Translating OWL and Semantic Web Rules into Prolog: Moving Toward Description Logic Programs

1 Translati ng OW L and Sema ntic W eb Rules int o Prolog: Mo v ing T oward De scriptio n Logic P rograms Ken Sa muel 1 , Le o Obrst 1 , Suzette S toutenbe rg 2 , Karen Fox 2 , Pau l Frank lin 2 , Adria n John so n 2 , Ken La ske y 1 , Debora h Nichols 1 , Ste v e Lo pez 2 , Jaso n Pe terso n 2 {sa muel, l obrs t, s uzette, kfo x, p f rank lin, abjohn so n, klaskey, d lnicho ls, slopez, jaso np}@mitre.org The MITRE Co rpora tion 1 7525 Co lshi re Drive , McLe an, VA 2 2102 -7508 2 1155 A cade m y Par k Lo op, Co l orado Spr i ngs, C O 80910-37 16 Submi tted 12 May 2006; revised 24 Sep 200 7; acc e pted 18 Octo ber 2007 Abstract . We are res earc hing the interac tio n betwe en the rule and the o ntolo gy la y er s of the Sema ntic W eb, by c o mparing two options: 1) usi ng OWL a nd i ts rule extension SWR L to develop an int eg rated onto logy /rul e language, and 2) layering rules on t op of an onto l ogy with Ru leML and OWL . To ward thi s end, we a re dev e loping the SWO RI ER sy stem, whic h enabl es effic ient au t o mated rea sonin g o n onto l ogies and rules, by translat ing a ll o f them into P rolo g and adding a se t o f g eneral rules t hat proper ly capture t he seman t ics of OW L . We have also enab l ed the user to make dy namic c ha ng es on the fly , a t run time. Thi s work addresses sev eral of the co ncerns expres sed in previous wo rk, such as neg at ion , c om plementary classes, disjunc tiv e head s, and car dinality , and it d iscusses altern ative appro a ches fo r dealing with inco nsi stencie s in the know ledg e base. I n additio n, fo r efficienc y , we i mp l eme nted t echni que s called extens ionaliz ation, av oiding rean aly s is, and co de minimiz ation. Keywo rds: S ema ntic W eb, lo gic prog r amming , kno wledge co m pilatio n, o ntolo g ies, rules 1. In troduction The we dding of S em a ntic Web t echnology a nd L o gic Pr og r amming h a s cr eated a new te chnical par adigm called de scription log ic programming . Recen t ly, re se ar che r s h a ve b egun focusing on the q u estion of how to utilize logi ca l rule s fr om a pa rtic ular dom a i n in order to im pr ove t he S em a n tic Web (Bechhofer et al. 2004; Hirtle et al. 2004; Horrocks et al . 2004). It is well established t hat the knowle dge developme nt language and t he knowledge runtime languag e m a y not be the sa me , s o the f o r me r should b e t ra n sformed to t he latte r fo r gre at er ef fi ciency a t run time (Cadoli & Donini 1997; D ar w iche & Mar q uis 2001). We have develo p ed SWORIER (S em a ntic Web O ntologie s a nd Rules for I ntero p e r abi li t y with Efficient R easoni ng), wh ich is a syste m t hat use s Logic P rog ra mming to r e ason a bout and answe r queries about ontolog ies and r ule s (Grosof et al. 2003; Hitz ler et al. 2005; V olz et al. 2003). OWL (We b On tol o gy Language) ontologie s ( Bechho fer et al. 2004), a long with r ule s in the S em a n tic Web R ule Language (SWRL) (Horrocks et al. 2004) or the R ul e Mar kup La n guage (Rule ML) (Hirtle et al. 2004) ar e a ll t ransl a ted into Pr olog using XS LTs (Exten s ible Style s heet Lang ua ge Transfo r m a tions). I n a ddition , we h a ve w ritt e n a se t of General Rules in Prolog in orde r to enforce t he s eman t ic s of OWL primitives. T o do this, i t w as nece ssar y to addr e ss a num b er of i ssu e s r el at ed t o negation, t he open wo r ld a ssum ption, c ompleme ntar y a nd disjoint cl asses, disjunctive con clusions, enume r ated classes, eq ui v alent individuals, e r ror me ss age s, e xist en tial quan tification , car d inality constraints, d uplicate facts, cy clical hie r ar ch i e s , and anonym ous c lasse s. R ecen t work has suggest ed that some of these pr o b lem s a re unsolvable (Volz et al. 2003), but w e b elieve we h a ve found s o lution s f or the m. 2 We h ave imposed str ong efficiency req u irem ents, dem a nding t hat que r ie s a re answe r e d in a matte r of s econds. And, unlike pr evious wo rk, SWORIER can assimil at e dynamic changes that ar e provided at r un time, in cluding a dding new facts, remov ing facts, a n d s wapping r ule s ets, which als o m ust be done in s econd s. T o achieve this level o f e fficiency, we establi s hed t hree te chniques: e xt en si on alization, a vo iding r e analysis, a n d code min imization. This paper is or gani zed as follow s : First, Sec t ion 2 pr ovide s t he r e ader with bac kgro u nd info r m ation. Then, Section 3 descri b e s SWORIER's sy st em de s ign. Sec t ion 4 add resses th e ch allenges f ound in pr evio us r esearch. Sec t ion 5 adds a capabili ty t o handle dyna mi c changes. Sec t ion 6 a n alyz e s and a ddre ss e s the e fficien cy of t he s ystem , and then S ection 7 di scuss e s rel a t ed work. Finally, Sec t ion 8 summ a riz e s the paper, offe rs concl usions, a n d discusses future wo rk. 2. Back gro und We are i n vestigating the inte ra ction between rules and ontologies i n t he Sem a ntic Web to de t e r mine how a sta n dard l anguage should be st e x press them ( Stoutenburg e t al. 2006). In particul a r, to determ ine whe t her an ontology and the c orresponding r ules should be int eg r at ed or laye r ed , we s pecified , tr ansl ated, and exe cuted information in: 1) S WRL, which i n t eg ra te s OWL with rules (Horr o ck s et al. 2004), and 2 ) RuleML layered on top of OWL. T he ontologie s a nd instance s we r e developed in t he Cerebra OWL on t ology developmen t environme nt, 1 t he S WRL and Rule ML rules were cr eated in a te xt edi t o r, and AMZI! (2006) P rolog w a s used as the infe r en ce engine . W e tr anslated t he con structs fo r both the int eg r at e d and laye r ed a pproache s into Pr o log code, g auging e ac h approach in t e r m s o f e ff e cti vene ss, e fficien cy, di fficulty, restrictivene ss, transl ata bil ity, and sui tability fo r de pl oyme nt in an ope ra tion al s e tting. Figu re 1. A Mil itary T ask 1 http://cereb ra.com/inde x.h tml 3 Our initi al e xper ime nts wer e s e t in a mili tar y comm a nd a nd con t rol dom a in wi t h a supply convoy moving t hrough a n unsecured area. Figure 1 pr e s en t s an exam p le situat ion , where a convoy is moving north al ong t he pr im a r y route, appr oach ing t he location whe r e intelligence has