Sonic — Non-standard inferences go OilEd
Sonic—Non-standard Inferences go OilEd
Anni-Yasmin Turhan and Christian Kissig
TU Dresden,Germany
email:lastname@tcs.inf.tu-dresden.de
Abstract.Sonic1is the?rst prototype implementation of non-standard
inferences for Description Logics usable via a graphical user interface.
The contribution of our implementation is twofold:it extends an earlier
implementation of the least common subsumer and of the approximation
inference to number restrictions,and it o?ers these reasoning services via
an extension of the graphical ontology editor OilEd[3].
1Introduction and Motivation
Description Logics(DLs)are a family of formalisms used to represent termino-logical knowledge of a given application domain in a structured and well-de?ned way.The basic notions of DLs are concept descriptions and roles,representing unary predicates and binary relations,respectively.The inference problems for DLs can be divided into so-called standard and non-standard ones.Well known standard inference problems are satis?ability and subsumption of concept de-scriptions.For a great range of DLs,sound and complete decision procedures for these problems could be devised and some of them are put into practice in state of the art DL systems as FaCT[11]and Racer[9].
Prominent non-standard inferences are the least common subsumer(lcs),and approximation.Non-standard inferences resulted from the experience with real-world DL ontologies,where standard inference algorithms sometimes did not su?ce for building and maintaining purposes.For example,the problem of how to structure the application domain by means of concept de?nitions may not be clear at the beginning of the modeling task.This kind of di?culties can be alleviated by non-standard inferences[1,7].
Given two concept descriptions A and B in a description logic L,the lcs of A and B is de?ned as the least(w.r.t.subsumption)concept description in L subsuming A and B.The idea behind the lcs inference is to extract the commonalities of the input concepts.It has been argued in[1,7]that the lcs facilitates a“bottom-up”-approach to the modeling task:a domain expert can select a number of intuitively related concept descriptions already existing in an ontology and use the lcs operation to automatically construct a new concept description representing the closest generalization of them.
Approximation was?rst mentioned as a new inference problem in[1].The approximation of a concept description C from a DL L1is de?ned as the least This work has been supported by the Deutsche Forschungsgemeinschaft,DFG Project BA1122/4-3.
1Sonic stands for“Simple OilEd Non-standard Inference Component”.
concept description (w.r.t.subsumption)in a DL L 2that subsumes C .The idea underlying approximation is to translate a concept description from one DL into a typically less expressive DL.Approximation can be used to make non-standard inferences accessible to more expressive DLs so that at least an approximate solution can be computed.In case the DL L provides disjunction,the lcs of C 1and C 2is just the disjunction (C 1 C 2).Thus,a user inspecting this concept does not learn anything about the commonalities of C 1and C https://www.wendangku.net/doc/b816443598.html,ing approximation,however,one can make the commonalities explicit to some extent by ?rst approximating C 1and C 2in a sublanguage of L which does not provide disjunction,and then compute the lcs of the approximations in L .Another application of approximation lies in user-friendly DL systems,such as OilEd [3],that o?er a simpli?ed frame-based view on ontologies de?ned in an expressive background DL.Here approximation can be used to compute simple frame-based representations of otherwise very complicated concept descriptions.OilEd is a widely accepted ontology editor and it can be linked to both state of the art DL systems,Racer [9]and FaCT [11].Hence this editor is a good starting point to provide users from practical applications with non-standard inference reasoning services.The system Sonic is the ?rst system that provides some of these reasoning services via a graphical user interface.Sonic can be downloaded from http://lat.inf.tu-dresden.de/systems/sonic.html .2The Sonic Implementation
Let us brie?y recall the DLs covered by Sonic .The DL A L E o?ers the top-and bottom-concept ( ,⊥),conjunction (C D ),existential (?r.C ),value re-strictions (?r.C ),and primitive negation (?C ).The DL A L C extends A L E by disjunction (C D )and full negation.Extending each of these DLs by number restrictions ((≤n r ),(≥n r ))one obtains A L EN and A L CN ,respectively.For the de?nition of the syntax and semantics of these DLs,refer to [5,6].A TBox is a ?nite set of concept de?nitions of the form A .=C ,where A is a concept name and C is a concept description.Concept names occurring on the left-hand side of a de?nition are called de?ned concepts .All other concept names are called primitive concepts .Sonic can only process TBoxes that are acyclic and do not contain multiple de?nitions.
