3 Conceptual Graphs and Cognitive Mapping

Transcription

1 3 Concepual Graphs and Cogniive Mapping 3.01 Inroducion Chaper 2 provided iniial evidence ha concepual graphs are a suiable knowledge-based decision suppor ool for sraegic managemen accounans. This chaper sars o pursue a more subsanial confirmaion of concepual graphs echnical capabiliy in he sraegic analysis problem domain, by comparing hem wih he cogniive maps of Eden (1991). Eden s mapping echnique, which is a leading knowledge-based srucured diagram echnique for sraegic planning, is based on he advanced personal consrucs mehodology begun by Kelly (1955). The cogniive mapping echnique boh a) employs a highly srucured approach, and b) is designed as a pracical human exper end-user suppor ool. Given all he discussions so far, i hereby offers a valuable comparison wih concepual graphs. Should concepual graphs sufficienly enrich Eden s cogniive maps hen he choice of concepual graphs will be furher srenghened accordingly. As is basis, he examinaion employs he realisic office locaion problem ha Ackerman, Cropper, and Eden (1991) choose in highlighing he benefis of cogniive mapping. An analysis of he same problem is performed using concepual graphs The Example Problem The example iself is as follows (Ackerman e al. 1991, page 41): We need o decide on our accommodaion arrangemens for he York and Humberside region. We could cenralise our service a Leeds or open local offices in various pars of he region. The level of service we migh be able o provide could well be improved by local represenaion bu we guess ha adminisraion coss would be higher and, in his case, i seems likely ha running coss will be he mos imporan facor in our decision. The office purchase coss in Hull and Sheffield migh however be lower han in Leeds. Addiionally we need o ensure uniformiy in he reamen of cliens in he region and his migh be impaired by oo much decenralizaion. However we are no sure how grea his risk is in his case; experience of local offices in Plymouh, Taunon and Bah 64

2 in he Souh Wes 1 may have somehing o each us. Moreover curren managemen iniiaives poin us in he direcion of greaer delegaion of auhoriy The Cogniive Map for he Example Problem Ackerman e al. cogniively map he above problem and produce he diagram in Figure 3.01 as a resul. This figure illusraes wo essenial elemens underlying his cogniive mapping inerpreaion. Namely hese elemens are conceps and links. Each concep is represened as one emergen pole, which describes one side of he problem, and a conrasing pole which is Figure 3.01: Cogniive map for offices locaion problem (Source: Ackerman e al. 1991, page 47) mean o focus he concep by a meaningful conras o he firs pole. Poles may lead o oher poles by means of direced links. All his is clarified furher by examining he map as i appears in COPE, which depics hese cogniive 1 The passage acually saes Souh Eas bu his is a ypographical error as confirmed by he references o 'Souh Wes' laer in he aricle. 65

3 maps in compuer sofware 2. To begin wih, he map s conceps are represened by he following able in COPE: 1 open local offices...cenralise services a Leeds 2 local represenaion...[no] local represenaion 3 increased running coss...[no] increased running coss 4 higher adminisraion coss...[no] higher adminisraion coss 5 improve level of service...[no] improve level of service 6 oo much decenralisaion...[no] oo much decenralisaion 7 risk of impaired reamen of cliens...ensure uniformiy of reamen 8 lack of undersanding abou risk...[no] lack of undersanding abou risk 9 use experience of s w local offices...[no] use experience of s w local offices 10 lower purchase coss of local offices...higher cos in Leeds 11 greaer delegaion of auhoriy...[no] greaer delegaion of auhoriy 12 follow curren managemen iniiaives...[no] follow curren managemen iniiaives Noe COPE adds a sequenial number o signify each concep enered by he user, and auomaically adds he prefix [no] o creae a defaul conrasing pole for any concep where a conrasing pole was no enered. The links are enered by aking he wo appropriae concep numbers and placing a + symbol beween hem. The concep before he symbol leads o he concep placed afer i. For example, 10+1 shows ha lower purchase coss of local offices leads o open local offices. This also sipulaes he conrasing pole higher cos in Leeds leads o he conrasing pole cenralise services a Leeds. The cogniive mapping mehodology also happens o sress ha i is imporan he emergen pole should always represen wha he user can bes idenify wih. However, his is likely o creae problems when i comes o making links as his consrain means poles may lead o poles of he oher kind. The - symbol hus replaces he + symbol o comba his problem. This is illusraed by he following links able in COPE: 1 > >+5 3 >+4 6 >+7 8 >.1 9 >-8 10 >+1 11 >+1 12 >+11 The above able reads from lef o righ. The number before he > symbol signifies he concep ha leads direcly o all he conceps signified by number afer he > symbol. Each + shows a pole o pole, and conrasing pole o 2 COPE, an acronym for Cogniive Policy Evaluaion, runs on an IBM PC or compaible and is available from he Sraegic Decision Suppor Research Uni, Universiy of Srahclyde, UK. 66