repo r t ed a n enemy sni per is sta tioned . New information can becom e available at a ny time , suc h a s the discovery of a the a t e r o bject or the beginning of a sand st or m . The s y st em h as rules that trigge r ale r ts an d r ecomm end a t ions to r e p o rt to the c on voy comm a nde r. For exam p le, in the s ituation shown in Figur e 1, a n enem y u nit is within the c onv oy's region of inte r est (the c ircle surr ound ing the c onvoy ), so the s ystem m i gh t t ell the convoy c omm a nde r, "ALERT: In t ellige nce r e port o f enem y sniper in the vicini t y." and "RECOMMENDA T ION: T ake alt e rnate r oute ." Most know ledge representation language s a nd knowledge -based syst em s utilize a restricte d ve rsi on of First Order Logic (FOL). FOL, howeve r , is s emi- decidable . It is dec idable in that if a t heo r em is logically en tailed by a FOL theo r y, a pr o of will even tual ly b e fo und, but it is unde cidable in t hat if a t heo r em is not logically entailed, a pr oo f of t hat m a y neve r b e f ound. But decid a bility he r e does not mea n t ra ctabil ity , a nd in gene ra l even inferenc e i n t he simple r propo sitional ca lcul us is NP -com p lete (Ca d oli et al. 1999), i.e . , usua ll y u nable t o b e pr oce ss ed in le ss than e xp onenti al time. Figu re 2. System Des ign To m ake inference tr acta ble , vario us appr o ache s i n t he field of know ledge compilation , which involve s c onve rting a knowledge bas e into a more concise or tr actable r e presen tati on, have been devised (Cadoli & Donini 1997; Darw iche & Mar q uis 2001). On e approach is to syntacti cally restric t the know ledge r e presen tat ion l a nguage , sacr if icing e xpressivene ss fo r tractabili t y and efficiency (de Bruijn et al. 2004). Logi c pr ogramm ing (LP), de scription logi c (DL), a nd de scr iption logic pr ogra mm i ng (an eme r ging f ield t hat wed s DL a nd LP ) t ake thi s approach (Ait-Kaci 1991; Grosof et al. 2003; Hi tzle r et al . 200 5; V a n R oy 1990; V olz et al. 2003). F o r e xa m pl e , OWL is a DL that de fines a tra ctable subs e t of F irst-Or d e r Logic (B echhofe r et al. 20 04; Daco nta et al. 2003) . A n a lternative i s to employ t heory a pproxim a tion (Kaut z & 4 Selm a n 1994; Kautz & S e lm a n 1991) , i n which the querie s th a t are logi cally en ta iled by a knowledge base (a “t heo ry”) can b e c orre ctly a n s we r ed , while , for the rest o f t he quer ie s, t he respon s e i s “u nknow n”. Some researche rs preproce ss the knowledge in v ar io us w a ys t o rel ax ei t he r the c om p letene ss o r the s oundne ss r eq u ir eme nts, pe r haps by gene rat ing c e rta in defaul t concl us ions (Cadoli & Don ini 1997). Anothe r p o ssible optimiz ation is to e xt en s ionalize t he rul e base, as di scussed in Se ction 6.1. 3. System Desig n Fig ur e 2 s hows t he s yste m design of S WORIER. A de velope r cr e ates ontologies, knowledge bas e s, and / o r rules in the for m a li s m(s) of OWL, Rule ML, and/ o r SWRL. Ex ample s of OWL, Rule ML, a nd S WRL are in Ta ble 1a , 1b, a nd . 1c, respec ti vely . T hi s i nfo r m ation is transl ated into Pr o log code using XS LTs, resul t ing i n the code s hown in T able 2a, 2b, and 2c. (We include wo rds like "is" a nd " of" in our pr e dic ate na me s to avoid am b igui t y. Otherwi s e , there is the danger of misin t e r pr e t ing t he r ole s of the a rguments. For exam p le, member(X, Y ) co ul d be interpreted a s "X is a mem b er of Y " or "X has a me mbe r, Y", while isme mberof( X, Y) is mo r e clear. ) Final ly, a s e t of General Rules (defined in S e ction 3. 2) is app ended t o t he XSLT output to fo r m a com p le t e Pr olog prog ra m , which can b e que ri ed by the user . Tabl e 1. Exam ples o f OWL , Rul eML, and S WRL a. b. redFo r ceT h eat erOb ject < /op r> X redFo r ceT h eat erOb ject < /op r> X c. < rule ml:v ar>T < rule ml:v ar>G < rule ml:v ar>G < rule ml:v ar>S < rule ml:v ar>T < rule ml:v ar>S 5 3.1. Translating F acts SWORIER use s a syntax diffe r en t fr om t h at t y p ic ally found in previous work . F o r e xa m p le, Volz et al. (2003) would pr od uce the tra nsl ation of T a ble 2 d, in st e a d of t he tra nsl a tion in T able 2a. But we note that the s yntax used by Volz et al. (2003) ca nno t r epre s en t "eve r y class that smith is a me mbe r o f " with X (smith) , because m os t P rolog im p lem entations disallow predi ca t e variables. I n c on tra st, by m aking the class n a me s and pro perty na me s b e ar gumen ts instead of pr edi cate s, S WORIER has the f lexibili ty to gene r alize on t hem with, for e xa m ple, ismemberof(s mith, X) . Tabl e 2. Tran sl ati o n s a. ismemb erof(s mith, sniper) . haspro pertyw ith(sm ith, ha sComba tInten t, fri endlyIn tent). b. ismemb erof(X , redF orceThe aterOb ject) :- isMem berOf( X, red ForceTh eaterO bject) . c. ismemb erof(s mith, sniper) . haspro pertyw ith(T, hasSpe ed, S) :- hasPr operty With(T , isDes cribed By, G) , hasPr operty With(G , hasSp eedObs ervati on, S) . d. sniper (smith ). hasCom batInt ent(sm ith, fr iendly Intent ). 3.2. Gene r al Rule s The Gene ra l R ules ar e m ea n t t o c aptur e the s em a n t ics o f the pri mi t ives in OWL. For e xa m p le, t he rule s in T able 3a enforce t he tr ansitivi ty of subclass. No t e th a t the r e a re t wo dif fer en t predi cat e s : iss ubclassof and isSubClassOf . One predicat e wo uld b e insuffi cient, bec aus e Table 3b has lef t r e cursion, r e sulting in an infini te loo p. Tabl e 3. Th e Tran s itive Clos u re o f S ub class a. isSubC lassOf (C, D) :- iss ubclas sof(C, D). isSubC lassOf (C, E) :- iss ubclas sof(C, D), i sSubCla ssOf(D , E). b. isSubC lassOf (C, E) :- isS ubClas sOf(C, D), i sSubCla ssOf(D , E). Wi t h two differen t subclass pr e dicat e s, some q u estion s m ust be a nswe r ed . Should t he use r sub mi t queries with iss ubcla ssof or isSubC lassOf ? Al so, which for m s hould th e input from t he XSLTs be? If the input us ed is SubClas sOf , t h en neither of t he r ules in T able 3a wo u ld eve r s ucceed , thus the in put m ust use i ssubclassof . O n the othe r h a nd, querie s should us e is SubClassOf be cause the iss ubclassof se t of facts is inc om p lete none of the subclass relation s hips t hat ar e derived b y tra nsi ti v ity ar e ca ptured b y issubclassof . Note that the is subclassof set of facts is a subse t of t he is SubCl assOf set of facts, be caus e of the first r ule in Ta ble 3a , w hich is called the conversion rule for subcl a ss. For consi st en cy, we creat ed two cas e s of each predicat e , a ll -lowe r cas e a nd ca mel cas e . 