The comparison of rule pairs is usually involved in traditional approaches to verify knowledge base. The efficiency of these approaches is low when used in the verification of large-scale knowledge base because of the comparison. An alternative method of detecting logical errors in knowledge base is presented in this paper. This is achieved by analyzing the reachability and the transition sequence of Petri nets which is the established model of rule base

Wang, CN

Wu, JL

Wu, QF

Zhou, CL

吴清锋

Xiamen University Institutional Repository

2005 International Conference on Control and Automation (ICCA2005)June 27-29, 2005, Budapest, HungaryStudy on Knowledge Base VerificationBased on Petri NetsQingfeng Wu*, Changle Zhou, Jinlin Wu, Chaonan Wang* Institute of Artificial Intelligence, Xiamen UniversityComputer Science Departnent, Xiamen University, Fujian, P.R. China, 361005E-mail: pollysecond@sina.comAbstract-The comparison of rule pairs is usually involvedin traditional approaches to verify knowledge base. Theefficiency of these approaches is low when used in theverification of large-scale knowledge base because of thecomparison. An alternative method of detecting logical errorsin knowledge base is presented in this paper. This is achievedby analyzing the reachability and the transition sequence ofPetri nets which is the established model of rule base.I. INTRODUCTIONW5 .t ITH the technology development of Expert Systemand problems to be solved becoming more and morecomplicated the number of rules in knowledge baseincreased ramatically and the structure also become morecomplicated. In addition to this, the introduction ofnewrules into knowledge base and the modification of existedrules can affect the other rules in the base. Therefore, theverification and maintenance of knowledge base is the keypart of the knowledge system and determined the validity ofthe whole system [1].The comparison of rule pairs is usually involved intraditional approaches to verify the knowledge base, forexample in reference [2], van Melle and etc. checked theredundancy and conflict by comparing every rule pair intheknowledge base. But in practice the scale of knowledgebase becomes larger and larger so this method cannot meetManuscript received December 31, 2004. This work was supported byNational Science Foundation of P.R. China (60275023)Qingfeng Wu is with the Computer Science Department, XiamenUniversity, China (phone: 86-0592-2182334; fax: 86-0592-2186546;e-mail: pollysecond@sina.com)Changle Zhou is with the Computer Science Department, XiamenUniversity, China (e-mail: dozeroJxmu.edu.cn)Jinlin Wu is with the Computer Science Department, Xiamen University,China (e-mail: jlwugxmu.edu.cn)Chaonan Wang was with the Computer Science Department, HarbinUniversity of Science and Technology(e-mail: wang-chaonan~hotmail.com)WM-1.4the need ofefficiency. There are some other methods such asdecision table, graphics and so on. In reference [3], theknowledge verification tool, KVB is introduced. Thestrategy ofKVB to verify is verifying locally first and thenverifying globally. But this tool is not so effective when thescale of the knowledge base is large and has high degree ofrelationship between rules.The method based on Petri Nets can avoid the rule pair'scomparison by analyzing the relation between rules with thereachability and transition sequence of Petri Nets. Forexample in reference [4], the author extended the token anddirected arc and established the knowledge base model. Inreference [5] the method to find mistakes is presented. Butwhen the Petri net model is used in verification, its runningrules should be extended. In reference [6], the model cannotexpress the negation logic, and the method in reference [7]involves the search of a tree, so when the reasoning takesmany steps and the base has high relative degree theworkload of verification is high. A model based on coloredPetri Net is presented in this paper and the mistakes of theknowledge base can be detected by analyzing thereachability and transition sequence of the model.II. OBJECT