Agents in Cyberspace - Towards a Framework for Multi-Agent Systems in Information Discovery

This article proposes a formal framework for Multi-Agent Systems in the context of Information Discovery. Information Discovery is a synthesis of Information Retrieval and Information Filtering. The Information Discovery Paradigm is given. In addition, the different types of agents needed in Information Discovery applications are described in terms of the operations they support and the knowledge and information they use. A correct filtering topology, consisting of sound filter paths, is identified. Three fields are identified in which Information Retrieval and Information Filtering benefit from their synthesis: query expansion, query generation or autonomous IR, and profile adaptation.


Introduction
The amount of information made available through di erent media is growing rapidly.In parallel, our need for accurate information increases as well.Therefore, for a single user, the quest for relevant information no longer is a sinecure, even with the help of state of the art search engines.
Two main approaches to obtaining relevant information have appeared: Information Retrieval IR see 6 and Information Filtering IF.See 1 for an adept comparison of these strongly related plans of attack.In IR, the user formulates his short term information need in the form of a query, which is subsequently processed by a retrieval engine.In IF, long term interests of the user are captured by user pro les, against which descriptions of incoming documents are matched.
The old paradigms of IR and IF, i.e., single user and single resource, have clear shortcomings in a networked setting plagued with an information glut.A new paradigm is needed which consists of a synthesis of the old paradigms for IR and IF and which supports a networked environment, i.e., multiple users and resources.The combination of IR and IF is what we call Information Discovery ID.As shown later, IR and IF can mutually bene t from their synthesis.Moreover, if IR and IF can be integrated in a single application, the user only has to work with a single system at little or no expense of increased complexity.
The amount o f a vailable information has become too large for a single user to cope with properly.T o relieve the user's burden, an information broker is introduced as an intermediary between users and resources.The broker aids users in the quest for relevant information.Agent technology is used to develop the information brokers.We adhere to the view of agents as autonomous, intelligent, proactive, reactive, and socially able software programs.ID applications highly require communication, since agents are to solve complex tasks cooperatively, and proactiveness, mainly to relieve the users from taking the initiative.The information broker performs its tasks in cooperation with other agents and only prompts the user when necessary.W e will thus consider the ID paradigm from the point of view of multi-agent systems.Much research has been done into agents see e.g. 5 and especially in the eld of formal logics see e.g. 10 , 4 , and 8 .
However, the use of agents in ID has, to this moment, been rather pragmatic and ad hoc.Most of the agents used in ID are not developped from a formal point of view.A more elaborate investigation into the types of agents needed in ID is necessary.The majority o f `agents' used in ID systems does not conform to the notion of agency.Mostly, the principles of communication, intelligence and proactiveness lack completely or only exist in a rudimentary fashion.The Informant1 , for instance, uses a strictly scheduled form of proactiveness.The users are informed on a pre-set regular interval.The agents that can be created by the Verity2 system lack communication and intelligence.In addition, a yet more restricted form of proactiveness is used: the interval is set to one day.Autonomy Agentware's agents3 have been made intelligent b y the use of neural networks.
Multi-agent systems for ID will be considered from a theoretical basis.In doing this, however, the practical context will not be denied.There are several reasons for the need of a theoretical and formal framework.In the rst place, a framework is needed in which multi-agent systems for ID can be designed and de ned.Second, the framework is needed to analyse, characterise, and compare multi-agent systems through their statical properties.In the third place, we need to go beyond time consuming empirical performance measurements such as recall and precision and move on to the fundamental certainty of logical proofs.The performance and behaviour of ID systems should thus be described on an axiomatic level see 2 .
The goal of this article is to make a rst step towards a theoretical framework in which the way ID agents cooperatively make relevance decisions, also called aboutness decisions, can be described, analysed, and compared.
The overview of this paper is as follows.Section 2 provides the ID paradigm.Section 3 describes the types of agents needed in ID.In Section 4, the theoretical framework is provided.Section 5 o ers concluding remarks.