2 Also, e ac h pr edi cat e has a co nve rsion r ule . T he XSLT f acts alw a y s use t he al l-lowe r case f orm s of predi ca t e s , while t he us er que ries a re a lway s in ca melcas e . (Howeve r , the develo per decides how to spell the na me s of c on stants, such as hasSpee d in T a ble 2c.) And any rules, othe r tha n rec ursi ve rul e s and c onve rsion rule s, follow the convention: 2 A ny predicates t ha t ar e n ot used fo r input or outpu t ar e written in an unde r sco re case, suc h a s is_sub _class _of_bu t_not_e qual_t o . Also , for some pr edicates, th e r e ar e two sources of recursio n, r equiri n g thr ee case s of t he predicate. A n examp le of th is is the membe r r elation, f or w h ic h th e three c ases are ismem berof , is_membe r_of , a n d isMe mberOf . 6 All predicates in the body of the rule are camelcase, and the predicate in its head is all-low ercase . A s a n example , s ee t he s econd r ule in T able 2c. Using ca mel cas e pr edi cates in the rule's body guarantee s t hat the r ule is tr igge r ed b y eve r y thing t hat can b e de r ived f o r that pr edic ate in eithe r case . And usi n g t he a ll-lowe rcas e pr edi cat e f o r t he rule's head insures that any facts gene r at ed b y the r ule will hold f o r both case s of the predicat e . 3.3. Transl ating Rul e s Some of t he in puts pr ovide d t o SWORIER are RuleML or S WRL rule s that we r e cr eated by the develo p e r . It is not difficul t t o tra nsl a te these r ule s into Pr o log, b e ca use t hey ar e w ritten in Ho rn Clause f o r m . H oweve r , we cannot con tr ol w hic h rules a re pr ovide d no r h ow t hey ar e w ritt en . Pr oblem s ca n eme r ge , suc h as the infini t e loop in T able 2b, whi ch was gene r at ed b y t he RuleML r ule in T able 1b. I n a ddi t ion, the o r der in which r ules a re li st ed and the order of t he te r m s in the r ules' bodie s can have significant effe cts , m uc h li ke orde r of join eval uati o n in database language s such a s SQL. Another conce r n is that the input c ould incl u de r ules t hat prod uce duplicate c opie s of a fa ct. (Se e S e ction 4.9.) And the rules migh t b e inefficien t. The r e a re ways t o c orrec t o r a t le ast mitig at e s ome of these pr oblem s. F or exa m p le, w e co ul d appl y tr ansfo r m a tions as for logic querie s in t he form of rewrite rules such a s “ magic s e ts ” optim ization (Ca doli et al. 1999; Sippu & Soi s alon-Soininen 1996) . B ut c urr e ntly, we m us t im p ose st rong r e quiremen ts on t he deve lope r, who m a y need t o b e very f a mili a r with Pr olog prog ra mm i ng t echniq ues, the logical cons eq u ence s o f t he facts in t he ont o logies, and the Gene ra l Rules. 4. Chal l en ges We ar e following t he gro undbreaking work of Volz et al. (2003), who we r e a mon g t h e fi rst rese ar che rs to i nve stigat e OWL-t o -Prolog tr ansl ation. T hey discussed a n u m b e r of pr oblems that the y encounte red in t he c ours e of their work . N ow we a re pr o p o sing s ol ut ions for seve r al of the s e problem s, some of which ar e curr e n tly implemented in SWORIER. 4.1. Neg ati o n Neg a tion in Prolog is not the sa me as neg ation in OWL, Rule ML, and SWRL. Prolog has finite-failure negation , whi c h me a n s t hat not(T) is t rue if it is no t p ossible to prove t hat T is true. Alte rnatively, with the logi cal negation of OWL, RuleML, and SWRL, no t(T) is true if it can b e proven t hat T is false . (I n both cas e s, no t(T) is false if T ca n be proven tr ue .) I n order to close t his gap, we h ave cr e ated a Pr olog pr edi cat e called lo gicNot , and w e a re develo ping r ules t o capture t he s em a ntics of logical neg ati on . T he l ogicNot pr e dicate ta kes one a rgumen t , which must be a term : logicNot( ) . Three exa m ples ar e pr e s ented in T able 4. Tabl e 4. logi cNot logicN ot(isM emberO f(jones , snip er)). logicN ot(iss ubclas sof(the aterOb ject, convoy )). logicN ot(log icNot( isclass (theat erObje ct))). 7 4.2. The Ope n World A ss umption In Prol og, the closed world assumption holds, which me a ns t hat a nything t h at ca nno t b e proven true m ust b e fals e . Al t e r native ly, OWL has an open w orld ass umption , me a ning that a te r m is fa lse only if it can b e pr oven fals e . S o, in Pr olog, a term can only b e true or false, whil e OWL also allow s for the p ossi b ility t hat its truth value ca nnot be determined from t he available info r m ation. Thi s distinc ti on is addr e ss e d wi t h the l ogicNot predi cat e, which w as presen t ed in Sec t ion 4.1. If the us er wants to a sk a true / false question, Q, then it is necessary t o s ubmi t tw o que ries t o S WORIER: Q and lo gicNot(Q) . Table 5 s how s how the s y st em' s r e spons e s to t he s e que ries should be inte rpr e t ed . Tabl e 5. A Tru e/Fal se Q u ery ?- Q. ?- logic Not(Q) . Is Q true ? yes no yes no yes no no no unknow n yes yes err or 4.3. Comple men tar y and Disjoint Classes Volz e t al. (2003) claime d t hat "OWL f e atur e s t he c o mplemen tOf pr im itive , whi c h canno t b e i mpleme nt ed in H orn L ogic s due t o the fact, that th e re m ay b e no negation in th e he a d..." With t he introd u ction o f t he log icNot pre dicate, this is no longe r a probl em. We ca n handle the c ompleme ntar y cl asses as well a s the disjoint classe s with the rules in Table 6. Tabl e 6. Com plem entary and Disj o int Cla sses disjoi ntClas ses(C, D) :- comple mentar yClass es(C, D ). logicN ot(isM emberO f(I, C) ) :- disjo intCla sses(C , D), i s_memb er_of( I, D). isMemb erOf(I , C) : - compl ementa ryClas ses(C, D), lo gicNot (is_me mber_of (I, D) ). 