2.1Implementing the Inferences
Sonic implements the lcs for A L EN -concept descriptions and the approximation of A L CN -by A L EN -concept descriptions in Lisp.The algorithm for computing the lcs in A L EN was devised and proven correct in [12].This algorithm consists of three main steps:?rst recursively replace de?ned concepts by their de?nitions from the TBox,then normalize the descriptions to make implicit information explicit,and ?nally make a recursive structural comparison of each role-level of the descriptions.In A L EN the last two steps are much more involved than in A L E since the number restrictions for a role,more precisely the at-most restrictions,
necessitates merging of role-successors.The lcs algorithm for A L EN takes double exponential time in the worst case.Nevertheless,the lcs for A L EN realized in Sonic is a plain implementation of this algorithm.Surprisingly,a ?rst evaluation shows that for concepts of an application ontology with only integers from 0to 7used in number restrictions the run-times remained under a second (on a Pentium IV System,2GHz).The implementation of the lcs for A L E as described in [2]uses unfolding only on demand—a technique known as lazy unfolding.Due to this technique shorter and thus more easily comprehensible concept descriptions can be obtained more quickly,see [2].To implement lazy unfolding also for A L EN is yet future work.
The algorithm for computing the A L CN to A L EN approximation was devised and proven correct in [5].The idea underlying it is similar to the lcs algorithm in A L EN .For approximation the normalization process additionally has to “push”the disjunctions outward on each role-level before the commonalities of the dis-juncts are computed by applying the lcs on each role-level.The A L CN to A L EN approximation was implemented in Lisp using our A L EN lcs implementation.An implementation of the A L C to A L E approximation is described in [6].It was the basis for the implementation presented here.The worst case complexity of approximation in both pairs of DLs is double exponential time,nevertheless this is not a tight bound.A ?rst evaluation of approximating randomly generated concept descriptions show that,unfortunately,both implementations run out of memory already for concepts that contain several disjunctions with about 6dis-juncts.The implementation of the algorithms for both inferences are done in a straightforward way without code optimizations or sophisticated data structures.This facilitated testing and debugging of Sonic .
Let us illustrate the procedure of lcs and approximation by an example.Con-sider a A L CN -TBox with role r ,primitive concepts A ,B ,and concept de?nitions:C 1.=?r.A ?r.B (≥3r ),C 2.=?r.(A B ) (≥2r ),C .=C 1 C 2and D .=?r.(A B ) ?r.(?A B ).If we want to ?nd the commonalities between C and D ,we ?rst compute the A L EN -approximation of C and then the A L EN -lcs of D and approx (C ).We compute approx (C )by ?rst unfolding C and then extract-ing the commonalities of C 1and C 2.Both have a value restriction and the lcs of these restrictions is ?r.B .Both C i induce the number restriction (≥2r ),since (≥2r )subsumes (≥3r ).C 1has a value and an existential restriction induc-ing the existential restriction ?r.(A B ),whereas in C 2the number restriction requires at least two distinct r -successors which in addition to the value re-striction also induces the restriction ?r.(A B ).Thus we obtain approx (C )=?r.(A B ) ?r.B (≥2r ).In the concept de?nition of D the occurrence of A and ?A induce that at least two r -successors exist.Thus the commonalities of C and D are lcs (approx (C ),D )=?r.(A B ) (≥2r ).