4 conrasing pole, link. The - is a pole o conrasing pole, and conrasing pole o pole, link. The link 9-8 hereby means use experience of s w local offices leads o [no] lack of undersanding abou risk, and [no] use experience of s w local offices o lack of undersanding abou risk. Anoher link, '.', is a 'connoaive' link and is employed when he user knows here is an insufficienly definable ye somehow valid connecion beween conceps. This link is applied o he relaionship beween conceps 1 and 8 as overcoming lack of undersanding abou risk may lead o eiher operaing cenralised services or opening local offices. As an opion he user can direc COPE o draw he map in graphical form, as shown by he COPE screen below for he conceps linked o concep 1 : 3 ** increased 2 ** local running coss 6 ** oo much represenaion decenralisaion ^ ^ ^ 8 ** lack of \ 1 open local / 10 lower undersanding abou offices... purchase coss of risk. cenralise services <- local offices... ^ 11 ** greaer / delegaion of auhoriy a Leeds higher cos in Leeds Conceps which are preceded by ** indicae here are oher conceps aached o hem. These oher conceps can be brough up on screen in his modular form as required, and here are oher commands ha similarly show paricular direc or indirec diagrammaic relaionships beween conceps. As can be seen from he above, he graphical form also suppresses he defaul [no] conrasing poles. The above problem is now explored using concepual graphs. The concepual graphs represenaion of he above problem is based on he same cogniive map as idenified above. This approach should ensure a common comparaive basis, ye highligh vividly any disinguishing feaures beween he wo represenaions. 67

5 3.04 Modelling he Poles in Concepual Graphs Saring wih he poles hemselves, hey appear o fall ino wo caegories. The firs caegory has user-defined conrasing poles whils he second s conrasing poles remain undefined. Concenraing on he defined conceps o risk of impaired reamen of cliens ensure uniformiy of reamen cenralise services a Leeds open local offices lower purchase coss of offices in Hull, Sheffield andharrogae higher cos in Leeds Figure 3.02: The iniial concepual graphs for he defined conrasing poles begin wih, hese may be modelled iniially by he concepual graphs in Figure In his figure he pair of poles become a concepual graph by placing each pole ino a separae concepual graph concep and ogeher surrounding hem wihin a negaive conex. These negaive conexs signify ha whaever is conained wihin hem, aken as a whole, is false. Therefore each graph provides conras by saing ha i is false ha boh poles can exis simulaneously. As elaboraed below, if one of he conceps is rue hen he oher becomes false. Take he middle graph in Figure 3.02, which refers o he poles cenralise services a Leeds.open local offices, as a represenaive insance. Les say we decide o see wha happened if cenralise services a Leeds was chosen. As a concepual graph his could be shown iniially as in Figure Figure 3.03: cenralise services a Leeds The rue graph of Figure 3.03 dominaes is maching concep inside he aforesaid middle graph in Figure Hence his inside concep can be removed, or deieraed, o yield Figure