4.4. Multiple Terms in the Head One no t able lim itat ion of H orn rules is t h at t he he ad ( concl us ion) of a r ule cannot have mo r e than one t e r m . T hi s m ea n s, i f t he c oncl usion of a r ule i s t he c onjunc tion of t er m s, i t i s nece ssar y to cr eate m u ltiple rules. For e xa m p le, the logic al sta teme nt i n T able 7a r eq u ires t wo rule s in Pr o log, as shown in Ta ble 7b. But for the logical rul e i n Ta ble 7c, "... no Hor n cl aus e can be sta ted, since di s ju n ction in the head wo uld occ ur. .." (Volz e t al, 2003). We propo s e t o add r e ss this pr oble m b y cr eating a new Pr o log pr edic at e that can be put in the head. S o Ta ble 7c can then b e tr ansl ated into Table 7 d b y using this new or pr e dic at e, whi ch takes two argum ents, each o f whi ch must be a ter m . Of co urs e , we must supplemen t G ene ra l Rul es in orde r to prope r ly establish t he corr ect sem a ntics of disj unction. Some e xa m pl es of t h ose rul e s ar e shown in Ta ble 7 e. No t e that the last rule requir e s the lo gicNot pre dicat e . Un fortunately, t he hea d of t he last r ule in Ta ble 7 e is a variable , which is not a llowe d in Pr o log . Howeve r , a lth ough it m ay not b e p ossible t o solve this problem in gene r al, because w e ar e lim iting o ur a naly s is to OWL, the r e ar e a fi ni t e number of pr edi cates wi t h wh ich that variable can be instantiated , and t his s e t of pr edicate s doe s not req u ire a ny knowledge of the par ticul a r ontologie s or rule s that are pr ovide d b y the develope r . So we can cr eate one r ule for e ac h predi ca t e , a nd some e xa m pl e s ar e pr e sen t ed in Ta ble 7f . 8 Tabl e 7. Con j uncti on and Disjun ct ion in t h e H ead a. IF I is in C, THEN I is an indiv idual , AND C is a class. b. isindi vidual (I) :- isMemb erOf(I , C). isclas s(C) : - isMe mberOf( I, C). c. IF C and D are co mpleme n tary classe s, AND I i s an indiv idual, TH EN I is in C, OR I is in D . d. or(ism embero f(I, C ), isme mberof (I, D) ):- compl ementa ryClas ses(C, D), is Indivi dual(I ). e. or(P, Q) :- P. or(P, Q) :- or(Q, P). or(or( P, Q), R) :- or(P, or(Q, R)). Q :- o r(P, Q ), log icNot(P ). f . isMemb erOf(I , C) : - or(P, isMem berOf( I, C)) , logic Not(P) . isSubC lassOf (I, C) :- or( P, isS ubClas sOf(I, C)), l ogicNo t(P). logicN ot(Q) :- or( P, logi cNot(T )), lo gicNot (Q). or(Q, R) :- or(P, or(Q, R )), lo gicNot (P). 4.5.En u me ra ted Classe s "The owl :oneO f prim itive can be partially supported." ( Volz e t al, 2003) Thi s primi t ive, which corresponds to our P rol og pr e dic at e, isset , defines a class, C, exte nsionally b y provid ing a set o f all and only the individuals in the class, a 0 , ..., a n . For e xa mple , Ta ble 8a decl a res that there ar e e xactly three me mbers of the class c ombat Intent : friendlyInte nt , hostileInt ent , and u nkno w nIntent . Tabl e 8. Enum er ated Cla ss a. isset( combat Intent , [frie ndlyIn tent, hostil eIntent , unkn ownInt ent]). b. isMemb erOf(a i , C). for a ll i c. or(=(I , frie ndlyIn tent), or( =(I, h ostile Intent) , =(I, unkno wnInte nt))) : - isMe mberOf (I, com batInt ent). Volz et al. (2003) observed t hat Ho r n L ogic r ules could b e develo p ed th at would draw the conclusions in T a ble 8b. But the y als o sa y that, "to support the othe r d ir e ct ion ... whi ch s tates that eve r y i n sta n ce o f C is one of t he list ed a i . .. r e quir e s a disjunction in t he consequent of th e rule , whi ch ca n not b e provided b y .. . Ho rn Clauses." (Vol z et al. 2003) Howeve r, wi th t he o r predi ca t e , i n troduced in S ection 4.4, this should no longer be a pr oble m . T able 8c pr e s en ts th e rule that capt u res the s em a n tics of the e xa m p le in Ta ble 8a. 4.6.Err or Messag e s It is desirable for S WORIER t o t est the data fo r consi st en cy. For this purpose, we foll ow Volz et al. (2003) by impleme nting rul e s t o ca tch inconsi st encie s, suc h as tho s e in T able 9. (In orde r to c he ck f or errors, the develo per m ust submi t the query: er ror(X).) In e ac h of the s e e xa m p les, the inconsi st ency i s a dd ressed by sending a n e r ror me ssa ge t o t he develope r. H oweve r, the r e ar e ot he r w ays to handle most inconsistencies. Examples w ill b e pr esen t ed i n S e cti on s 4.7 and 4.8. Tabl e 9. Error Me ssage s error( ['A te rm can not be both t rue an d fals e.', P] ) :- l ogicNo t(P), P . error( ['The empty class c annot contai n anyt hing.', I]) : - isM emberOf (I, no thing) . 4.7. Existen tial Quan t ific ation 9 Pr o log impli citly assume s t hat a ll variable s in any r ule ar e u nive rsa lly q uantifi ed . Howeve r, OWL c an sp ecify existenti a lly quantified va riable s . F or e xa m ple , t he OWL code i n Table 10a s tates that eve ry t heater obje ct is de scr ibed by a t least one observation a rt if act. T here ar e three w a ys to enfo rc e this r e str ic t ion . The simplest is to r epo rt a n error me ssa ge if i t is viol a t ed , a s in Section 4. 6. Volz et al . (2003) us es t he techniq u e of s kolem i zation. And t he t hird approach is to add new facts to the knowledge ba se , whi ch is disc uss ed in S e ction 4.8. Skolem i zation s olve s t he probl em o f a vi olated exist enti al restriction b y le tting a sp ecifi c te r m r epre s ent t he missing individual. This t erm m ust be una m b iguous, so its a rgumen t variables ar e se lected t o m a ke it distin ct. Fo r e xa m p le, give n the r e s triction in Table 10a , if ther e is a the ater obj e ct, I, t h at is no t de scribed b y a ny obse rvation artifacts, then the t er m unnamedIndiv idual(I, describ edBy, observationArtifa ct) i s used to repre sent the r equi r ed obs e r vation ar tifact. In gene ra l, the two r ule s i n Ta ble 10b a re applied in orde r to insure th at thi s t e r m sa tisfie s the e xistential restr ic tion . Tabl e 10. An Exi ste ntial Constraint a. b. haspro pertyw ith(I, P, unn amedIn dividu al(I, P, C2)) :- hasso mevalu esofpr opertyf rom(C1 , P, C 2), is MemberO f(I, C 1). ismemb erof(u nnamed Individ ual(I, P, C2 ), C2) :- hasso mevalu esofpr opertyf rom(C1 , P, C 2), is MemberO f(I, C 1). 4.8. Car d in a lity In OWL, the r e are th r ee cardinality pri mi ti ve s: ( 1) minCardi nality , ( 2) max- Cardinality , and ( 3) cardinality . Each of t hese primitive s ta ke s t hree ar gume nts: a cl ass, a prope r ty, a nd a num b er. The pr imi t i ve s ' me a nings a re t hat e a ch individual in the given cl ass partici pates i n the gi ven property wit h (1) at least, ( 2) a t m ost, o r (3) e xa ctly the given num b er of unique individ ua ls. Tabl e 11. Ca rdinalit y R ul es a. < owl: onPr operty rdf : res ourc e="# desc ribe dBy " /> < owl: card inalit y rd f :da taty pe=" &xsd ;non Neg ativ eInt eger "> 1 < /owl :car dinali t y> b. equi vale ntin dividu a ls( I 1, I2) :- i sMem berO f(I , th eate robj ect) , h asPr oper tyW ith( I, d escr ibed by, I1), h asPr oper tyW ith( I, d escr ibed by, I2). c. enfo rceC onst raints :- i sMe mber Of(I 1, t heat ero bjec t), n ot( hasP rope rtyW ith( I1, des crib edby , I2 )), g ens ym(n ewIn divi dual , I 3), a sse rt(h asPr oper tyWi th( I1, desc ribe dby, I3) ). 