1 Introduction The information retrieval (IR) roblem can be decribed a the quet to nd the et of relevant information object correonding to a given inf

Transcription

1 Preferential Model of Query by Navigation P.D. Bruza School of Information Sytem and Reearch Data Network CRC Queenland Univerity of Technology Autralia bruzaici.qut.edu.au B. van Linder Phili Reearch The Netherland lindernatlab.reearch.hili.com November 28, 1996 Abtract Thi article can be een a integrating nonmonotonic reaoning and information retrieval. Searching i realized via navigating through an information ace called a hyerindex. The uer reference uggeted by the ath are rereented a default. and/or recluion relationhi. The emantic of navigation ath are dened in the tyle of model reference logic. Some information retrieval related roertie of thee emantic are given. Sound inference rule correonding to thee emantic are alo rovided. Thee rule may be ued to infer decritor which are conitent with the reference for information inherent in the uer' navigation ath. Such inference can be ued for query exanion or to dynamically alter the information ace through which the uer i browing. 1

2 1 Introduction The information retrieval (IR) roblem can be decribed a the quet to nd the et of relevant information object correonding to a given information need, which i rereented by a requet. IR begin with a uer who wihe to atify an information need. The information need i tyically formulated in the form of a requet, denoted by q. The intention i that the requet q be a good a oible decrition of the information need N. The information being queried i modelled a a et of information object, or document. An often ued remie in IR i the following: if a given document d i about the requet q, then there i a high likelihood that d will be relevant with reect to the aociated information need. Thu, the information retrieval roblem i reduced to determining the aboutne relation between document and requet. Many information retrieval mechanim have been develoed, and there i a wide variation in how they determine aboutne. Recent invetigation have centred around formalizing the notion of aboutne by axiomatizing it roertie in term of a neutral, underlying theory of information [5, 9]. Thi work i incomlete, however, a the aarent nonmonotonic behaviour of aboutne ha only briey been touched uon. Recent reearch ha been lling thi ga [15, 10]. Our work ha focued on referential tructure a a mean of exreing the nonmonotonic character of aboutne [6, 7]. Berger & Huiber are following a imilar line uing ituation theory [1]. We view referential tructure a being a natural choice for underinning information retrieval. In a nuthell, the given information need imoe a referential ordering on the et of information object being queried to atify that need. Thi article begin by formalizing certain information retrieval fundamental. In articular, the aboutne relation between a document and decritor i introduced. Thereafter, the notion of default and recluion are introduced a a mean of rereenting uer reference for information. The emantic of thee notion i exreed in term of referential tructure. It i hown how default and recluion can be gleaned from the uer' navigation ath through an information ace of decritor called a hyerindex. The referential emantic imlied by uch a ath are alo dicued. Information related roertie of the referential tructure are highlighted. In articular, ound inference rule are reented which allow the oibility to reaon about the uer' reference for information. 2 Information Retrieval Fundamental Information retrieval i a roce which decide whether one information carrier (a document d) i about another information carrier (the query decrition q). A the reviou entence ugget, thi article will ditinguih between two tye of information carrier; document and (query) decritor. Decritor are not only ued to rereent the uer' information need in the form of a query, but can alo be ued a a mean to characterize a document to facilitate it retrieval. Document will be aumed to be drawn from a nite et D of document. Decritor, on the other hand, will be drawn from a language of which the rimitive element are referred to a keyword. 2