OF KNOWLEDGE BASE VERIFICATIONIn Al systems production rules is a kind of generallyadopted knowledge expression method, so the verificationofknowledge especially for production rules is discussed inthis paper. First the object of knowledge verification iskeeping the system correct, integrate and consistent, so thefollowing phenomena should be detected in rule base:(1) Redundancy. If the same result can be obtained withthe same premise when a rule is deleted from the knowledgebase, there is redundant rule. The following are somedetailed situation:a. Rule equivalence.If P A Q R,Q AP -+ R these two rules are totallyequivalent.b. Transmit redundancy.9970-7803-9137-3/05/$20.00 i 2005 IEEEIfP * Q,Q R,P - R , the third rule is redundant. Itis not the same with the multiple reference routes. ForexampleP-X>Q,Q--+S,P---R,R - SThis is multiplereference route and not redundant. In knowledgeverification the existence of multiple reference routes is nota mistake.c. Hypotactic rules.When the conclusions of rule 1 and 2 are the same, andI has more restrictions than 2, then I is the hypotacticrule ofR2. For example R :PAQ->R,R2 :P-*R.(2) Conflict rules. If a rule in the knowledge base supportsnot only the affirmation of some conclusion but also thenegation ofthe same conclusion, then there is conflict rule inthe knowledge base.a. Conflict rules.For example, P Q,P -Qb. Conflict rules chain. Two groups of rules get conflictconclusion with the same premise. For exampleP->Q,Q-R and P S,S>T,TR aretwo conflict rule chains.(3) Circularity. If a group rules can form circularity, thenthey are circulate rule chain. P -* Q,Q -- R, R -X P.(4) Dead ends. Ifthe conclusion ofa rule can neither matchthe premise of any other rules, nor the final conclusion, thisconclusion is called dead end. This can be classified asredundancy and will not lead to system crash, but it canlower the efficiency.(5) Unreachable goals. If there is no reference path inknowledge base to reach the system target conclusion withany initial conditions, this conclusion is an unreachable goal.III. PETRI NETS DEFINITIONThe first step to verify knowledge is to precisely formalizethe original knowledge. There are many ways to formalizeknowledge, for example logic system, production system,linguistic network, frame system, object-oriented and soon.Adoption of formalization methods will affect theknowledge verification. Petri net is a proper tool fordescribing and studying systems that are characterized asbeing asynchronous and concurrent. It has rich ways todescribe systems and technique to analyze their actions [9].In addition formnalized knowledge with all above methodscan be easily transferred into those with Petri Nets. So PetriNet is adopted in this paper as the tool to model knowledgebase so the verification can be relatively uniform.First a kind of colored Petri Net is defined to expressknowledge and then knowledge base model based on PetriNet is built up.Definition 1 Colored Petri net is a six-tuple.E ={P,T,F, C_-I+I} .1. P is the place set and T is the transition set.Fc Px TYTx P is flow relation set.2. D is a given color collection, and Power(D) is thepower of collection D.C: PYT -> Power(D) means for any P E P, C(P)is the collection ofpossible colors in the place P. Fort E T, C(t) is the collection ofpossible colors intransition T3. I and I+ are negative and positive functions of P x Trespectively. For any (P, t) P xTL(P,t) E [C(t)MS -+ C(P)MS]L and the condition ofI (p,t) = 0is (P, t) F /+I(P,t) E [C(t)MS - C(P)MSIL,andthe abundant essential condition ofI+(p,t) = Ois(t,p) 0 F.C(t)Ms is the multi-set of C(t), [C(t)ms - C(P)MS ]Lis the collection of linear function from C(t)Ms toC(P)MSDefinition 2 Supposep E P,t E T, = {pI(p,t) E F}and t = {pI(t, p) E F} are the input and output placecollection respectively.Definition 3 Define M: P -+ DMS as the mark ofcolored Petri net systemI IVp E P: M(P) E C(P)MS should be satisfied. Amulti-set of the color set C(p) is assigned to every placep and this describes the distribution of tokens in thesystem.Definition 4 IfVt E