10 Volz et al. (2003) c laim s t hat, "the u nr e s tricted us e of cardinality con str ain ts cannot b e supported e fficien t ly in L ogic P rog ra mming envi ronments... " It is true that, in theor y , the r e a re an unlim ited num ber of cardin alit y c onstraints that the develo p er coul d imp ose . Howeve r, we can e xt end SWORIER's syst em design (from F igure 2) by introduci ng a new modul e , a s shown i n Fig ur e 3. Any cardinality constra in ts found in t he ontologie s a re s en t t o this Cardinal ity Rules mod u le, w hich produces one or two Pr olog rules fo r each constra in t. Since ther e ar e a fi ni t e num b er of car din a lity constra in t s in any ontologie s, it i s po ss ible to de velop all a nd only th e nece ssar y cardi nality rule s, a n d th us, the pr o blem i s tr actable . An e xa mple cardin ality c onstraint is e xpr e ss ed by the OWL code i n Ta ble 11a , whi ch says th a t eve r y theate r object is de scrib ed by e xa ctly one individ ua l. Fo r this con stra in t , i t is nece ssar y to gene ra te t wo r ules, one t e sting t o make sur e that there is no more t han on e individ ual, and t he othe r checking that t he r e is at l e a st one i n dividual t h at satisfie s the r estriction . We have t wo option s for the first rule: 1) If two diffe r en t individual s a re found that both desc rib e the sa me theat e r object, we c o u ld r e port an e rr or to the develop e r , as in S ec t ion 4.6, or 2) w e co ul d enforce t he constra in t wi t h t he rule in which sa ys that if any t he at e r obj e ct is described by two individual s, the n those t wo individuals m ust b e e quivalen t. F or the s e cond rul e , t here ar e three options: 1 ) If a t he a t e r object e xists t h at is no t described by a ny indivi d uals, we c ould r eport an error to the develo per, a s in S ection 4.6, 2) the c on s train t coul d b e en forced b y skol em ization , which was e xp lained i n S e cti o n 4.7, or 3) the pr oblem could b e fi x ed b y a dding new facts to t he knowledge bas e . The last o pt ion i s demonstra te d in T able 11c, whe r e t he P rolog pr edic ate, gensym , sets I3 t o a new u n ique c onstant, a nd the a ssert predi ca t e a dds t he r equi r ed fa ct t o the knowledge ba se. (T he que ry, enforceConstr aints , w ould b e run o f fline in orde r to cre ate all of the r equi r ed facts. ) Figu re 3. Th e Cardinal ity R u les Modul e 11 4.9.Duplic ate Facts It is desi ra ble t o pr even t S WORIER from generating the sa me fa ct mo r e t h a n once . T o dem onstr ate the r ation a l e , c on sider t he pr ogram in t he Table 12a. The q u e r y, fac t(X, c, 1) wo u ld cause the system to return two co p ie s of fact(a, c, 1) ; o ne b e ca use of rule 1, and th e othe r through the interaction b e t ween rules 2 and 3. Al though i t is no t difficult to r em ov e repe titive facts in a po st -processing procedure , a signific ant co st in efficien cy can st ill r esul t. Con s ider, fo r example , t he que r y fact 3(a, c, 3) . To det e r mi ne t he a nswer, the s y st em tests the f irst ter m in t he b ody of li ne 3, fac t(a, c, 1) , and it succeeds t wice . T hen t he s yste m runs two t ests on the s econd t erm, f act (a, c, 1) , each t i me f inding two r e sults. T hus, t h e thi r d te r m , s low(c) , must be tested four time s, unnece ssar il y q uadrupling t he time sp en t proce ssing t hat term. And f or t he query fac t3(a, c, 5) , the slo w(c) te s t is r un 16 t imes. So it s hould b e c lear that, w hen d up lic ate fa cts are gene r ated, they can p otenti all y s low down th e prog ra m signific antl y . To block duplicate facts, we can add the t e r m , not(Y=c) to rule 2, a s shown in T able 12b. T hi s pr even ts fa ct(a, c, 1) f rom b eing ge ne ra ted via rule 2. But gi ven t he q u e r y fact(a, Y, 2 ) , the system fails to r e t urn fa ct(a, b, 2 ) , whi ch should be proven b y rule s 2 and 3. This is because , in orde r to t e s t not(Y=c ) , Prolog tr ie s t o prove Y= c . But this is e asy, s ince Y is a n un b o u n d var iable , so it can be s et to c . T h is causes Y=c to succee d , and s o not(Y=c) fail s, a nd the r ule is incorre ctl y blocked. By c hang ing rule 2 as shown in T able 12c, we c a n in sur e th a t Y is bo u nd before not(Y=c) is teste d. Now t he pr og ra m works correctly, and t he dupli cat e s ar e blocked . But unfo rtunately, the s y st em must inve st ig a t e the fact(X, Y, N-1) te rm , even i f t he bl ock, not(Y=c) , i s doomed t o fai l. In a dd ition, rul e 2 is no longe r t ail recursive , s o t he Prolo g com p ile r cannot utilize a s igni f ican t e fficiency improveme nt. Tabl e 12. Du p licate Fa cts a. 1. fact (a, c, N ) :- N>= 0. 2. fact (X, Y, N ) :- N>0 , fa ct(X , Y, N-1). 3. fact 3(X, Y, N) : - fa ct(a , Y, N-2 ), fac t (X, c, N-2 ) , s low( Y). b. 1. fact (a, c, N ) :- N>= 0. 2. fact (X, Y, N ) :- not (Y=c ), f act( X, Y, N -1) . 3. fact (X, b, 1 ). c. 1. fact (a, c, N ) :- N>= 0. 2. fact (X, Y, N ) :- N>0 , fa ct(X , Y, N-1), not (Y=c). d. 1. fact (a, c, N ) :- N>= 0. 2. fact (X, Y, N ) :- isL ette r(Y) , no t(Y=c) , N> 0, fact ( X, Y, N -1). We believe we ca n m a ke t hese r ule s b oth correct and e fficien t. T he key is that we r equi r e all c on sta n ts t o b e de clar ed wi t h predicat e s like i sclass , isindividual , i s property , and is datatype . The n , by specifying the r equi r ed type of Y a t th e b eginning of the rule 's body, as in rule 2 in Ta ble 12 d, t his has the desi r ed e ff e ct of binding Y , enabling t he b locke r not(Y=c) to be te st ed . 