3 Denition 2.1 (Decritor Language) For a given et K of keyword, the language L K i dened to be the mallet ueret of K uch that if i 2 L K and j 2 L K then (i j) 2 L K : (Outer bracket around i j will be often be ignored for reaon of imlicity). oerator denote information comoition. It allow more comlex decritor to be contructed from more rimitive one. Examle of information comoition are readily found in information retrieval. Conider the Boolean retrieval query huttle ^ deign which illutrate how the conjunction i ued to comoe two individual keyword. The reulting exreion rereent the need to be informed about the deign of the ace huttle. Information comoition doe not tyically enjoy the ueful roertie of commutativity and aociativity [7]. For examle, ytem information (ytem information) veru information ytem (information ytem). The roertie of deend on the decritor language choen and the rule which govern comoition. A ecial keyword, the emty keyword, denoted, ha the roerty that it decribe all document. Under information comoition it behave a would be exected, namely i = i = i. Not all information carrier can be meaningfully comoed. The reaon for thi i that they are incomatible; the information they hare clahe, or i contradictory. In other word, carrier i and j are aid to reclude each other, denoted i? j. It can be argued that green martian reclude blue martian under the aumtion that martian are either blue or green, but not both. The intuition behind thi henomenon can be exlained in term of oible world [13]. After characterizing a world a being a \green martian" world, it cannot be re-characterized a a \blue martian" world. Information recluion arie naturally in information retrieval. For examle, if one i earching for document about river ollution, then document about air ollution are robably not intereting. Hence, river ollution? N air ollution whereby the N emhaize that the recluion relationhi i a roduct of the given information need N. Thi tye of recluion will be invetigated in more detail later. Document are indexed by an indexing function to facilitate their retrieval. More ecically, indexing yield a characterization (d) 2 }(L K ), for all document d 2 D. The trile hd; ; Ki will be referred to a a retrieval model a it i againt thi framework that uer querie are iued. Traditional information retrieval ytem match the decritor in q with the decritor in a characterization (d). If the overla between (d) and q i ucient document d i deemed to be about q and i returned. Within the logic-baed aroach, however, aboutne can be conidered model-theoretically [4, 5, 7]. When adoting thi view two quetion mut be addreed. The rt i, what are the model, and econdly how the atifaction (aboutne) relationhi i dened between a given model and a decritor. In thi article, we take the view that the model are abtraction of the document themelve. Such an abtraction S d of a document d conit of it characterization (d), which i anned by a reexive, ymmetric binary relation R d L K L K. Thi relationhi cature the fact that certain decritor tand in relationhi to each other within the document. By way of illutration, conider document d to be The 3

4 The ace huttle ha a breadth of 9 metre. The deign of the launch ad take thi into account. where (d) = face huttle; breadth (9 metre); deign (launch ad)g. Oberve that (ace huttle; breadth) 2 R d a thee two decritor are related, wherea (ace huttle; deign) 62 R d. The relationhi between decritor are imortant for reciion. For examle, it would not be deirable to return d in reone to the query deign ^ huttle. For thi reaon, ome ytem augment the baic Boolean language with roximity oerator. For examle, adj(huttle,deign) or that roxim(huttle, deign,5). The former tate that huttle and deign hould be adjacent, wherea the latter exree that huttle and deign mut be found within 5 word of each other. Both are yntactic method to aroximate that huttle and deign hould be related. So far it ha been etablihed that a model of a document d i a tructure S d = h(d); R d i derived from a document d. It will be convenient to blur the ditinction between d and it aociated model, o from thi oint on d will denote the model, not the actual document of which it i an abtraction. With the model in lace, aboutne can now be conidered model-theoretically: Denition 2.2 (Aboutne) Let M = hd; ; Ki be a retrieval model. The aboutne relation j= M a element d 2 D and an element from L K i inductively dened by: d j= M a i, i 2 (d) d j= M a i j, d j=m a i and d j=m a j and (i; j) 2 R d between an The notation [i] M will be ued to ignify the et of document which are about decritor i within retrieval model M. That i, [i] M, fd 2 D j d j= M a ig. A tated earlier, all document are about the emty keyword: [] M = D. 3 Preferential Structure, Default and Precluion Conider the keyword decritor migration. Thi can be een a dicriminating a et of document dealing with migration. For examle, there may be an object dealing with the migration of arrow, whilt another may be about the migration of almon. Driven by their ecic information need a uer will refer ome document over other. For examle, in the above cae, a uer may refer the document about the migration of almon becaue that i what ()he want to be informed about. Oberve that the information need imoe a referential ordering on the underlying et of document D. Baed on the above intuition, the reference relation can be formalized a follow. Let d 1 N d 2 denote that document d 1 i referable to document d 2 in the light of information need N. It i natural to aume that N i irreexive and tranitive. Stated imly, N i a trict artial order on a et of document D. The air hd; N i will be referred to a a referential tructure. 4