Information Discovery
This section describes the ID paradigm, relates ID to multi-agent systems and gives necessary formal preliminaries.

The Information Discovery Paradigm
An ID system considers three main spaces of interest, as described in 9 : a user space, a resource space and a broker space.See Figure 1 for a schematic overview of the ID paradigm.The user space consists of several users having a number of di erent long term information needs as well as a short term information need.The information needs are to be satis ed with relevant information, i.e., relevant documents.These documents are drawn from a number of

IRSG98
Example descriptors are France : wine and animals _ beasts, if the single keywords are drawn from the set of keywords K.If those are interpreted as queries, the rst states that the user is interested in documents about France but not about wine and the second states that the information need is satis ed by documents about animals or about beasts.Brackets are omitted if not necessary.
The semantics of the descriptor language which is used in the examples, follows the standard interpretations of the logical operators for conjunction and disjunction.In addition, it adheres to the Closed World Assumption for negations.This choice is, however, not crucial.

Types of Agents in Information Discovery
This section analyses the types of agents used in ID.In addition, a formal representation of these agents is given.

User agents
User agents derive user goals, interests and information needs.This process is called user modeling see 7 for information on the user modeling component within the Pro le project.A user agent forms an abstraction of the user, called a user pro le, the representation of which is actually worked with.Each user is appointed a number of user agents.This allows for di erent views on user behaviour.
A user agent enables the user to specify a query, a description of a short term interest, which belongs to a single information need.In addition, it adds abstractions of the long term interests of the user to the user pro le.Each long term interest corresponds to a distinct information need.The set of all possible information needs is denoted by N .See  De nition 3 User Agent A user agent is a tuple hq;Pi, where q 2 L K is the user query and P L K N is the user pro le.The elements of the user pro le, called pro le topics, combine a descriptor to an information need.

IRSG98
Example David works at a software house and spends his leasure time at sea.His long term interests concern computers and internet information need N comp , and wind or waves information need N sea .David has formulated his short term interest in a query about sur ng.This is modeled by the following user agent u david = hsur ng; fcomputer ^internet; N comp ; wind _ waves; N sea gi.
In the semantics of a user agent, distinction is made between the di erent pro le topics.This is done because these may correspond to di erent information needs and may t h us be unrelated.Di erent pro le topics therefore cannot be freely combined.The semantics of a user agent is therefore de ned with respect to the view the agent has, i.e., the information need the agent considers or focusses on.Informally speaking, the user agent that considers information need N can only use the corresponding descriptor, i.e., descriptor p from the pro le topic p; N.
De nition 4 User Semantics Let u = hq;Pi be a user agent within multi-agent system M = hU; B; R; Ci, i.e., u 2 U.Then, the semantics of the user agent in the multi-agent system is de ned as: i for every information need N 2 N : u; N j = M q ii for every pro le topic p; N 2 P : u; N j = M p The formula u; N j = M p reads: within u's focus on information need N, the descriptor p is valid.Item i expresses that the short term query q is valid in all information needs, since it is not clear if it is related to any one of them.This is only a rst approximation; in later stages of our research, this assumption will be re ned.It should be noted, however, that this assumption leads to the loss of discrepancy between query and long term interests.In particular, with this assumption the query can always be augmented with terms from the long term interests.For certain cases, this is an undesired property which can be overcome by making the communication between agents explicit.This can, for instance, been done by using messages.The user agent m a y then mold the query and send the result to a broker.The broker, unaware of user descriptors which do not appear in the message, cannot take more terms into account.Item ii expresses that for a pro le topic p; N, within u's focus on N, only the corresponding descriptor p is valid.
Example To illustrate the di erent points of view the user can specify, consider again David from example 3.1.The query sur ng is interpreted in 2 di erent w ays, i.e., with respect to the 2 di erent information needs.
Considering the rst information need, that about computers and internet, the following expressions are valid: u david ; N comp j = sur ng and u david ; N comp j = internet.By using the standard interpretation of logical conjunction, we obtain u david ; N comp j = internet ^sur ng.
On the other hand, considering the second information need, we obtain in a similar way u david ; N sea j = wind ^sur ng_wave ^sur ng but not u david ; N sea j = internet ^sur ng.