4.10.Cyclic Hierar ch i e s Cyclic cl ass hie ra rchie s and cyclic property hie r ar ch ies can be problem a t ic . Suppose t he given OWL ontology incl udes the facts shown in Ta ble 13a. T hen the computation of the transi tive c losure of subclass, using t he rul e s f rom T able 13b, pr od u c e s an infini t e number o f respon s es t o t he q u e ry, is SubClassOf(X , Y) , as the s ystem loops ar ound and a round th e cycle . Even though we m a y claim that a c y clic hie r arch y is e rr oneo us, we c annot prevent t h e develo p er from creating one . S o S WORIER sho u ld be able to h andle it. 12 We pr opo s e changing the subclass transi tive cl o sure rule s ( Ta ble 3a) in to t he r ule s in Table 13b. T he i de a is t o st op t he c ycle when it r e ac hes the beginning again, which occurs when the t wo pa ra me t e rs of isS ubClassOf are eq ual. For thi s purpose, we cr eate a new pr edicate is_sub_class_of_b ut_not_equal _to that incl u des all of t he subc lass rel ations, exce pt fo r the r efle x ive ones. (The first r ule catches t hem .) N o t e that we us e the t echniq u e discuss ed i n Sec t ion 4.9, by including isclass pre dic at es to i nsure that the variable s a re bound b efore running a ny n ot tests on them. Tabl e 13. Cycl ic Hierarchies a. issubc lassof (armed Force, coalit ion). issubc lassof (coali tion, p olitic alGrou p). issubc lassof (polit icalGro up, ar medFor ce). b. isSubC lassOf (C, C) . isSubC lassOf (C, D) :- is_ sub_cl ass_of _but_n ot_equa l_to(C , D). is_sub _class _of_bu t_not_e qual_t o(C, D ) :- i ssubcla ssof(C , D). is_sub _class _of_bu t_not_e qual_t o(C, E ) :- iscla ss(C), iscla ss(E), not(C= E), issub classo f(C, D ), is_s ub_cla ss_of_ but_no t_equal _to(D, E). 4.11. Anonym ous Classes OWL can define classes call ed a nonymo us c lasse s without actua ll y na min g t hem . T a ble 14a has a n example of an anonymous class, a nd Table 14b has our sugge st ion of how t o tra nsl ate it. An anonym ous class, unnamedCl ass(hasComb a tIntent, frien dly-Intent) , is gene r ated like anonymo us individ uals that were presented in S ec tion 4.7. Tabl e 14. An o nym ous Classes and Prop erties a. b. hasa llva lues ofprop e rty f rom ( un name dCla ss(has C omb a tIn tent , fr iend lyIn ten t), ha sCom batI ntent, fr iend lyIn tent). 5. Dynam ic C han g es Ano t he r use ful ca pability is to c h ange the knowledge base a t r un time . F o r e xa m ple , in our convoy ta sk, in t elligence r eports can come in at any ti me d ur ing a scenario, and we w a n t SWORIER to be able t o incorporate the new i n for m a tion in t o t he knowledge ba s e . T h is m ust b e done within a few second s. So, we have en ab led S WORIER to accom mod a t e dynamic changes of facts, adding o r removing facts at run time . (We h ave not yet tri ed dyna m i cally c hanging c lasse s, prope r ties, o r r ule s. ) Unfortunately, dyna mi c ass e rt ion s significantly decre a s e efficien c y, because the P rolog compile r can no longe r b e used. It is no t possible to a ssert or retract any facts w ith predi ca t e s that ar e compiled . T h is issue i s a d dressed in Section 6.3. SWORIER is also capa ble of dynamic ally c hanging rules, but only in a r e str ic t ed way. We r eq uire t hat a ll o f t he de s ir ed r ule s e ts ar e a v ailable in advance. T h is can still b e q uite us e ful. For e xa m pl e , under l ow vi s ibility conditions, differen t rule s might be desir ed from t he rules us e d with high vi sibility. Both rule sets can be develo p ed in a dvan ce, a nd the n SWORIER can gene r ate a separa te prog ra m f or each case. T he s e r ules migh t be c on s ide r ed dif fer en t p olicie s or rule s invoked b y di ff e rent contexts. A t run time , when vi sibility i s high , the us er que ries a r e submi tt ed to t he first prog ra m . But whe never vi s ibility is lost, such as a t the ons e t of a sa n dstor m , the two programs ar e swapped , a n d the us e r queries are sen t to the second pr og r am . 13 Fig ur e 4 shows t he s y st em aft er it is extende d to a ccomm odate dynamic changes. Not e that whe never facts are added or r em oved from t he knowledge ba se , bot h pr og ra m s m ust be modi f ied appropriately . Figu re 4. Dyn a mic Chan ges o f Facts and R ul es 6. Eff iciency Ini tially, the SWORIER system w as too slow. A s s hown in Ta ble 15a , it t o ok 1.9 ho urs to inco rporat e two dyn a mi c change s i n to the knowledge base: A report of the c onvoy' s curren t posi t ion a nd sp eed and inform ati on a bout a m otorized infa n try unit a pp roaching i t from a he a d. A fter t hose changes we r e m a de, 1.5 hours we r e needed to r espond t o t he f ollowing que ries: What ar e the po s ition s and sp eed s o f al l known units, and what ar e the curren t alerts a nd recomm endat ions? Tabl e 15. Resp on se Time (online ) Exten s ionalizati o n Code Minimization Dynam ic C han ges Qu er ie s a. no no 1.9 hours 1.5 hours b. ye s no 25.2 min ut es 58 min ut e s c. ye s ye s 10 mi lliseconds 130 mi lliseconds The time efficiency t hat is r equired depends on t he appli cation. F o r our m ilitar y ta sk, once a mi ssion b egins, the s ystem's r e sp on s e s must be ve r y fast. I f i t take s mo r e th a n a few second s to a nswe r a q u ery at run time , t he syst em i s e ffectively us ele ss. Howeve r, b efo r e t he mi s si on begin s, m ore ti me i s gene r ally a vailable fo r knowledge compilation. Stil l, thi s of fli ne proce ssing wo u ld usually need t o be done in hours, no t days. 14 6.1. Exten s ionalization In orde r t o m a ke the system tr actable at r un time , we implemen t ed an o ffline t e c hnique to speed up t he pr ogram . We modified S WORIER to extension a lize all of t he facts th a t can be de rived fr om t he input (th a t a user m ight want t o q u e r y on), c onve rting t he progra m f r om an intension a l for m to an e xt ensional fo r m . F ig ur e 5 shows the modified system de s ign. Figu re 5. Exten sio nalizat ion Table 16a show s s ome sa m p le intensional code , a nd the c orresponding exten sional code ca n b e fo und in Ta ble 16b. T he e xt ensionalization algorithm r uns gene r alized que ries ( i sClass(C) and eq uivalentClasses (C, D) in orde r to der ive al l of the de s ir ed facts and sa ve t hem in the extensional pr ogram . (Note t hat it is e as y to keep duplicate facts out of the exten s ion a l code, because t hey a lways l ook iden tical.) Then, at r un time , the e xt en si on al program us e s t he deri ved facts. Since it only c on sists of facts in ca melcase f orm , s eve ra l of t he rules do no t apply t o t he e xt en s ional code. Only the fa cts that are adde d dynamically t o the knowledge bas e h a ve all- lowe rcase predic at es. 15 Tabl e 16. In ten sio nal and Exten sio nal Code a. iscl ass( regi onOfIn t ere s t). iscl ass( roi) . equi vale ntcl asses( r egi o nOf Inte rest , ro i). isCl ass( C) : - iscl a ss( C ). equi vale ntCl asses( C , D ) :- equ ival entc lass es( C, D ). equi vale ntcl asses( C , C ) :- isC lass (C). equi vale ntCl asses( D , C ) :- equ ival entc lass es( C, D ). b. isClass (regi onOfIn t ere st). isClass (roi) . equi vale ntCl asses( r egi o nOf Inte rest , ro i). equival e ntC lass es( r egi onOf Inte rest , re gion OfI nter est) . equival e ntC lass es( r oi, roi ). equi vale ntCl asses( r oi, reg ionO fInt eres t). This pr e proce ss ing t echnique en a bled t he s ystem t o work much faster, a s show n in T able 15b. Howe ve r , it still r eq u ir ed 25. 