5 The goal of an information retrieval ytem i to deliver the referential tructure to the uer. Thi turn out to be dicult in ractice. Part of the roblem lie with the fact that the query iued to the retrieval model i often an incomlete decrition of the aociated information need. A a conequence, information retrieval ytem attemt to aroximate the referential ordering via document ranking. The referred document are thoe document which bet atify the uer' information need N. Thee correond to the minimal model in the referential tructure. Thi et will lay an imortant role throughout thi article. Denition 3.1 (Preferred Document) Let P = hd; N i be a referential tructure baed on retrieval model M. The et of referred i-document in P, denoted M P (i), i dened by: M P (i) = fd 2 [i] M j 8 ^d2[i]m [ ^d 6 N d]g 3.1 Default and Precluion in Information Retrieval Aume for the moment that there i a uer with an information need dealing with migration. Furthermore, aume the information need i atied by being informed about the migration of bird. Oberve that if the uer enter the query migration, ()he exect information about the migration of bird. In other word, that the migration i of bird i aumed, that i, taken a a default. Thi default i exreed a follow: migration j N bird which read \in the light of the information need N, the referred migration document are about bird. Oberve that the default i arameterized with the information need N. Remember that it i thi need that i imoing the referential ordering on the underlying document. Default arie out of biae imoed by the information need at hand. They are intimately tied to the underlying referential tructure in the following way: i j N j mean that all referred i?document are alo about j. The notation j N j will be hortened to j N j. It intuition i that the mot referred document are about j. Precluion between decritor arie becaue reference for document about i exclude document about j. More ecically, i referentially reclude j i all referred i?document are not about j, denoted i? N j. The above intuition behind default and information recluion can be formalized uing the tyle of Shoham [16]. Their relationhi with the underlying referential tructure i etablihed a follow: Denition 3.2 (Semantic) Let P be a referential tructure. Let i; j 2 L K. Then, P j= i j N j, M P (i) [j ] M P j= i? N j, M P (i) \ [j ] M =? P j= i j6 N j, P 6j= i j N j P j= i 6? N j, P 6j= i? N j 5

6 3.2 Where do the default and recluion come from? Default and recluion relationhi are in eence rereentation of uer reference. Some information retrieval ytem ue a roce of relevance feedback a a mean of uer reference information. In thi roce, the uer identie which document, or art of document, they nd relevant (i.e. oitive relevance feedback). Thi information i then ued to formulate a new query. Some ytem alo uort negative relevance feedback. We have been exerimenting with Query by Navigation (QBN) within a o called hyerindex brower a a mean of caturing uer reference information via relevance feedback. Eentially, navigation through the hyerindex give oitive and (oibly) negative relevance feedback with reect to certain term. In order to rovide the intuition behind QBN within a hyerindex a mall examle i reented. For more detail about hyerindice and QBN the reader i referred to [4, 3, 2, 8]. Aume that the uer ha entered the query internet to ome information retrieval mechanim. (From thi oint on, thi initial query will be ignied by q). Once the query ha been evaluated, a hyerindex brower i contructed baed on the characterization of the document in the query reult. The uer interface to the hyerindex brower i deicted in the to of gure 1 with a fragment of the underlying hyerindex hown in the lower art of the gure. A hyerindex i a artial ordering hl K ;!i, whereby i! j mean that decritor i contain the information carried by decritor j. Naturally, the emty decritor i informationally contained in every other decritor. Eentially, QBN involve moving over the hyerindex tarting from, which correond to an information need which would be atied by all document. In our examle, the uer made the rt te toward rening their given information need by entering the keyword internet. Thi i the current focu of the earch. The decritor urrounding the focu give oibilitie to rene the focu, i.e., make it more ecic, or to enlarge it, i.e., make it more general. In the deiction of the uer interface, renement are denoted by 4 and enlargement by 5. Renement ignify decritor which are more ecic than the focu. Moreover, they alo rovide clue regarding variou context baed on the focu. Thi contextual information aid the earcher whoe information need i not clear. In thi cae, the earcher chooe to rene the focu by activating internet ecurity reulting in a new creen (ee to of gure 2). In other word, the uer i exreing that their referred internet document are about ecurity. Thi i reciely the intuition behind the default: internet j N ecurity The uer may then rene internet ecurity into internet ecurity oftware. In hort, a renement ath through the hyerindex tart with an initial decritor q; q 2 L K which i rened via a number of te. Each renement te correond to a default in the following fahion: Denition 3.3 (Renement Path) A renement ath i a nite-length equence [ 0 ; 1 ; : : : ; m ] uch that 0 = j N q j = q i 1 : : : i j?1 j N i j 6

7 Internet 4 Internet Direct 4 Guide for Internet. 4 Internet Security 4 Internet Solution internet direct guide for internet!!!!!!!!! ! internet ecurity Q Q Q Q internet Q Q internet olution Figure 1: Before rening Internet Security 4 Internet Security Firewall 4 Internet Security Software. 4 Mid-range Internet Security 5 Internet 5 Security internet direct internet ecurity internet ecurity rewall oftware A A guide for!!!!!!!!! A internet! internet ecurity A AA A Q internet ecurity Q Q Q Q Q A... mid-range internet ecurity internet olution Figure 2: After rening 7