T: X(t) E C(p)MS, thenX:T-+ DMS isastepofEDefinition 5 SupposingX is the next step of the system ofwith the mark ofM , the subsequence step M isVP c- P:M (P) = M(P) + Z I+ (P, t)(X(t)) - EtI (P, t)(X(t))teT teTrepresented byM[X >M998IV. FORMALIZATION OF RULE BASE WITH PETRI NETSAll the rules in the knowledge base can be representedbyRi:A(ri) A A2(r,)...AAA,,(r,) C (r,) A C2(ri)-... C. (r,)The mapping rules between knowledge base and the modelwhich is defined above is as following: transition representsthe execution of a rule; places are the premise andconclusion of rules; the logical relation ofpremise andconclusion is represented by directed arcs. For rule Ri,supposing ti is its transition, then the premiseAl (ri) A A2 (ri )... A An (ri) is t and the conclusionC,Q)A C2 ( )- A Cm (ri ) is t*. Graphicrepresentation of rule 1 is as figure 1.A1 (ti) ( \ c (ti)C2(t )Fg. I Graphic of Rule 1ri * Cl (ti)A1(ti) 1 C2(t1)A2~~~~~~~~c(titi)1A2(ti)Fg.2 Extended Petri Net ModelTokens in places represent if the clause ofpremise andconclusion is true. The negative and positive functiononP x T, which are I- and I+, determine the number oftokens, which is consumed and produced when the rule isexecuted. Places' sharing between different rules means thelogic relationship between them. After transition is fired,tokens are released to its output place, this means theconclusion clause become true when the rule is executed.But according to the running rules of Petri net, thepremise status of rule as shown in figure 1 becomesuncertain because the token in place is consumed after therule is executed. This is not to be expected. The initial factsand the facts produced in the process of reference should bereserved and can be used by multi rules. This problem can besolved by adding reverse arc between transitions of t£ andPE t1 , that is let the it' to be the adjoint places. Butthis can lead to new problem. Because the facts are reserved,ttransition i can be fired heaps of times. Place i is addedas shown in figure 2. After transition i is fired the token ini is consumed, so at the next time transition t; cannot befired because it lacks of token. In this way, the rule can beused only once and the known facts can be reserved.Apparently places in the above Petri net model can beclassified into two categories, P {PC PR} ri E PR . Forthe convinces of analysis, c can be divided into threesub-sets, C {PCE "CI CG } . CE is the collection ofclauses which can obtain information through users' inputand system database. CI is the collection of clauses whichare produced in the reference process and PCG is thecollection of clauses which are the system conclusion.Definite color set D= {b,w,f}, and the possible tokens inplace are b,w and f. Color w means the clause or theconclusion represented by the place is true; color b meansthe clause or the conclusion represented by the place is false.Tokens in PR has the color of f which means if the rule hasever been fired. The initial mark MO ,MO (PR) = [ilf],means there are no rules fired initially.MO (P ) . xB + yW, x, y are positive integers andnot equal to zero, which means there are no conflict factsinitially.V. KNOWLEDGE VERIFICATION AND EXAMPLEAccording to the above mapping method, rules areformalized in the form of Petri net and the rules areconnected by sharing places so a Petri net model ofknowledge base is built up. Constructer mistakes can bedetected by analyzing the reachibility and transitionsequence of the Petri net.(1) For the minimal initial mark MO that can firetransition sequence T. , if there is redundancy in theknowledge base, there will be another transition sequenceTk and i, Tj nTk =0,MO[T >M,M [T > M"which makes MO(pi)=O M (pi)=lb+lf orlw+lf , M"(pi)=2b+2f or 2w+2f , andj,kcan be exchanged. As referred in the discussion ofverification object, transmitted redundancy andmulti-reference route are different and it is not a redundantmistake. An additional constraint should be included thatthere is at least one transition sequence which has only one999transition.