2 min ut es t o inc orpo ra te t he sa me t wo dyn a mi c changes as in the previous t e st , and to a nswe r the t wo querie s t ook 58 min ut e s . T hi s is still unacce ptably slow. In a ddi t ion, the o ffline e xt en si onaliz ation pr oce ss caus ed the A MZI Pr olog a pplic ation to cras h , as shown in Ta ble 17a . We pre su me that the computer ran out o f me mo r y. Tabl e 17. Exten sionalization T ime (o fflin e ) Avoidin g Reanal ys is Code Minimization Exten s ionalizati o n a. no no CRASH b. ye s no 13 ho urs c. ye s ye s 6.5 hours 6.2. Avoiding Rean alys is In t he pr ocess of exten sionalizing the code, it was very common t o t e s t a ter m s eve r al time s wi t h t he sa me argumen t s. Thi s unnecessary pro cessing c a n b e ve r y slow . For e xa m pl e , given t he code i n Ta ble 18, t he system must te st is SubClassOf(convoy , theaterobjec t) a t least twice: O nc e when s e ar chin g for al l o f t he tr ue isS ubCla ssOf te r m s, and again when tr y ing to prove is MemberOf( convoy1, t heaterobject) . Tabl e 18. Reevalu a ting a Term ismemb erof(c onvoy1 , convo y). issubc lassof (convo y, mili taryun it). issubc lassof (milit aryunit , thea terobj ect). isSubC lassOf (C, D) :- iss ubclas sof(C, D). isSubC lassOf (C, E) :- iss ubclas sof(C, D), i sSubCla ssOf(D , E). isMemb erOf(I , C) : - ismem berof( I, C). isMemb erOf(I , D) : - isSub ClassO f(C, D ), isM emberOf (I, C) . The proof of is SubClassOf (convoy, theaterob ject) take s five st eps. 3 In gene r al, a very s low t e st m a y b e r un s eve ra l time s. To avoid t he r eev a luation of a t erm, e a ch time 3 1. isSubClassO f(conv oy, th eaterob ject) :- issubc lassof (convo y, thea terobj ect). (F A ILS) 2. isSubClas sOf(con voy, t heater object) :- issubc lassof (convo y, D), isSubC lassOf (D, th eaterob ject). 3. issubclas sof(con voy, m ilitar yunit). 4. isSubClas sOf(mil itaryu nit, t heatero bjec t) :- 16 an is SubClas sOf te rm is t ested, t h at term is asserted as a success or fa ilure . Then, the next time the t e r m need s t o be tested, the a n s we r is found in the new assertion, so it is not ne cessar y to run the full test again . Tabl e 19. Th e Code Mini m ization Algorit hm Base Case 1: IF an d THEN P is a buil t - in pr edi cat e (reserv ed ke yw o rd) i n Pro l o g, P is n o t findall , P is a satisfi able pred ic at e. Base Case 2: IF THEN P is a pred i cat e in a f act , P is a satisfi able pred ic at e. Base Case 3: IF an d THEN an d P is the predicate in t he head of a r u l e, R, each pred i cat e in R's b od y is P, P is a satisfi able pred ic at e, R i s a sat i sf iable ru l e. Inductive Case 1: IF an d THEN an d P is the predicate in t he head of a r u l e, R, ev er y pr edi cat e in R ' s body is sat i s fiable , P is a satisfi able pred ic at e, R i s a sat i sf iable ru l e. Inductive Case 2: IF an d an d THEN a rul e, R, has a t erm , T , in i t s body, wh ere T is assert(F) , asserta(F) , or assertz(F) , P is the predicate of F, all o f t he predic ates pr ecedin g T in the b o dy o f R a re satisfi able pred ic ates, P is a satisfi able pred ic at e. a. Inductive Case 3: IF an d THEN A is the second argum ent o f a findall , all o f t he predic ates in A are satisfi able pred ic ates, t h e findall is t reat ed as if i t was a satisfi able pred i cat e Base Case: IF THEN P is a pred i cat e that can be ca lle d f ro m o utsi de t h e ru l es, 4 P is a t es t able pred i cat e. Inductive Case 1: IF THEN findall is determi ned t o be a testabl e pred icate, each pred i cat e in P's seco nd argumen t is also testabl e. b. Inductive Case 2: IF an d THEN an d P is a pred i cat e such t hat P or not(P) i s f o und in t he body of a r ule , R, R's h ead can b e det er mi ned to have a testable pred i cat e, P is a t es t able pred i cat e, R i s a t est abl e ru l e. issubc lassof (milit aryunit , thea terobj ect). 5. issubc lassof (milit aryunit , thea terobj ec t). 4 These are the pred icates in que r ies, dy n amically asserted facts, a nd the c all to i n iti ate exte nsionalizat ion. 17 Avoiding r eev a luation of isS ubClassOf makes t he offline e xt en si onaliz ation process tractable , though it stil l takes more than 13 hours, a s shown in T able 17b. We a lso tr ied im p lementing t he a voiding r eev aluation technique on isMemberOf . But, fo r our task, very few ismemberof facts are known u ntil r untime , a nd the c ost of ove r head o ut weighs the b enef it, m a king extensionalization slowe r. 6.3.Minim izing Code Ano t he r efficiency improvement ca n b e impl em ented if certain knowledge i s available prio r to run t ime . G iven a list o f all o f t he pr edic ates t h at a re us ed in 1) the on tology, 2) th e dynam ic ch anges, and 3) the q uerie s, i t may b e p ossible to elim inate some of the rules, th us im pr oving e fficiency o f the e xt ension alization process . In addi t ion , the sa me t e chnique c an be used to el imin at e r ule s in the run time program. The ide a is t o f igure o ut which of the rul e s a re actuall y necessary, bec ause the unne cessar y rule s ca n be dropped , improv ing efficiency. If a r ule ca n neve r s ucce ssfull y fir e , the n it is unne c essar y. A lso , if no query will eve r r e sult in testing a r ule , then t hat rule is u nnece ssa ry. More pr ecisely, a rule is a necessary r ule only if it is both satis fiable a n d testable . To de t e r mine which r ules ar e sa tisfi able and t estable, it is nece s sar y t o figure out which pr edicate s ar e sa tisfi able a nd t e stabl e , respec t ively. T he al gorithm t hat define s sa tisfi able r ule s and predi ca t e s i s presented in Ta ble 19a, a n d T abl e 19b shows how t o de t ermine wh ic h r ule s a nd predi ca t e s a re t e stabl e . (In a ddi t i on , we w e r e able t o d rop m ore rul e s b y a ssu m ing t hat the knowledge base was alre ady consi st en t, el imin at ing the need to t e st for consi st en c y.) A fter removing all of the unnec e s sar y rule s, the extension alization proc e ss only took 6. 