8 for 1 j < m A renement ath i aid to be oible, if and only if there i a referential tructure P that uort all of the default in the equence. If a renement ath i oible, then what doe the aociated referential tructure look like? Thi i an imortant quetion a it etablihe the (referential) emantic correonding to the uer' navigation ath. A tated earlier, the referential ordering N i determined by the information need at hand. The renement ath give ome clue about thi ordering via the articular traveral that ha been taken through the hyerindex. Conider the internet examle again which ha yielded the following renement ath: j N internet; internet j N ecurity; internet ecurity j N oftware Such a ath can be viewed contructively in term of an underlying referential tructure. Initially, no reference are known, o all document are equally referred (ee gure 3). The initial default in the above ath tate that the referred document are thoe about the internet. Thi ugget a two tiered referential tructure. The document in the uer tier are thoe which are about the internet, and thoe in the lower tier are thoe which are not. (Oberve in gure 3 that the notation 6 i i ued to characterize thoe document that are not about i). Every document d i in the uer tier i referred to every document d j in the lower tier. Similarly, the econd default lead to a three tiered referential tructure, whereby the mot referred internet document are thoe about ecurity. The econd mot referred are thoe internet document which are not about ecurity, and nally the leat referred document are thoe not about the internet. Finally, the third default lead to a four tiered referential tructure. The key obervation here i that the default in the renement ath can be viewed a reference that are ucceively alied to a referential tructure yielding a new referential tructure. Thi new tructure embodie all the reference that have been alied u to that oint. i, i i, / i/ / i initial referential tructure ~ i i ~ Figure 3: Renement Structure In general, a renement equence of j + 1 default lead to a tructure like the one deicted in gure 4. In thi gure the tier have been numbered. The mot referred document are thoe in tier zero, the next mot referred in tier one etc. Such a tructure 8

9 0 1 j-1 j.. q+i i j-1, i j q+i i j-1, i j / q, i/ 1 / q Figure 4: General Renement Structure i referred to a a renement tructure. The ordering relation within thi tructure will be ignied by. Thi relation can be viewed a an aroximation of baed on N N the only information available, namely the renement ath which the uer ha taken. The renement tructure hd; i correonding to the renement ath imoed on the N retrieval model M will be denoted (M). Renement tructure are indeed referential tructure. Prooition 3.1 Let M be a retrieval model and be a oible renement ath of M. Then (M) i a referential tructure. Proof: From gure 4 and the receding dicuion it i clear that the tier in the renement tructure artition the et D. (The et of document in tier i will be referred to a D i ). Furthermore, for all d 2 D i ; ^d 2 D j : if d N ^d then i < j, and if i < j then d N ^d Stated otherwie, renement tructure (M) i a ranked model. Ranked model are a ecic tye of referential tructure [14]. Hoefully the reader ha oberved how by alying ucceive default in a renement ath new tier (rank) are added to the underlying referential tructure. We have een how renement ath lead to ranked model. From now on, we will view a referential tructure P to be a ranked model (D 0 ; : : : ; D n ) of n; n 1 rank. A default i j N j can be alied to P if there exit a rank k; 0 k n uch that D k contain the referred i document. The eect of rening the referential tructure P with the default i j N j will be formally recribed by the function r which take a default and referential tructure a inut, and yield a referential tructure. Baically, if a default i j N j i going to have an eect on referential tructure P, it will lit the rank k into two rank; one containing i? document that are alo about j, and the econd containing the remainder. 9