6 Figure 3.04: open local offices The exisence of he graph: open local offices means is maching graph in: cenralise services a Leeds open local offices can be removed o give: cenralise services a Leeds Figure 3.05: cenralise services a Leeds is false when 'open local offices' is rue Figure 3.04 shows ha open local offices is false. This occurred because cenralise services a Leeds is rue. Should he decision be open local offices insead hen cenralise services a Leeds would be false accordingly. The whole picure for his scenario is shown in Figure Unlike he earlier cogniive map ha only passively records he poles, a compuer-based concepual graph processor could make hese new asserions auomaically as he appropriae new graphs are added o is base of knowledge. The imporan repercussions of hese inferences will become eviden laer. Noe ha he above rue-assers-false form does no asser one pole as rue should he oher be false. For example he poles cenralise services a Leeds or open local offices canno be assered as rue from heir conrasing pole being false. To do his would require he addiional false-assers-rue graph shown in Figure In his figure here are nesed negaive conexs. Remember ha in concepual graphs, a whole negaive conex and is conens can also be deieraed provided i maches an appropriaely dominaing negaive conex and is conens. Figure 3.06: cenralise services a Leeds open local offices 69

7 This removal can be illusraed from he graph in Figure 3.04 ( open local offices is false). This graph dominaes he maching par in he false-assers-rue graph of Figure 3.06 because i is surrounded by a lesser number of negaive conexs. Hence is maching graph can be removed from he laer figure o yield he resul shown in Figure Figure 3.07: cenralise services a Leeds This resul has lef wo negaive conexs around cenralise services a Leeds. These double negae o give he same graph as in Figure 3.03 ( cenralise services a Leeds is rue). In he presen cogniive mapping echnique he false-assers-rue aspec is insufficienly clear. The presen approach may prefer he user o assume if one pole is false hen he oher is rue, ye i is quie possible ha he decision maker may for insance do nohing or decide o open mobile offices insead. In his case he above false-assers-rue graph would be incorrec. The bipolar naure of he presen mehod canno cope wih his scenario. Even worse, i could provide a oo narrow framework which sifles originaliy of hough: The model does no lend iself o decision makers realising oher alernaives, such as mobile offices. In view of his deficiency, he false-assers-rue aspecs canno be ransposed o he concepual graph represenaion in a manner which guaranees validiy Refining he Graphs Moving on, i is possible o leave he concepual graphs in his rue-assers-false wo concep form and manipulae hem as elemenary proposiional logic saemens 3. Ackerman e al. sress ha he senences should remain as hey are because he decision maker can idenify wih wha he or she saed direcly. Wih concepual graphs he above conceps could be 3 The deails of proposiional logic and predicae logic can be found hrough any seminal ex on logic (For insance, Kowalski 1979a). Sowa (1984, Appendix A.5: Symbolic Logic, pages ) also discusses hese maers. 70

8 8(a): impaired clien reamen risk ensure uniformiy of reamen 8(b): cenral office: Leeds local offices: Hull, Sheffield and Harrogae 8(c): refined noneheless o he more powerful predicae logic level 4 hereby capuring more abou he problem, ye arguably remain human exper readable. The refinemen is demonsraed by he graphs shown in Figure 3.08, which refine he graphs in Figure 'lower purchase cos' 'higher purchase cos' cenral office office characerisic higher purchase cos 8(d): 'lower purchase cos' 'higher purchase cos' local offices offices characerisic lower purchase cos The graphs in Figure 3.08 now include relaions, referens and coreferen links as well as essenially more proper hierarchical ype labels. The lef-hand graph inside he nesed negaive conex of Figure 3.08(d) (or 8(d) for shor) may be read as The characerisic of an office Figure 3.08: Refined concepual graphs is a higher purchase cos for example. The referen Leeds conforms o he ype label cenral office and Hull, Sheffield and Harrogae conforms o local offices. Par 8(a) is merely a shorening of one of he concep s phrases. This graph could easily be refined furher, as indeed may all he graphs hroughou he enire offices example, hence 8(a) may be viewed as an example of an inermediae sep in model developmen. The greaer degrees of refinemen are demonsraed by 8(b), 8(c) and 8(d). In 8(b), Leeds is an insance of a cenral office in ha Leeds will have is own peculiariies bu shares he same characerisics as any cenral office in general. This would permi inferences o be made abou Leeds from boh wha is known abou cenral offices in general and Leeds in paricular Generalising he Model The above shows ha a knowledge-base can be buil up based on he appropriae degree of generally applicable knowledge. This also prevens 4 See foonoe 3. 71