Resource agents
The term information source will be used for a collection of documents.Resource agents have access to information sources.By a process called characterising or indexing, resource agents derive document characterisations, abstractions of documents.A resource agent supports the IRSG98 characterisations of the documents in its source.Each information source is accessed by a number of resource agents.This allows for di erent views on a complex information source.
A resource agent accesses information sources, which are modeled as a set of documents.In addition, it is able to deliver document c haracterisations, which consist of a set of keywords.In this article, we i n terpreted the characterisation as a conjunction of the individual keywords.wave ^sur ng Then, the tuple r surf = h ; Di is a resource agent.
Similar to user agents, where the view of the agent can be focussed on a speci c information need, resource agents can focus on speci c documents, and thus have di erent views as well.This is re ected in the semantics of a resource agent.
De nition 6 Resource Semantics Let r = h ; Di be a resource agent within multiagent system M = hU; B; R; Ci, i.e., r 2 R. Then

Broker Agents
Broker agents form intermediaries between user agents and resource agents.They act as information brokers, providing users with relevant information.Broker agents match document characterisations with user pro les or queries to establish degrees of relevance of documents with respect to user interests.Matching is modeled by t wo operations of the broker agent: aboutness and anti-aboutness.Aboutness states when a descriptor is about another descriptor.Anti-aboutness describes when a descriptor is non-about another descriptor.Matching can be applied in the context of IF or of IR.In IF, a document pro le is matched against several user or group pro les.In IR, a number of document c haracterisations are matched against a speci c query.

IRSG98
De nition 7 Broker Agent A broker agent is a tuple h.; .i , where .L K L K is the agent's aboutness relation and .L K L K is the agent's anti-aboutness relation.If b = h.; .i is a broker agent, then .b denotes .and .b denotes . .Example A naive o verlap broker can be speci ed in our framework as b naive = hoverlap; disjointi, where overlap = f ; jPosAt PosAt 6 = ?gdisjoint = f ; jPosAt PosAt = ?gassuming the function PosAt : L K !K, where PosAt gives the set of atoms keywords that appear possitively in .
The aboutness relations of the broker agents are relations on the descriptor language.A particular instance of the aboutness relation holds in an agent i that instance is part of the agent's aboutness relation.
De nition 8 Broker Semantics Let b = h.;.i be a broker agent and M = hU; B; R; Ci a m ulti-agent system, such that b 2 B.Then, b j = M ., def ; 2 .b b j = M ., def ; 2 .b Example The naive o verlap broker of the previous example makes the following aboutness decision: b naive j = wind ^sur ng ^Hawaii .wave ^sur ng ^sea.H o wever, for reasons of naivety, it also makes the following statement b naive j = internet ^sur ng.wind ^sur ng.The overlap broker can be made less naive b y i n troducing a knowledge base containing additional domain knowledge.To incorporate the knowledge base, the relations overlap and disjoint have to be rede ned using the information in the knowledge base, for instance, synonyms.
It should be noted that the broker's aboutness relation is symmetric with respect to user queries and document contents.That is, the origin of initiative, i.e.IR or IF, is not taken into account b y a single aboutness relation.If a discrepancy is to be made, however, two di erent brokers can be used.The di erence can then be obtained by using the rst broker's aboutness relation in the case of IR and the second broker's aboutness relation in the case of IF.

Multi-Agent Systems in ID
This section formalizes the framework for multi-agent systems in Information Discovery Subsection 1 and elaborates on the two major tasks of the system: Information Retrieval Subsection 2 and Information Filtering Subsection 3.