10 Denition 3.4 (Renement) Let P = (D 0 ; : : : ; D k ; : : : D n ) be a ranked model baed on retrieval model M, and i j N j be a default. Let D k ; 0 k n be the rank containing the referred i- document. Then, where r (i j N j; P ) = ( ^D0 ; : : : ; ^Dk ; ^Dk+1 ; : : : ^Dn+1 ) ^Di = D i ; 0 i < k ^Dk = fd 2 D k jd j= M a i ^ d j=m jg a D k+1 ^ = D k? ^D k D^ i+1 = D i ; k + 1 < i n if there i no rank D k then r (i j N j; P ) = P 3.3 Proertie of Renement Structure Imagine the uer begin with the query q and rene thi through ucceive te through the hyerindex. How can the reference imlicit in the renement ath be ued to benet information retrieval? One oibility i query exanion. In thi roce the initial query q be exanded (by comoing term to it). Thee exanion are intended to be more recie decrition of the given information need than q i. Thee exanion can be red at the underlying retrieval model. Oberve that query exanion mut be done in a way which i conitent with the uer reference locked into the renement ath. That i, afe exanion of q are ought after. Denition 3.5 (Safene) Let P be a referential tructure and let i; j; k 2 L K. The term k i afe for i j N j with reect to P, denoted S P (k; i j N j), i P j= i j N j ) P j= i k j N j The left cloure yield the et of decritor that can be ued to exand a given decritor i in a way which i conitent with the underlying referential tructure. Denition 3.6 (Left Cloure) Let P be a referential tructure and let i; j; k 2 L K. The left cloure of i j N j with reect to P, denoted BCl P, i dened by BCl P (i j N j), fk 2 L K j S P (k; i j N j)g 10

11 When the left cloure evaluate to the decritor language L K then the relation j N i deemed monotonic. Denition 3.7 (Monotonicity) The relation j N i monotonic with reect to a given referential tructure P and a et of default i 8 i jn j2[bcl P (i j N j) = L K ]. Monotonicity i an undeirable roerty for information retrieval a it correond to unbridled query exanion. A a renement ath conit of a equence of default, the left cloure of each of thee can be comuted. The reultant cloure hould not be treated equally however. Thoe default earlier in the equence (i.e. the te earlier in the navigation ath) will robably rereent le ignicant reference than thoe default toward the end of a ath. A a conequence, the cloure of the default in the renement ath hould be ranked accordingly. Denition 3.8 (Ranked Left Cloure) Let be a renement ath with length m uch that i a oible renement of the model M. The ranked equence of afe exanion of with reect to (M), notation S (M) (), i dened by S (M) (), [BCl (M) ( 1 ); : : : ; BCl (M) ( m )] How hould the ranking of left cloure be ued? We enviage that element within individual cloure can be ordered. The minimal element of thee ordering rereent the mot otentially relevant decritor with reect to the reference exreed by the re- nement ath. Such element could be reented to the uer a art of the hyerindex, which would allow the uer to elect thoe which bet comlement their information need. Once elected thee can be red o a exanion of q a dicued above. The reult i a browing ace that dynamically organize itelf according to the reference imlied by the uer' navigation ath u to that oint. 3.4 General Navigation Path In general, navigation ath through the hyerindex can involve enlargement a well a renement. For examle, imagine the uer ha rened internet into internet ecurity into internet ecurity oftware. At thi tage the uer may decide that internet ecurity oftware i not an at decrition of their information need. In the hyerindex, the uer can enlarge internet ecurity oftware into either internet ecurity or ecurity oftware. (See the fragment of the hyerindex deicted in gure 5). Let u now look at the reference imlied by each of thee two enlargement and their correonding eect on the underlying referential tructure. Firt the enlargement from internet ecurity oftware to internet ecurity will be conidered. How hould uch an enlargement be interreted? One oibility i that the uer i no longer intereted in the oftware 11

12 ????.....???? internet ecurity?? internet ecurity oftware ecurity oftware Figure 5: Enlargement oibilitie of internet ecurity oftware aect of internet ecurity, but i till intereted in other aect of internet ecurity. In other word, the referred internet document are thoe about internet ecurity, but not about oftware. That i, the referred internet ecurity document reclude oftware, or internet ecurity? N oftware The eect of uch a recluion on the underlying referential tructure i a follow. The rank k i located that contain the referred internet ecurity document() which are not about oftware. All document about internet ecurity and oftware in rank le than k are demoted to rank k + 1. The eect of thi tye of reference on the underlying referential tructure i recribed by the function e. Similar to r, thi i a function that take a reference (thi time in the form of a recluion) and a referential tructure and yield a referential tructure. Denition 3.9 (Enlargement) Let P = (D 0 ; : : : ; D k ; : : : D n ) be a ranked model baed on retrieval model M, and i? N j be a recluion. Let D k ; 0 k n be the rank containing the referred i-document, which are not about j. where e (i? N j; P ) = ( ^D0 ; : : : ; ^Dk ; ^Dk+1 ; : : : ^Dn+1 ) ^Di = D i? fd 2 D i jd j= M a i ^ d j=m a jg; 0 i < k ^Dk = D k ^Dk+1 = S 0i<kfd 2 D i jd j= a i ^ d j= a jg ^Di+1 = D i ; k + 1 < i n if there i no rank D k then e (i? N j; P ) = P 12