9 unnecessary duplicaion when he same knowledge applies o more han one paricular concep. The degree can be appreciaed by developing he Leeds example in a lile more deail. I may be ha cerain hings are applicable o Leeds in is own righ, Leeds as a Yorkshire cenral office, as a norhern cenral office, or an English cenral office as well as a cenral office. The same principles apply o he local offices. Taking he cenral office case as represenaive, he ype hierarchy would hen include (where subype < superype): cenral office < office. English cenral office < cenral office. Norhern cenral office < English cenral office. Yorkshire cenral office < Norhern cenral office. The mos specialised conformiy for Leeds is Yorkshire cenral office. This means Leeds conforms o all of he above cenral offices, bu no o say Souhern cenral office (Souhern cenral office < English cenral office). Thereby any inference in respec of Souhern cenral offices would no apply o Leeds bu any for Yorkshire, Norhern, cenral office and office would. The graphs in 8(c) and 8(d) concern he purchase coss of he offices. Examining 8(c), he lef graph shows ha if a purchase cos is higher hen i canno be lower and vice versa. The righ graph shows ha if one is false he oher is rue. The coreferen link in boh cases esablishes ha hey refer o he same cos. These graphs are herefore so general in naure ha hey can be used beyond he offices example. Turning o 8(d), hese graphs imply ha a cenral office is an office which has a higher purchase cos whils local offices are offices wih a lower purchase cos. Should cenral office or local offices dominae hese graphs respecively, he appropriae inference would be made accordingly. This is demonsraed in Figure Concepual graphs hereby also raise he user s awareness hrough heir inheren srucure: As he user refined he graphs so hey become more and more based on hierarchical ype labels and specific insances wihin hose labels, he user would have o hink abou he appropriae degree of relevance. The graphs as hey currenly sand apply o any local or general office. Alernaively hey may be wrien o infer abou Yorkshire offices only, 72

10 The graph: Yorkshire cenral office: Leeds maches conceps in: cenral office in which case cenral office and local offices in he appropriae dominaed graphs would insead read Yorkshire cenral office and Yorkshire local offices respecively. office characerisic higher purchase cos giving: cenral office: Leeds office: Leeds characerisic higher purchase cos resuling in: office: Leeds characerisic higher purchase cos

11 inpu pole and encircle i wih a negaive conex, as denoed in Figure An alernaive migh be o wrie, wihou using a negaive conex, no emergen pole insead. The graphs would hen be based on he form given by Figure cenral office: Leeds local offices: Hull, Sheffield and Harrogae office: Leeds offices: Hull, Sheffield and Harrogae characerisic characerisic higher purchase cos lower purchase cos Figure 3.10: Resriced graph o accoun for lack of knowledge in exising problem Unlike heir defined counerpars, he false-assers-rue scenario can be seen o be valid for undefined conrasing poles, hence he graph form local represenaion improved service level increased running coss higher admin coss lack of undersanding abou risk use local office experience emergen pole General form: local represenaion improved service level increased running coss higher admin coss lack of undersanding abou risk use local office experience emergen pole Figure 3.11: Concepual graphs for conceps wih undefined conrasing poles in Figure 3.13 would also need o be added ino he knowledge base for each alernaive. This reveals he alernaive is superfluous because he erm emergen pole is false clearly equaes o no emergen pole is rue. Anoher quesion is hus raised asking if here is any need o include such poles in concepual graphs anyway. For insance given local represenaion was rue or false, his would merely asser local represenaion is rue or false respecively. This auology shows such conceps in fac urn ou o be meaningless. Therefore hey can be excluded from he concepual graphs represenaion. 74