5 hours, as show n in T able 17c. And the online pr oce s ses can r un m uch fast er, bec ause t he Pr olog com p ile r can b e applie d to all o f t he pr edic ates that are not changed dynamically. T a ble 15c show s t hat it r eq uir es only 10 milli s econd s to a ssim ilat e the t wo dyn a mi c c h anges and 130 millise conds to answer t he t wo q u e r ie s. (T he dynamic changes and q u eri e s used in our e xperiments a re br iefly de s cribed ne ar the beginning o f S e ct ion 6.) These r esul ts sat isf y th e requi r eme n ts of o ur mili tar y task . 7. Rela ted Work Re cent r e search has a dd r e s sed similar issue s a nd pr oblems concerning the inte ra ction of Sem a n tic We b on t ology and r ule technologie s and logic prog ra mm ing. R el ated wo rk i ncl udes rese ar ch on a nswe r s e t progra mm i ng (E iter et al. 200 4; H e ym a ns & Ve r me ir 2003), disjunc t ive logic programming (Ma edche & Vo lz 2003; Minker & S e ipel 2002), c onstructive neg ation (Barták & Rom a n 1998), and D esc ript ion Logic Pr ogramm ing (DLP) (Grosof 2003). Howe ve r, we have not ye t had a n opportunity t o investigate this ot he r work eno ugh t o intelligen t ly comme nt on it. Our prelimin a ry expe rimentation with answe r s e t pr ogramming , howeve r , s eem s to demon st ra te across-the-bo a rd g ains in efficiency , c ompared t o o ur Prolog implemen tati on . But thi s wo rk is as ye t i n compl e t e. 8. Discu ss ion The S WORIER system , given ontologie s and r ule s, ser ve s a s an engine t hat r e s pond s t o que ries. T h is type o f w o r k will r e sult in a signifi cant enh a ncem ent to the S em a ntic Web, by provid ing a generally us eful s e rvice t o a ny a pplication t h at r e quires infor m a tion from t h e Sem a n tic Web. S WORIER is als o a men a ble t o dyna mi c c h anges, q u ickly assi mil ating new facts or re t ra cti ng ol d facts i n an o p erational se tt ing . Al t hough it c annot h a ndle dyn a m ic addi t ions, 18 dele t i on s, or modifi cations o f r ules a t this t ime , it can switch b e t wee n pr ede fined sets of r ules o n the fly. Pr e viously there has been little wo rk involving rule s a nd dyn a mi c change s. We h ave bu il t our work on t he f o undation deve loped in a paper written by Vol tz et al. (2003). We have addr essed five of the probl em s that thi s pa pe r suggested were u nsolv able. 1) B y defining logical negation in Prolog , wh ich m a ke s it possible t o satisfy the open world assum pt ion , it is now p ossible t o properly capt ure t he s em a n t ic s of compleme ntar y class e s , a s wel l a s di s joi nt cl asses. 2) D isj unction in t he he ad o f a rul e is ca ptured wi th t he us e of a new di s junctive operator. 3) Th e disj u n cti ve ope ra tor e nables the analysis of enume ra ted c lasses. 4) T hrough an o ffline analy s is of t he given ontologie s, S WORIER can autom at ically develop rul e s that enforce all and only t he give n car din a lity c on str ain ts. 5) Using a dif fer en t syntax to e xpress OWL facts in Pr olo g, add r e ssing pr ope rt ie s of equivalen t individual s h as been sim p lifie d. Al s o, we dealt wi th th r ee othe r issue s : duplicate facts, cy clical hie ra rchie s, and a nonymo us cl ass es. We have a lso introduced a ltern ative appr oache s f or dealing with inconsistencie s in t he given i nfo r m ation. When a n incon s istency is d iscove r ed , it is always p ossi bl e t o si m p ly s end an e rr o r me ss age t o t he develo per. Howeve r , f or many inconsist en cies, the possibility of fix ing th e problem autom a tically i s available . And, wi t h e xist en tial constraints a nd minimum cardin ality con stra in t s, t h is can b e done by addi ng new facts to the knowledge ba se or by applying th e skole mization method . W e h a ve not ye t conf irmed w hich o f the s e alt e rnatives is pr efe ra ble in which s ituations. W e expect t hat by in troducing pr agm a s (in str uction s/annotations to t h e knowledge compil ati on pr o cess), we ca n allow the develo p e r to choos e t he sp ec ific b eh avior he /s he w ants. Efficie ncy pr oblem s have b een a dd r essed t h rough 1) extension a lizat ion , which is a tabling m et hod that c onve rts a set of rul e s and facts into a set of facts, 2) a v oiding r eanaly sis, which saves r e sults t he f irst time they a re dete r mined t o a v oid r unning the sa me costly evaluation again , and 3) code minim ization, whi ch dele t e s r ule s that ar e unnecessary, for both offline and online pr ocessing . In our expe riments, the offline c om p ilation proce ss now c om p lete s in 6.5 hours, t w o dyna mi c c hange s ar e inc orpo ra te d int o t he knowledge ba se in 10 millisecond s, and two q ueries can be ans we r ed in only 130 mil lisecond s. In the futur e , we ho p e t o a nalyze a nd c onve rt the deve lope r's rules i n t o a ppropriate ly optim ized rules, perh aps via the use of r ew rit e r ule s a s for m agic se ts optimization and related rule t e chniques for logi c queries (Cadoli et al. 1999 ; Sippu & So isalon -S oininen 1996). (Se e Sec t ion 3.3.) Al so, t he ide as presen t ed in S e cti on 4 c oncerning m ult iple t e r m s in the he a d, eq ui v alent individuals, car di nalit y i ssues, c y clic hierachies, a nd a nonymous classes have not yet been implemen t ed . I n addit ion , there a re several pr imitives in OWL that a re not ye t impl em ented in SWORIE R, in c luding: cardi n ality, o r, and subPr o pe rtyOf, 5 and t he l og icNot predicate, introd u ced in Section 4.1 is only partially implemen ted. Ackn ow ledgment s The autho rs’ a ffi l iation wi th T he MITRE C o rporation i s pr ovided f or iden t ification pur pose s only , and is no t intende d to convey or imply MITRE's conc urr ence wi th, o r suppo rt fo r, the posi t ions, opinions or viewpoints expr e s sed by t he authors. 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