13 Let u now conider the referential emantic of an enlargement from internet ecurity oftware to ecurity oftware. Thi ha two oible interretation; a broadening of the aociated information need, or a comlete change of tack. Thee will be dicued in turn: broadening The uer decide that internet ecurity oftware i too ecic, o enlarge it into ecurity oftware. The intention here i that the mot referred document have become thoe about ecurity oftware including thoe about internet ecurity oftware. In term of reference thi i exreed by the default: j N ecurity oftware The eect of thi on the underlying referential tructure i to romote all ecurity oftware document to the to rank (rank zero). Thi i formally recribed by the function b : Denition 3.10 Broadening Let P = (D 0 ; : : : D n ) be a ranked model baed on retrieval model M, and j N i be a default. where b ( j N i; P ) = ( ^D0 ; : : : ; ^Dn ) ^D0 = D 0 [ fd 2 D i jd j= M a ig; 1 i n ^Di = D i? fd 2 D i jd j= a ig; 1 i n change of tack The uer decide that they are no longer intereted in the internet, er e. The intention here i that the referred document are about ecurity oftware excluding thoe about internet ecurity oftware. In term of reference thi would mean: ecurity oftware? N internet A change of tack collae the underlying referential tructure into two rank. In our examle, the to rank would comrie the ecurity oftware document not about the internet. The econd rank would contain the ret. A change of tack i formally recribed by the function c. Denition 3.11 (Change of tack) Let P = (D 0 ; : : : ; D n ) be a ranked model baed on retrieval model M, and i? N be a recluion. j c (i? N j; P ) = ( ^D0 ; ^D1 ) where 13

14 ^D0 = fd 2 D i jd j= M a i ^ d 6j=M a jg ^D1 = D? ^D0 A the name ugget, a change of tack, imlie that reviou reference are forgotten. Semantically thi i achieved by the collaing of the referential tructure. The uer can now begin to follow their new tack. A general navigation ath tart with a decrition of the information need q, which can be rened. The uer can thereafter navigate through the hyerindex by rening, enlarging, broadening or changing the tack of the earch. A we have een, navigating through the hyerindex in thi fahion imlie reference in the form of default or recluion. Denition 3.12 (General Navigation Path) A navigation ath i a nite-length equence [ 0 ; 1 ; : : : ; m ] uch that 0 = ( j N q; r) k = (i j N j; r) or ( j N i; b) or (i? N j; e) or (i? N j; c) for 1 k < m, and where r denote a renement, e an enlargement, b a broadening and c a change of tack. Recall that a renement ath recribe a referential tructure (M) baed on retrieval model M. Thi reult will now be generalized: A navigation ath recribe a referential tructure (M). The ordering relation within thi tructure will be ignied by. Thi N relation can be viewed a an aroximation of N baed on the only information available, namely the navigation ath which the uer ha travered through the hyerindex. The tructure hd; i correonding to the navigation ath imoed on the retrieval N model M will be denoted (M). General navigation ath do indeed recribe referential tructure. Prooition 3.2 Let M be a retrieval model and be a navigation ath of length m. Then (M) i a referential tructure. Proof: By induction on the length m of the ath. If m = 0, then no reference have been exreed. A a conequence all document in D are equally referred yielding the referential tructure P = (D 0 ), where D 0 = D. Aume that alication of i(0 < i < m) reference have led to the referential tructure P. Now conider i+1 : 14