12 Figure 3.12: emergen pole no emergen pole Figure 3.13: emergen pole no emergen pole 3.08 Modelling he Links in Concepual Graphs The cogniive map links may be modelled iniially as implicaions in concepual graphs as shown in Figure The naure of hese graphs are explained by Figure As can be seen from hese figures, wihou worrying abou he graphs affeced by double negaion for he momen, he leads from pole becomes a concep which is enclosed in a negaive conex. This conex also encloses anoher negaive conex ha encloses he concep of he leads o pole. The negaive link found in COPE becomes redundan because he order in which he poles are drawn are irrelevan in concepual graphs. The user could sill reain he visual order hrough arranging he shape of he graphs according as o wha, say, ha user would like o see a he op or boom par of his or her graph drawings. The concep use local office experience has been refined o use local office experience:#256 as i describes a paricular office experience idenified by he serial number #256. This number may be a reference o he relevan documenaion on his issue for example. As for he double negaed graphs, he effec in he case of he graphs describing he false local represenaion, increased running coss, and oo much decenralisaion implicaions of cenral office: Leeds is hey now appear o be like exising cogniive mapping conceps insead of is links. Hence hese graphs show here are links ha emerge o be addiional conrasing poles. Concepual graphs have yielded his fac explicily and drawn i o he user s aenion, whils i remains unnecessarily implici and hereby easily undeeced in he exising cogniive map. 75

13 local represenaion improved service level General form of implicaion (illusraed by X assers Y, no Y assers no X): local represenaion improved service level X Y cenral office: Leeds local represenaion Say X in fac is equal o no Z. This would resul in: cenral office: Leeds increased running coss Z Y increased running coss higher admin coss Similarly, say Y was equal o no W. This would give: increased running coss cenral office: Leeds higher admin coss oo much decenralisaion X oo much decenralisaion ensure uniformiy of reamen W lack of undersanding abou risk use local office experience: #256 Figure 3.15: Modified implicaion in concepual graphs lack of undersanding abou risk use local office experience: #256 Figure 3.14: Concepual graphs denoing he links in he cogniive map All he above of course highlighs anoher quesion as o wheher he presen cogniive mapping echnique should indicae ha all defaul conrasing poles are accurae enough o aach oher poles logically o i. There is he disinc possibiliy ha such links could be erroneous, wih he resul of he user being mislead by he model. For insance, picking up on he mobile office dimension discussed earlier, i seems ha local represenaion.[no] local represenaion leads o improve level of service.[no] improve level of service respecively. However i may be possible o have [no] local represenaion and improve level of service hrough use mobile offices. I would hen be false ha [no] local represenaion implies [no] improve level of service. The dubiey of his whole premise is heighened somewha when COPE apparenly conradics iself by suppressing such links in is own graphical oupu form. All his reveals a poenially serious flaw in Eden s cogniive mapping mehod. 76

14 3.09 Modelling he Oher Knowledge in he Example Problem The concep use local office experience has some background informaion relaing o i abou he source of ha informaion from some acual offices in he Souh Wes. This may bes be described by he graph in Figure This graph can be added o he knowledge base and hen called upon as necessary. If he earlier graphs in Figure 3.08(d) had no been resriced o hose in Figure 3.10 hen he graph in Figure 3.17 would be assered from he background Souh Wes offices graphs in Figure This insance underlines how useful he powerful hierarchical naure of concepual graphs can be, as brough ou earlier. Figure 3.16: use local office experience: #001 source local offices: Plymouh, Taunon, Bah and ohers Figure 3.17: office: Plymouh, Taunon, Bah and ohers characerisic lower purchase cos A his poin all he conceps and links have been discussed apar from greaer delegaion of auhoriy, follow curren managemen iniiaives and he relaionship beween lack of undersanding abou risk and he choice of office. The firs wo conceps are modelled by Figure This figure reflecs ha hese wo conceps are a saemen of fac, whereas he previous conceps depend basically on which office ype is chosen. Furhermore, adding he usual implicaion graph shown in Figure 3.19 would imply, from he above preference graph ha local offices: Hull Sheffield and Harrogae would be rue when i is really undecided. This siuaion can be avoided by making he saemen apply o local offices in general. Alhough Figure 3.20 saes here exis some local offices, i canno purpor ha hose local offices are in Hull, Sheffield and Harrogae. 77