Formalizing the Framework
The semantics of a MASID M is captured by a binary relation j = M stating the validity o f formulae in agents.The left hand side of this relation denotes an agent.In the case of user and resource agents, this includes a point of view.A uniform agent language is de ned to capture this.The right hand side of the relation contains a formula.Formulas are either IRSG98 descriptors, in the case of user and resource agents, or, in the case of broker agents, antiaboutness statements.This is captured in the aboutness language, which is de ned shortly.
Let D denote the set of all documents considered in a multi-agent system, i.e., the union of all the resource agents' document sets.
De nition 9 Agent Language Let M = hU; B; R; Ci be a multi-agent system.The agent language, denoted L Agent , is de ned by: L Agent = U N B R D A uniform language is to be de ned, capturing all possible formulae agents support.This language, called the aboutness language, consists of the descriptor language, since user and resource agents support descriptors, and aboutness and anti-aboutness statements.
De nition 10 Aboutness Language Let L K be a descriptor language.Then the aboutness language, denoted L About , is the smallest superset of L K such that: if ; 2 L K then . 2 L About and . 2 L About .
The semantics of a multi-agent system for Information Discovery is now given as a relation between the agent language and the aboutness language.It expresses when an element of the aboutness language is valid in an agent, i.e., an element of the agent language.
De nition 11 Semantics of MASID Let M = hU; B; R; Ci be a MASID.The semantics of M is given by the relation j = M L Agent L About for which every agent supports some semantics for descriptors, every user agent supports the User Semantics De nition 4, every resource agent supports the Resource Semantics De nition 6, and every broker agent supports the Broker Semantics De nition 8.
Broker agents can be characterized by the way in which they make aboutness decisions in a network of other broker agents.Several types of broker agents are identi ed.

IRSG98
Example In preparing a case, a lawyer does not want to miss possibly relevant material.This is re ected in the de nition of a broker agent that is a lawyer.A form of meta-search, i.e., merging the results of a number of brokers, is obtained if a typical broker is used.All documents which are considered relevant b y at least one broker are rendered by a t ypical broker.An example of a typical broker is MetaCrawler 4 .A unanimous broker is best applied if certainty of relevancy is required.A gambling broker can be used in a ltering context to deliver a mix of 'randomly chosen' documents.It can also be used for system enhancements: by examining the documents a gambling broker passes on, one gaines insight i n t h e shortcomings of the brokers that did not know h o w t o e v aluate those documents.In an ideal situation, the users are able to specify what types of brokers should assist them in the quest for relevant information.
Each careful broker agent is also a typical broker agent.If a broker agent d o e s n o t communicate with other broker agents, it is unanimous, stubborn, a lawyer, optimistic, and gambling.
The di erences in relative p o wer, i.e., coverage of aboutness decisions, of broker agents can be exploited for e cient Information Discovery, as shown later.The comparison between broker agents with respect to their relative p o wer is modeled by a n e m bedment relation.
De nition 13 Embedded Broker Agents Let M = hU; B; R; Ci b e a m ulti-agent system and let b; b 0 2 B and q 2 L K .
Broker agent b is embedded in b 0 , denoted b b 0 , i e v ery aboutness decision of b is also made by b 0 : .b .b 0 , i.e., 8 ; 2 L K : b j = M .b 0 j = M . .The broker-query pair bq i s left embedded in b 0 q 0 , denoted bq L b 0 q 0 , i every aboutness decision of b regarding q as rightmost part is also made by b 0 regarding q 0 , i.e., 8 2 L K : b j = M .q b 0 j = M .q 0 .Lemma 4.1 The relations and L are re exive, transitive, and not necessarily connected.In processing a query, rst a large with respect to the embedment relation broker having a c heaply evaluable aboutness relation is used to quickly discard of many irrelevant documents.After this, a smaller broker agent probably with a more expensive aboutness relation is used to produce the eventual outcome.Potentially, this cuts down expenses drastically.Huibers and Denos use a similar approach i n 3 to obtain an ordening on documents.
The next subsection focusses on Information Retrieval issues within a MASID.The subsequent subsection considers Information Filtering issues.