15 { if i+1 = (i j N j; r), thi indicate that default i j N j i to be alied a a renement on P via r (i j N j; P ). Thi yield a referential tructure (ee denition 4) { if i+1 = ( j N i; b), thi indicate that default j N i i to be alied a a broadening on P via b ( j N i; P ). Thi yield a referential tructure (ee denition 10) { if i+1 = (i? N j; e), thi indicate that the recluion i? N j i to be alied a an enlargement on P via e (i? N j; P ). Thi yield a referential tructure (ee denition 9) { if i+1 = (i? N j; e), thi indicate that the recluion i? N j i to be alied a a change of tack on P via c (i? N j; P ). Thi yield a referential tructure (ee denition 11) 4 Sound Inference Rule for Preferential Structure A quetion deerving attention i what inference rule are ound with reect to referential tructure. Thi quetion i largely anwered by the work of Krau, Lehmann and Magidor [12]. Their account i baed on a rooitional language whereby information comoition i realized by conjunction. Rule involving imlication and dijunction are not ertinent a thee connective do not feature in the decritor language L K : i j N i Reexivity ij j N k; i j N j i j N k Cut i j N j; j j N i; i j N k j j N k Equivalence i j N j; i j N k i j N jk And i j N j; i j N k ij j N k Cautiou Monotonicity i 0 j N i 1 ; i 1 j N i 2 ; :::; i k?1 j N i k ; i k j N i 0 i 0 j N i k Loo The following lemma etablihe which rule are ound when information comoition enjoy the ame roertie of conjunction. Thi reult iggyback on the work of Krau et al mentioned above. Lemma 4.0 Let M be a retrieval model. Let (M) be a referential tructure baed on navigation ath. If 8 d2d 8 i;j2 (d) [(i; j) 2 R d ] then (M) uort Reexivity, Cut, Equivalence, And, Cautiou Monotonicity, Loo. 15

16 Proof: When the condition 8 d2d 8 i;j2 (d) [(i; j) 2 R d ] hold, every decritor i related to every decritor within a given model d. Thi enure that ha the ame modeltheoretic roertie a conjunction, namely: d j= M a i j, d j=m a i and d j=m a j Preferential tructure are ranked model which are a retriction of the cumulative ordered model of Krau, Lehmann and Magidor (ee denition 4.1 of [12]). Thi account alo rove the above rule to be ound in uch model (ee lemma 3.16). The above lemma relie on the fact that information comoition ha the ame roertie a conjunction. A tated earlier, thi cannot be guaranteed. The following lemma etablihe which rule are ound when thi requirement i droed. Lemma 4.0 Let M be a retrieval model. Let (M) be a referential tructure baed on navigation ath. If 8 d2d 8 i;j2 d [(i; j) 2 R d ] then (M) uort Reexivity, Equivalence, Cautiou Monotonicity, Loo. Proof: Reexivity, Equivalence and Loo do not involve information comoition o thee are uorted for the ame reaon they are in the reviou lemma. And i not uorted: Conider d to be a referred i? document, which i about j, and i alo about k. If (j; k) 62 R d, then d i not about j k. Cut i not uorted: Conider the et of referred i? document which are about j. A trict ubet of thee are referred i j document, which are about k. A a conequence, there i at leat one referred i?document that i not about k. Cautiou monotonicity i uorted. The ame argument can be ued a i in the roof of lemma 3.16 of [12] and the fact that [i j ] M [i ^ j ] M. Recently a rincile dubbed rational comoitional monotonicity ha been rooed [6, 7]. Like Cautiou Monotonicity, thi rincile decribe a conervative form of information comoition. i j N j i 6? N i k j N j Rational Monotonicity turn out to be ound with reect to referential tructure. Prooition 4.1 Let M be a retrieval model. Let (M) be a referential tructure baed on navigation ath. Then (M) uort Rational Comoitional Monotonicity. k 16

17 Proof: i 6? N k imlie from denition 3.1 that there exit a document d uch that d i a referred i?document and d j= M k. From a i j N j, we know that d i alo about j. A it i a referred i? document it i alo about j. Aume, for the moment, that thi document d i about i k. There cannot be any i + k-document more referred than d, for if there wa it would alo be about i, which would contradict that d i a referred i?document. Hence d i a referred i k document, which we already know i about j. The ound inference rule can be ued to infer decritor that are conitent with the reference exreed in the navigation ath. Thee inference can be fed dynamically into the hyerindex thu creating an information ace which i enitive to the uer' reference for information. Rational Comoitional Monotonicity i articularly intereting a it introduce decritor k which can be afely 1 comoed to the left hand ide of a default. Oberve that thee decritor k need not be decritor that the uer ha exlicitly encountered during their navigation ath. 5 Concluion and Further Reearch Thi article integrate nonmonotonic reaoning and information retrieval. Preference tructure, a emantic framework from nonmonotonic reaoning, are ued to underin navigation ath through a browable information ace. Thi framework i very uitable a it cature exactly the intuition behind a document ranking. Moreover, the reference locked u in thee tructure can be rereented a default and recluion relationhi, which in turn can be reaoned with via an inference ytem. A contribution of thi aer i the identication of a ound inference ytem with reect to the underlying referential tructure. The imact on information retrieval could be the following. A uer navigate through an information ace, viiting certain decritor along the way. In the background an inference ytem could be deducing other decritor that are conitent with the reference imlicit in the ath. Reult from the inference ytem could alo be fed dynamically into the brower, or ued indirectly to exand the query which initiated the navigation. How to actually do thi i a matter currently under invetigation. A major iue i the fact that reference \age" with reect to the length of the navigation ath. To ome extent thi aging roce i reected in the articular referential tructure that correond to the ath travered. The quetion arie a to how bet utilize the ranked left cloure acquired during rening. We are currently deigning a reference reaoning baed information retrieval mechanim uing our exiting hyerindex brower [11]. Acknowledgment The work reorted in thi aer ha been funded in art by the Cooerative Reearch Centre Program through the Deartment of the Prime Miniter and Cabinet of Autralia. 1 A tated in denition