2.2Linking the Components
In order to provide the lcs and approximation to OilEd users,Sonic does not only have to connect to the editor OilEd ,but also to a DL system
Fig.1:Interface of Sonic since both,lcs and approxima-tion,use subsumption tests dur-ing their computation.A con-nection from Sonic to the ed-itor OilEd,is realized by a plug-in.Like OilEd itself,this plug-in is implemented in Java. Sonic’s plug-in is implemented for OilEd Version3.5.3and re-alizes mainly the graphical user interface of Sonic—its lcs tab is shown in Figure1.Sonic’s Java plug-in connects via the JLinker interface by Franz Inc.to the
Lisp implementation to pass concepts between the components.
To classify an ontology from within OilEd,the user can either connect OilEd to the reasoner FaCT(via CORBA)or to any DL reasoner supporting the DIG (“Description Logic Implementation Group”)protocol.The DIG protocol is an XML-based standard for DL systems with a tell/ask syntax,see[4].DL devel-opers of most systems have committed to implement it in their system making it a promising standard for future DL related software.
Sonic must have access to the same instance of the reasoner that OilEd is connected to in order to have access to the information from the ontology,more precisely,to make use of stored concept de?nitions and of cached subsumption relations obtained during classi?cation by the DL reasoner.Obtaining the con-cept de?nitions from OilEd directly,would result in storing the ontology in all of the three components and,moreover,the results for lcs and approximation might be incorrect,if OilEd and the DL reasoner do not have consistent data.
Since Sonic needs to retrieve the concept de?nition of a de?ned concept in order to perform unfolding—a functionality that Racer provides—we decided to use Racer in our implementation.Sonic connects to Racer Version1.7.7 via the TCP socket interface described in[10].Note,that in this setting the Racer system need not run locally,but may even be accessed via the web by OilEd and Sonic.
2.3Sonic at Work
Starting the OilEd editor with Sonic,the lcs and approximation inferences are available on extra tabs—as shown in Figure1.Once the OilEd user has de?ned some concepts in the OilEd ontology,has connected to the DIG reasoner Racer and classi?ed the ontology,she can use,for example,the lcs reasoning service to add a new super-concept of a number of concepts to the ontology. On the lcs tab she can select some concept names from all concept names in ontology.When the lcs button is clicked,the selected names are transmitted to Sonic’s Lisp component and the lcs is computed based on the current concept de?nitions stored in Racer.The obtained lcs concept description is send to
the plug-in and displayed on the lcs tab in OilEd.Since the returned concept descriptions can become very large,Sonic displays them in a tree representation, where uninteresting subconcepts can be folded away by the user and inspected later.In Figure1we see how the concept description obtained from the example in Section2.1is displayed in Sonic.Based on this representation Sonic also provides limited editing functionality.The OilEd user can cut subdescriptions from the displayed lcs concept description or cut and store(a part of)it under a new concept name in the ontology.
3Outlook
Developing Sonic is ongoing work.Our next step is to optimize the current implementation of reasoning services and to implement minimal rewriting to obtain more concise result concept descriptions.Future versions of Sonic will comprise the already completed implementations of the di?erence operator[6] and of matching for A L E[8].
We would like to thank Ralf M¨o ller and Sean Bechhofer for their help on how to implement Sonic’s linking to Racer and to OilEd.
References
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2. F.Baader and A.-Y.Turhan.On the problem of computing small representations of least common subsumers.In Proceedings of KI’02,LNAI.Springer–Verlag,2002.
3.S.Bechhofer,I.Horrocks,C.Goble,and R.Stevens.OilEd:a Reason-able Ontology Editor for the Semantic Web.In Proceedings of KI’01,LNAI,Springer-Verlag,2001.
4.S.Bechhofer,R.M¨o ller,and P.Crowther.The DIG description logic interface.In Proceedings of DL2003,Rome,Italy,CEUR-WS,2003.
5.S.Brandt,R.K¨u sters,and A.-Y.Turhan.Approximating ALCN-concept descrip-tions.In Proceedings of DL2002,nr.53in CEUR-WS.RWTH Aachen,2002.
6.S.Brandt,R.K¨u sters,and A.-Y.Turhan.Approximation and di?erence in descrip-tion logics.In Proceedings of KR-02,Morgan Kaufmann,2002.