15 Figure 3.18: curren managemen iniiaive: #92 preference auhoriy syle: delegae Figure 3.19: auhoriy syle: delegae local offices: Hull, Sheffield and Harrogae Figure 3.20: auhoriy syle: delegae preference local offices I may be argued his is merely a convenien device on he par of concepual graphs o ge round his problem. Whils his would no be denied, he inheren naure of concepual graphs would demand evenually a more exacing analysis of he problem as par of he coninuing overall refinemen of he knowledge-base. Ensuing invalid inferences for insance would draw he user ino finding ou more abou he siuaion or, if ha is no possible, o apply exper judgemen. The appropriae graphs could hen be devised. In he above insance i may be wise o deermine if delegaion really mus mean local offices. This can perhaps be provided somehow in a cenral office environmen, or by mobile offices. Despie he exising cogniive map s link, reference o he office ex does no sufficienly clarify his. Therefore his link, even in he above convenien form, canno be included in he concepual graphs knowledge base. The above convenien argumen also applies o he concep office in Figure 3.21 ha describes he lack of undersanding abou risk relaionship. In COPE his implici relaionship in he cogniive map was refined ino a connoaive link, which he figure is inended o reflec. Even hough here is an elemen of convenience in he graph, i is less ambiguous han he firs one and herefore can be included in he knowledge-base. This, of course, is subjec o appropriae user-iniiaed revisions as discussed already. Figure 3.21: lack of undersanding abou risk affeced choice office 78

16 A and B mus be rue before C is assered as rue (If C is false hen so is A and B): A B Only one of A or Bneed be rue before C is assered as rue (However if C is false hen A and Bis sill false): A B C C C The exisence of he above lack of undersanding abou risk graph would have an effec on he graphs which describe lack of undersanding abou risk.use local office experience:#256 in Figure 3.14, in ha i would cause use local office experience:#256 o be assered as rue. In view of his asserion use local office experience:#256 could appear as a rue graph o begin wih. However, his is no done for wo reasons. The firs is o show ha as new knowledge is added, his has a dynamic effec on he presen knowledge. The second is ha i shows a line of reasoning ha he

17 impaired clien reamen risk ensure uniformiy of reamen oo much decenralisaion cenral office: Leeds Figure 3.23: Inerrelaionships beween he Leeds office and clien reamen risk 3.10 Allowing Inferencing Now he concepual graphs knowledge-base can sensibly sar o infer new knowledge. For example, given cenral office: Leeds is rue hen impaired clien reamen risk is assered as false. This is shown in Figure In his figure here are coreferen links o conceps labelled as, which may bes be hough of as i insead of he full concep s name, o aid readabiliy by avoiding repeiion 5. Furhermore, unlike concepual graphs, Eden s cogniive mapping echnique does no lend iself o proving false anecedens from false consequens. For insance, if ensure uniformiy of reamen was an over-riding consideraion hen local offices: Hull, Sheffield and Harrogae would be false. This can be seen in Figure Visual Cues Like he cogniive mapping graphical display illusraed by COPE earlier, he graphs can be arranged by he user o highligh paricular pars of he knowledge-base. Such a user-iniiaed visual cue was menioned earlier in respec of he negaive links in cogniive mapping. Boh Figure 3.23 and 3.24 may be viewed as visually arranged examples. Anoher example is Figure This figure shows he direc links arising from he choice of offices. However, unlike he exising cogniive mapping echnique, i can be 5 The essenially equaes o he universal superype, bu wih an aached coreferen link ha immediaely specialises i. 80

18 seen ha he concepual graphs model shows a much richer se of inerrelaionships whils remaining user-readable. ensure uniformiy of reamen impaired clien reamen risk local offices: Hull, Sheffield and Harrogae oo much decenralisaion Figure 3.24: Inerrelaionships beween he local offices and reamen uniformiy 3.12 Merging Graphs A feaure of cogniive mapping is ha maps can be broken down ino separae clusers o focus on sensible subses of he problem. Of course concepual graphs also suppors such modular subsrucures provided, like cogniive mapping, he appropriae conceps are correcly duplicaed. Anoher cogniive mapping feaure is ha separae maps, depicing differen perspecives abou a problem siuaion, can be merged. Like clusers, concepual graphs does no hinder his process. In fac hey can improve i hrough he ype hierarchy. For example, one individual may have mapped he offices problem as already discussed. Anoher may have mapped he conras as one beween mobile offices and free elephone suppor. Assuming here are no oher conceps ha may suiably relae he wo maps, here is no apparen connecion beween hese maps unless here is a compromise on he very erminology iself. However, by a hierarchical approach, each pary may reain heir own perspecive bu be able o agree a some oher concepual level. Here, hey may concur for insance ha offices (as a superype of boh local offices and mobile offices ) would lead o face-o-face service. Of course merging would sill require graphs o be redefined, bu wihin he much wider scope ha he hierarchy allows. 81