18 We thank Erik Proer for ueful comment on earlier draft of thi work. Reference [1] F.C. Berger and T.W.C. Huiber. A framework baed on ituation theory for earching in a theauru. The New Review of Document and Text Management, 1, [2] R. Boman, R. Bouwman, and P.D. Bruza. The Eectivene of Navigable Information Dicloure Sytem. In G.A.M. Kemen, editor, Proceeding of the Informatiewetencha 1991 conference, Nijmegen, The Netherland, [3] P.D. Bruza. Hyerindice: A Novel Aid for Searching in Hyermedia. In A. Rizk, N. Streitz, and J. Andre, editor, Proceeding of the Euroean Conference on Hyertext - ECHT 90, age 109{122, Cambridge, United Kingdom, Cambridge Univerity Pre. [4] P.D. Bruza. Stratied Information Dicloure: A Synthei between Information Retrieval and Hyermedia. PhD thei, Univerity of Nijmegen, Nijmegen, The Netherland, [5] P.D. Bruza and T.W.C. Huiber. Invetigating Aboutne Axiom Uing Information Field. In W.B. Croft and C.J. van Rijbergen, editor, Proceeding of the 17th Annual International ACM SIGIR Conference on Reearch and Develoment in Information Retrieval, age 112{121, Dublin, Ireland, July Sringer-Verlag. [6] P.D. Bruza and T.W.C. Huiber. How nonmonotonic i aboutne? Technical Reort UU-CS , Deartment of Comuter Science, Utrecht Univerity, The Netherland, March [7] P.D. Bruza and T.W.C. Huiber. A Study of Aboutne in Information Retrieval. Articial Intelligence Review, 10:1{27, [8] P.D. Bruza and Th.P. van der Weide. Stratied Hyermedia Structure for Information Dicloure. The Comuter Journal, 35(3):208{220, [9] T.W.C. Huiber and P.D. Bruza. Situation: A general framework for tudying Information Retrieval. In R. Leon, editor, Information retrieval: New ytem and current reearch, Proceeding of the 16th Reearch Colloquium of the Britih Comuter Society Information Retrieval Secialit Grou, age 3{25. Taylor Graham, Drymen, Scotland, [10] A. Hunter. Uing default logic in information retrieval. In C Froidevaux and J Kohla, editor, Symbolic and Quantitative Aroache to Uncertainty, volume 946 of Lecture Note in Comuter Science, age 235{242,

19 [11] R. Iannella, N. Ward, A. Wood, H. Sue, and P. Bruza. The oen information locator roject. Technical reort, Reource Dicovery Unit, Reource Data Network, Cooerative Reearch Centre, Univerity of Queenland, Bribane, Autralia, Electronically available a: htt:// [12] S. Krau, D. Lehmann, and M. Magidor. Nonmonotonic Reaoning, Preferential Model and Cumulative Logic. Articial Intelligence, 44:167{207, [13] F. Landman. Toward a Theory of Information. Fori, [14] D. Lehmann and M. Magidor. Rational logic and their model: A tudy in cumulative logic. Technical Reort TR-88-16, Deartment of Comuter Science, Hebrew Univerity, Jerualem, Irael, [15] J-Y. Nie, F. Leage, and M. Brieboi. Information Retrieval a Counterfactual. Britih Comuter Journal, To aear. [16] Y. Shoham. Ecient Reaoning about Rich Temoral Domain. In R.H. Thomaon, editor, Philoohical Logic and Articial Intelligence, age 191{222. Kluwer, Deventer, The Netherland,