(2) For the minimal initial mark Mo that can firetransition sequence T , if there is conflict in the rule set,then there should be another transition sequence Tk and i,makes MO(pi) = 0,M'(pi)= lb+lf or lw+lf,M (pi) = lb +lw+2f .(3) If there is circularity in rule set, then for the minimalinitial mark Mo that can fire the transition sequence Tand3i Mo(pi) = lb+xf or lw±xf,x E {0,1}Mo[TJ > M,makesM (pi) = 2b + 2f or2w+2f.(4) If there is dead end in the rule base, there should existsome initial markMO 7MO(PCE) . [°], Mo(PCGO)= [°makes VT,MO[T > M', M'(PCG) = [0].(5) If there is unreachable goal in the rule base, any initialmark that satisfy MO(PCE) [0]' MO(PCI) = [0]MO(PCG) = [ , and VT,MO[T >M]k,Pk e {PCG},M (Pk O.Knowledge base verification is explained with knowledgebase R as the example. The graphic of knowledge base Rbased on Petri net is shown in figure 3.(1) Redundancy. For initial markMO = [lw,0,lw,O,...,0] and transitionsequence Tj={t2} , MO[T¾>M' M,[Tk>MMo(P2)= 0 M (p2)=lw lfM"(p2)=2w+2f so there is redundancy in ruleR,,,R2- especially R2 is the hypotactic rule of R1. Inanother situation with the initial mark ofMO = [lw,O, . ,O] and transition sequenceT =ftl,t3l(3) Circularity. With the initial mark ofMO =[0,0,0,0,lw,O,...,0] , MO(P5)=lw and thefollowing transition sequence T1 = {t5,t6, t7}MO[T >>M , M'(p5)=2w+f. Rule R5,R6,R7form circularity.(4) Dead ends. With the initialmark Mo = [0,0,0,0,0,0,O,0,lw,0,0,0], only transitiontl 0 can be fired, and the resultisM =[0,0,0,0,0,0,0,0,lw,lw,0,0]. There is no othertransition can be fired and the final conclusion is notreachable, that isVT,MJ[T >M ,M (PClG) [0].(5) Unreachable goal. With the initial mark,MO [lw,0,lw,0,lw,O,O,O,lw,O,0,0J rule R 1I will neverbe fired, that is VT,9MO[T >MM (P12) = 0, so theconclusion of p12 is not reachable.Vl. CONCLUSIONThe method presented in this paper to verify knowledgebase turns the detection of logic mistake among knowledgeto analysis of the reachiability and transition sequence ofPetri net. Knowledge model based on Petri net is built upfirst which can reserve facts and express negation logiccompared to ordinary Petri nets. The method to detectmistakes is presented at last.Tk ={t4}M (p4) = lw+lf , M (p4) = 2w±+2f , ruleRI' R3, R4 are circulate redundancy.(2) Conflict. With the initial mark of MO = [lw,O,...,O]and transition sequence Tj = t{tgfI}Tk = {t3,t8 } , MO [Tj >M , M [Tk >MMo(P8) = O 9 M (P2) = lb + lf sM(P2) = lw+lb + 2f, rule R3,R.,R are conflict.1000RI: PI > P22R2:IP1oAP3- P2R -P ->P43 2R4: P -*P4R :P -+P6-5 56R6 -P6 -P7R7: P7 + P5R8 :4 PR9 P2 +-JP8Rio pq -> loRI I PII,>PI2Fg.3 Knowledge Base ExampleREFERENCES[1] Wei-Tek Tsia, Rama Vishnuvajjala and Du Zhang, "Verification andValidation of Knowledge-based System", IEEE Trans Knowledgeand Data Eng, 11(1), pp202-212, 1999.[2] Van MelleW J, "System aids in constructuring computer consultationprograms", MI:UMI Research Press, 1981,70-80[3] Jie Zhang, Suzhen Zhang, Weisun Jiang, "Expert System KnowledgeBase Verification", Proceeding ofEast China University ofScienceand Technology, 22(5), pp583-589, 1996.[4] Liu Xiaoxia, " A Study on the Maintenance of a Rule Base UsingNumerical Petri Nets", [JI Mini-Micro Systems, 18(7), pp74-77,1997[5] Liu Xiaoxia, "Knowledge Base Maintenance Systems Using PetriNets", [J] Mini-Micro Systems, 23(7), pp859-861[6] Derek L. Nazareth, "Investigating the Applicability of Petri Nets forRule-Based System Verification", IEEE Trans, Knowledge and DataEngineering, 4(3), pp4O2-415, 1993.[7] Jiang Hao, Luo Junzhou and Fang Ningsheng, "A KnowledgeVerification Method Based on Color Petri Net", Journal ofSoutheastUniversity, 30(1), pp77-82, 2000[8] Mengshoel, O.J. and Delab, S. " Knowledge Validation: Principlesand Practice", IEEE Expert, vol.8, pp62-68, 1993[9] Chongyi Yuan. Theory of Petri Net. BeiJing. Publishing House ofElectronic Industry, 19981001

Study on knowledge base verification based on Petri nets

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Study on knowledge base verification based on Petri nets

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