Issues of Information Retrieval in ID
In the scenario for Information Retrieval in a MASID, a user agent sends a query to a number of broker agents, which, in turn, send requests for documents to resource agents, and, upon receipt of those documents, match document pro les with the query and send relevant documents back to the user agent for rendering.
The result of a broker agent processing a user query in the set of documents of a resource agent, is the set of documents of which the characterisation is about the query according to the broker's aboutness relation.That is, if u = hq;Pi is a user agent, b = h.;.i is the broker agent, and r = h ; Di is a resource agent: resultu; b; r = fd 2 Djb j = M d .q g Example Consider the agents from previous examples.We h a ve resultu david ; b overlap ; r surf = fd 2 f d 1 ; : : : ; d 4 gjb overlap j = M d .sur ngg = fd 1 ; d 3 ; d 4 g.
For reasons of e ciency, a broker agent that supports a competent aboutness relation at high costs, can be preceded by a less restrictive and rather cheap broker.We call this process serial composition, and it can, of course, be repeated several times.One and the same document c haracterization is matched by a n umber of increasingly complex broker agents.The series of brokers involved is called a broker lter path.
De nition 14 Broker Filter Path Let b 1 ; : : : ; b n be broker agents.Then, for every query q, the sequence b 1 q; : : : ; b n q is called a broker lter path.The broker lter path is sound i b n : : : b 1 , i.e., the broker agents are increasingly restrictive.Lemma 4.4 Let b be a sound broker lter path of which b n is the last broker agent.Then, T b i 2b .b i = .bn .
The simple scenario for IR can, of course, be augmented.In the remainder of this subsection, we discuss query expansion, user pro le adaptation and autonomous IR or query generation.
One of the bene ts of the synthesis of IR and IF is that the user pro le forms a naturally personalized context to expand the user query in.The user agent can expand the user query with respect to its user pro le, i.e., all the pro le topics available, obtaining a set of expanded queries which are sent to a broker agent for processing.This form of expansion is called pro le expansion.
A user pro le consists of several unrelated information needs.Furthermore, the user query is formulated in the light of a single information need.Instead of expanding the query to the complete user pro le, the user agent can also expand the query to the corresponding pro le topic, i.e., the pro le topic that belongs to the information need in the light of which the user query was formulated.To formalize this, we assume a similarity function, e.g., : L K L K !0; ::; 1 , where the similarity b e t ween descriptors and is larger i ; is higher.The procedure now is rst to nd the pro le topic p; N that maximizes q;p, and then to expand to this topic only.This form of expansion is called topic expansion.
Query expansion can also be used for user aided disambiguation of query terms.In example 3.1 we s a w that a query term has di erent i n terpretations in di erent pro le topics.To assess the correspondence of the pro le topics to the query, the query is expanded with respect to all the pro le topics.User relevance feedback on the retrieved documents then indicates the desired interpretation, i.e., the corresponding pro le topic.

IRSG98
Both pro le and topic expansion only take the user's own pro le into account.A form of widened expansion is obtained if the user pro les of related users are taken into account a s well.In order to contact the related users, communication channels in the multi-agent system can be followed.Query expansion can now take place with respect to a set of user pro les.In expanding the query to the individual pro les of this set, pro le or topic expansion can be used.
Another augmentation of the simple IR scenario is the adaptation of user pro les.Three moments for this can be identi ed.First, when the user speci es a new query.The similarity function can be applied to obtain the most similar pro le topic which can then be adapted according to the query.Second, on the rendering of the relevant documents, the characterisations of the documents as well as the query itself can be used for pro le adaptation.A more nuanced approach i s a c c hievable if relevance feedback is given, i.e., if the user is able to explicitly mark some documents as non-relevant.The document c haracterisations of these documents only are then used for pro le adaptation.Thus, by exploiting user queries for the adaptation of user pro les, IF bene ts from the synthesis with IR.
Autonomous IR is the third advantage of the synthesis between IR and IF.Whereas in the simple IR scenario the initiative is in the hands of the user, user agents, being proactive, can also start an IR task themselves, thus performing autonomous IR.In order to do this, the user agent generates a query which is subsequently sent to a broker agent.The user agent generates queries on the basis of the user pro le, thus serving the user in his information needs.

