pos, Y)]

c) The agent X is called information acquisition pro-active if X is observation pro-active and request pro-active.

Observation reactiveness of an agent

The agent X is called observation reactive if:

M Traces(X)t r [state X(M , t, input(X)) communicated_from(request, view(X,r), pos, Y) t’ state X(M , t, output(X)) to_be_observed (view(X,r)) ]

successful information provision, B or

& def

request

saturation, B successful information provision reactive, B

reactive observation

effectiveness, B

successful information

provision pro-active, B observation info

saturation, B or or spontaneous observation info saturation, B pro-active observation info saturation, B observation pro-activeness, B observation effectiveness, B & def

reactive

observation

info saturation, B reactive observation info saturation, B

request saturation, B strongly reactive information provision, B

observation reactiveness, B

weakly reactive information provision, B & def & def

observation effectiveness, B weakly reactive information provision, B

strongly reactive information provision, B observation reactiveness, B

weakly

reactive

information

provision, B reactive observation effectiveness, B observation info saturation, B & def

stongly information

providing pro-active, B

observation effectiveness, B weakly pro-active

information

provision, B observation

pro-activeness, B successful information

provision pro-active, B

& def & def Fig. 10. Successful information provision of B

Information acquisition effectiveness of an agent

a) The agent X is called observation effective if:M Traces(X) t r [state X (M , t, output(X)) to_be_observed (view(X,r))

t’>t sign state X (M , t, input(X)) observation_result(view(X,r), sign) ]

b) The agent X is called request effective if:M Traces(X) t r

[state X (M , t, output(X)) to_be_communicated_to(request,view(Y,r),pos,Y)

t’>t, sign state X (M , t, input(X)) communicated_from(world_info, view(Y,r), sign, Y) ]

c) The agent X is called information acquisition effective if

X is observation effective and request effective.

d) The agent X is called reactive observation effective if:M Traces(X) t r

[state X (M , t, input(X)) communicated_from(request, view(Y,r), pos, Y)

t’>t, sign state X (M , t, input(X)) observation_result(view(X,r), sign)]

e) The agent X is called pro-active observation info saturating if

X is observation pro-active and observation effective.

The relations between the environmental properties request saturation of agent A and observation effectiveness of agent A , and properties of the world, of agent B , and of interactions between agents and world can be found in Figure 11.observation effectiveness, A

& def

&observation

effectiveness, W interaction effectiveness between A and W interaction effectiveness from W to A

interaction effectiveness

from A to W request saturation, A &

interaction effectiveness from B to A request pro-activeness, B

Fig. 11. Observation effectiveness and request saturation of A

5.3 Properties of the World

For the component World assumptions on correctness and conservativity are made.Correctness of the world

The world W is called correct if:M Traces(W) t v, X

[ state W (M , t, output(W)) observation_result_for(view(X, r), pos, X)

M view(X, r) ]M Traces(W) t v, X

[ state W (M , t, output(W)) observation_result_for(view(X, r), neg, X) M

view(X, r) ]Conservativity of the world

The world W is called conservative if:M Traces(W) t r, sign, X

[ state W (M , t, output(W)) observation_result_for(view(X, r), sign, X)

t’>t state W (M , t’, output(W)) observation_result_for(view(X, r), sign, X) ]

Moreover, the world should be effective in providing observation results for observations initiated by the agents.

Observation effectiveness of the world

The component W is called observation effective if:

M Traces(W) t r, X

[state W(M , t, input(W)) to_be_observed_by(view(X, r), X) ]

[t’>t,sign state W(M , t’, output(W)) observation_result_for(view(X, r), sign, X) ]

It is also possible that the world provides observation information without an initiative from the agent (e.g., by automated sensors). In this case the world shows pro-activeness:

Observation pro-activeness of the world

The component W is called observation pro-active if:

M Traces(W) r, X t,sign

state W(M , t, output(W)) observation_result_for(view(X, r), sign, X)

6 Properties of Agent Components

The properties of the agents needed to prove the properties of the top level of the system were discussed in Section 5.2. The assumed properties of the sub-components of an agent, needed to prove the behavioural properties of that agent, and the logical structure of those proofs in the form of trees are discussed in this section. Properties of the component own process control play a role in the proof of each behavioural agent property.

6.1 Properties of Own Process Control

In the component Own Process Control the agent’s attitudes are explicitly represented. The attitudes are represented in the following manner:

attitude representation within OPC

pro-active observation observation_attitude(pro-active)

weakly pro-active information provision info_provision_attitude(weakly_pro-active) strongly pro-active information provision info_provision_attitude(strongly_pro-active)

pro-active requesting requesting_attitude(pro-active)

pro-active reasoning reasoning_attitude(weakly_pro-active) reactive observation observation_attitude(reactive)

weakly reactive information provision info_provision_attitude(weakly_reactive) strongly reactive information provision info_provision_attitude(strongly_reactive) Attitude determination successfulness of O P C

The component OPC is called attitude determination successful for the attitude pro-activeness of observation if:

M Traces(OPC) t t’≥t

state OPC(M , t’, output(OPC)) observation_attitude(pro-active)

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2、框架设计 框架设计是企业组织设计的主要部分,运用较多。其内容简单来说就是纵向的分层次、横向的分部门。 3、协调设计 协调设计是指协调方式的设计。框架设计主要研究分工,有分工就必须要有协作。协调方式的设计就是研究分工的各个层次、各个部门之间如何进行合理的协调、联系、配合,以保证其高效率的配合,发挥管理系统的整体效应。 4、规范设计 规范设计就是管理规范的设计。管理规范就是企业的规章制度,它是管理的规范和准则。结构本身设计最后要落实并体现为规章制度。管理规范保证了各个层次、部门和岗位,按照统一的要求和标准进行配合和行动。 5、人员设计 人员设计就是管理人员的设计。企业结构本身设计和规范设计,都要以管理者为依托,并由管理者来执行。因此,按照组织设计的要求,必须进行人员设计,配备相应数量和质量的人员。 6、激励设计 激励设计就是设计激励制度,对管理人员进行激励,其中包括正激励和负激励。正激励包括工资、福利等,负激励包括各种约束机制,也就是所谓的奖惩制度。激励制度既有利于调动管理人员的积极性,也有利于防止一些不正当和不规范的行为。 四、基本理论

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)(2)(7.021021d d a d d +≤≤+, )425200(2)425200(7.00+≤≤+a , 所以有12505.4370≤≤a 。初定中心距a 0=800 mm , 由式(9-14)得带长 2 122 1004)()(2 2a d d d d a L -+++=π, 2 (425200)2800(200425)2597.62 4800 π -=?+ ++ =?mm 。 由表9-2选用L d =2500 mm ,由式(9-15)得实际中心距 2.7512/)6.25972500(8002/)(00=-+=-+=L L a a d mm 。 (5)验算小带轮上的包角1α 由式(9-16)得 012013.57180?--=a d d α 000042520018057.3162.84120,751.2 -=-?=> 合适。 (6)确定带的根数z 由式(9-17)得 00l α ()c P z P P K K = +?, 由表9-4查得P 0 = 3.77kW,由表9-6查得ΔP 0 =0.3kW;由表9-7查得K a =0.96; 由表9-2查得K L =1.03, 47.403 .196.0)3.077.3(18 =??+= z , 取5根。 (7)计算轴上的压力F 0 由表9-1查得q =0.17kg/m,故由式(9-18)得初拉力F 0 2c 0α 500 2.5 (1)P F qv zv K = -+

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