19 local represenaion local represenaion increased running coss increased running coss oo much decenralisaion oo much decenralisaion cenral office: Leeds local offices: Hull, Sheffield and Harrogae office offices characerisic characerisic higher purchase cos lower purchase cos Figure 3.25: Direcly linked inerrelaionships surrounding he choice of office 3.13 Commens Abou Cogniive Mapping in Concepual Graphs In summary, from he offices example he concepual graphs represenaion has managed o reveal: a) Like he presen cogniive mapping mehodology, he conceps and relaions in concepual graphs can be based on a language ha he decision maker idenifies wih. Concepual graphs can also be arranged o reain he visual cues he end-user may require. b) Unlike presen cogniive maps, concepual graphs allow he furher refinemen of he problem hrough, say, he inerrelaion of generalised and specialised knowledge. Iniial concepual graph models may sar by being a lieral paradigm of cogniive maps a he exising level. Subsequenly hey may be refined by graphs which, as illusraed by he 82

20 office purchase coss, break down hese phrases along increasingly greaer expressive dimensions. c) Through is bipolar limi, which concepual graphs overcome, he curren cogniive maps could sifle creaive hough by he decision maker. d) The '[no] emergen pole', which is he defaul conrasing pole in he presen maps, urn ou o be meaningless when modelled as a concepual graph. e) Concepual graphs do no need any addiional devices o show he negaive links unlike he presen cogniive mapping echnique. Any user visualiy elemen herein need no be compromised by his link s absence. f) By always implicily linking conceps wih defaul conrasing poles curren cogniive maps obfuscae he disincion beween legiimae and poenially damaging relaionships. Concepual graphs, on he oher hand, remove his arbirary siuaion by focusing he user's mind on wha in fac are valid and invalid conrasing poles, including defaul ones. g) Even hough concepual graphs may permi convenien devices o quick-fix obsacles in he mapping exercise, hey ulimaely cause he user o improve he qualiy of he knowledge iself and refine he graphs accordingly. h) The presen cogniive maps fail o disinguish beween any and / or relaionships beween knowledge elemens. This relaionship arises when a pole has more han one link o i and here is a need o deermine wheher all he aneceden poles have o occur, or jus some of hem, for he consequen pole o occur Concluding Remarks Clearly concepual graphs can enrich cogniive mapping. Though i may successfully elici knowledge hrough is conrasing poles and links, cogniive mapping canno exrac properly he genuine impac of hese relaionships nor pu he user on enquiry o seek for furher dimensions ha may affec he problem. Moreover i can be wrong, as he references o mobile 83

21 offices have revealed for example. A concepual graphs processor could auomaically recognise and deal wih he conrasing aspecs of he cogniive mapping echnique. This would occur as a direc par of he negaive conexs upon which concepual graphs inference is based. As well as inference, he processor would also be able o check for any inconsisencies as hey are enered ino he knowledge-base. All his should free he user o declare merely wha he or she believes and hen review ha menal model, or is compuer paradigm, in he ligh of he processor's oupu. Alhough criical of he curren approach, his chaper does no seek o dismiss i. As Eden saes, he presen cogniive maps can be drawn quickly and hereby ge an immediae handle on he problem siuaion a hand. Therefore i remains a valuable iniial modelling ool. However as a more permanen building block of knowledge, is limiaions are simply oo significan o ignore. Concepual graphs supplies a similarly visual bu much more highly principled basis from which more meaningful knowledge can be evenually buil. Much has been made in his chaper abou he generaliy of concepual graphs. This is furher examined in he nex chaper. 84