Issues of Information Filtering in ID
The matching of user pro les with document c haracterisations, i.e., computing the result sets, is the same in IF as in IR.Again, the result sets are computed with the anti-aboutness relations of broker agents.The di erences in ltering with retrieval are that in IF the initiative is in the hands of the documents, and, that a topology of user agents can be exploited for e cient ltering.Since the switch of initiative cannot be modeled properly in our static framework, we will focus on the topology.
Example Figure 3 shows an example of a ltering topology: pro les higher up in the hierarchy are less speci c than the lower ones.Incoming documents are sent to the root of the hierarchy and nd their way d o wn to user agents by the normal matching procedures.
In a similar way to obtaining e cient brokers, i.e., by serial composition, e cient ltering can be achieved by serially combining user pro les.Starting, again, in a bottom up fashion, the user pro les are preceded by less speci c group pro les.Matching, then, starts with rather general group pro les, gradually proceeds through more complex group pro les, and, nally, ends in the user pro les.
As with serially composed broker agents, care must be taken in the way in which the pro les are actually combined.The series of pro les must be of increasing complexity t o guarantee that no relevant documents are discarded of at an intermediate stage.
De nition 15 User Filter Path Let q 1 ; : : : ; q n 2 L K be queries and let b 2 B be a broker agent.Then, the sequence bq 1 ; : : : ; b q n is called a user lter path.The user lter path is sound i 81 i n : bq i+1 L bq i .
Example Assume that every user agent in Figure 3  Then, all user lter paths in Figure 3 are sound user lter paths.In the opposite direction they are not sound user lter paths.Now, information is needed to derive the purpose of a communication channel.Several types of channels can be de ned between user agents.For instance, semantical channels like a c hannel from a student to a teacher, or from employer to employee, or, structural channels used for ltering.In order to be able to select the proper channels, the channels are labeled with their function.That is, a channel is a 3-tuple of which the components denote the source agent, the target agent, and the type of the channel, respectively.That is, a channel is an element o f L Agent L Agent T , where T is a set of channel types.The type for lter channels is lter.
The scenario's for query expansion, as described in the previous section, can now be re ned by using only channels of certain types.For instance, widened expansion can be performed with respect to a whole company, for example by using the company channels, or with respect to a single department, i.e., by only using the R&D-department channels.
Thus far, we h a ve described two w ays to improve the e ciency of a MASID: serial composition of increasingly complex broker agents or user pro les.In serially composed brokers the query remains the same, and in serially combined user pro les there is only one broker agent.To generalise this, a sound lter path, consisting of a number of brokers and queries, is one that does not discard of any documents at intermediate stages that are considered relevant in a later stage.This leads to a more general de nition of soundness of a lter path.
De nition 16 General Filter Path Let b 1 ; : : : ; b n 2 B be broker agents, and q 1 ; : : : ; q n 2 L K be queries.Then, the sequence b 1 q 1 ; : : : ; b n q n is called a general lter path.The general lter path is sound i every broker-query pair is left embedded in the previous broker-query pair, i.e., 81 i n : b i+1 q i+1 L b i q i .Lemma 4.5 If a broker lter path is sound, it is also a sound general lter path.If a user lter path is sound, it is also a sound general lter path.

IRSG98
In order to properly de ne a correct ltering topology, w e single out the channels that are used for ltering.We assume that serially composed broker agents and user lter paths only are constructed with channels of type lter.The ltering channels are de ned by C F = fha; a 0 ; t i 2 Cjt = lterg The de nition of a ltering topology re ects that the ltering topology should lead documents directly down to user agents and that lter paths are correctly constructed in terms of form and soundness.The de nition re ects that an acyclic topology is needed, consisting of series of user agents such that together with their associated broker agents they form sound lter paths.
De nition 17 Filtering Topology A m ulti-agent system M = hU; B; R; Ci is said to have a ltering topology i C F describes a forest, i.e., a set of trees, and every user agent participating in C F is attached to a broker agent, and every lter path in M is sound.
We n o w h a ve tools to formally decide if a multi-agent system for Information Discovery adheres to a ltering topology.If not, we are able to inspect the lter paths to locate the shortcomings.

Conclusions
This article provides a formal framework in which Multi-Agent Systems for Information Discovery MASID can be statically described, analysed, and compared.Multi-agent systems for information discovery can be compared with respect to their statical constructional properties, such as the number of agents used of the di erent t ypes, the types of channels that are possible, and the types of broker agents used.It can be checked, for example, if a MASID Adheres to a sound ltering topology.First, the Information Discovery paradigm was stated, identifying the types of agents needed.These agents as well as Multi-Agent Systems for Information Discovery were described in more detail and formalised.
Further research will focus on implementing a prototype of the Pro le see e.g. 9 system and describing it in the framework developed.To this end, the framework has to be augmented with, for instance, domain knowledge and a richer descriptor language.In addition, the dynamic aspects of MASIDs also form a main topic for further research.

Figure 1 :
Figure 1: The Information Discovery Paradigm

Figure 2
Figure 2 for a schematic representation of a user agent.

Figure 2 :
Figure 2: The information contained in a user agent.
Let M = hU; B; R; Ci be a MASID.Furthermore, de ne C b = fb 0 2 Bjb 0 ; b 2 Cg, i.e., all the broker agents b can communicate with.Broker agent b 2 B is called b j = M .C b : b 0 j = M .gambling :9b 0 2 C b : b 0 j = M ._ b 0 j = M .

Lemma 4 . 2
Let b; b 0 2 B be broker agents in multi-agent system M = hU; B; R; Ci.Then, broker b is embedded in broker b 0 , i.e., b b 0 , i for every query q 2 L K broker b is left-embedded in b 0 , i.e., 8q 2 L K : bq L b 0 q.Lemma 4.3 Let b be a unanimous broker agent connected to b 1 ; : : : ; b n .Then, broker b is embedded in all the attached brokers, i.e., for all 1 i n : b b i .Let b b e a t ypical broker agent connected to b 1 ; : : : ; b n .Then, the attached brokers are all embedded in broker b, i.e., for all 1 i n : b i b.
Figure 3: Filtering Topology De nition 5 Resource Agent Let D be a set of documents and : D !K a characterisation function.Then, the tuple h ; Di is a resource agent, where D is called the agent's set of documents and is the agent's document c haracterisation function.Example Consider a set of 4 documents about sur ng D = fd 1 ; : : : ; d 4 g, where d 1 = Sur ng the Internet, d 2 = Computer Applications, d 3 = Wind Sur ng in Australia, and d 4 = Wave Sur ng.In addition, consider a characterisation function such that Consider again resource agent r surf from example 3.2.If r surf focusses on document d 1 , the corresponding characterisation is valid, i.e., r surf ; d 1 j = sur ng ^internet.Focussing on document d 4 results in r surf ; d 4 j = wave ^sur ng.
, for every document d 2 D: r; d j = M d The sentence r; d j = M d describes that when resource agent r considers document d, the characterisation of that document, i.e., d, is valid.Note that in this way, one agent per collection of documents is obtained.Example