7.S.Brandt and https://www.wendangku.net/doc/b816443598.html,ing non-standard inferences in description logics—what does it buy me?In Proc.of KIDLWS’01,CEUR-WS.RWTH Aachen,2001.
8.S.Brandt.Implementing matching in ALE—?rst results.In Proceedings of DL2003, Rome,Italy,CEUR-WS,2003.
9.V.Haarslev and R.M¨o ller.RACER system description.In Proceedings of the Int. Joint Conference on Automated Reasoning IJCAR’01,LNAI.Springer Verlag,2001.
10.V.Haarslev and R.M¨o ller.RACER User’s Guide and Manual,Version1.7.7, Sept,2003.available from:
http://www.sts.tu-harburg.de/~r.f.moeller/racer/racer-manual-1-7-7.pdf.
https://www.wendangku.net/doc/b816443598.html,ing an expressive description logic:FaCT or?ction?In Proceedings of KR-98,Trento,Italy,1998.
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■编者说明 《电刑室手记》自1994年《电软》创刊号起至1995年第7期止，共连载 了10期，（缺1994年第5期和1995年第5期），共108则。 108则“电刑室手记”，用俏皮、辛辣和嘲弄的语气，记录了国内第一 本游戏杂志的生长历程，展现了游戏人的另一种生活…… 《电刑室手记》一推出，它那简洁的文字、恢谐的语言、调侃的风格、 搞笑的故事受到读者热烈欢迎，人气度直线上升，对推动《电软》的销量 起了重要的作用。它停办的直接原因是1995年7月的停刊事件。之后《电 软》变得庄重正经起来，那么“不正经”的手记自然也就没了容身之地…… 本站将陆续登载《电刑室手记》１０８则，望广大读者密切关注! 《电刑室手记》初无深意，不过将编辑部之鸡零狗碎，牛头马面，孤魂野鬼，搞笑乱弹，不登大雅之堂者，撮成一堆，以博一笑耳（有玩友称为“厕上极品”）。譬若大餐之后，芝麻落入桌缝中，弃之可惜。遂用掌震出，慢慢咀嚼，或亦为一种消遣。诸多玩友，“臭味”相投，弃屠龙之大雅，就雕虫之小技。要求开放电刑室，变私言为公器。佛家言：芥子可纳须弥（一粒草子里可容纳一座高山）。小小电刑室，能了断众玩友的恩怨情、辛酸泪吗？阿弥陀佛！善哉！善哉！ ▲001.编辑部为编游戏节目特辟一“电玩室”。而同楼其他单位人员时时光临逍遥一番，编辑部不胜其扰。编辑龙哥在门口大书“电刑室”三字，过路者见状皆大惊，避之犹恐不及。一来访电玩友遍寻龙 哥不着，见“电刑室”三字大喜道：“此真吾温柔乡也！”乃破门而入。 ▲002.来编辑部之电玩友甚众，然呼朋引类，泾渭分明。一半为北京高校之莘莘 学子，温文尔雅，乃主编之友。另一半为贩夫走卒，三教九流，龙哥之友。一日， 清华陈君曰：“非高智商玩不了游戏机。”一室灿然。徐徐又曰：“玩游戏机也不 乏低能儿。”三教九流皆怒目而视。 ▲003.龙哥好客，常以交友广自许。然遇特别能战斗者，亦使龙哥吃不消。一周六下午，两电玩友访龙哥于“电刑室”。玩“光明与黑暗”，兴起，挑灯夜战。龙哥先招待以酒肉，继之以大排档，后囊中羞涩，以方便面果腹。如是连续作战两夜一天，不知光明与黑暗。至周一早，两玩友方告辞上班，致谢。龙哥两眼血丝，连说别客气，以后再来。方欲小憩，两玩友忽奔回曰：“周六一定再来。”龙哥几欲昏倒。 ▲004.编辑部诸人皆俄罗斯方块高手，常有打遍天下无敌手之感叹。一街机老板来，据介绍，一枚铜板打穿街机三国。主编豪情万丈，邀之决战俄罗斯。老板却战再三，主编为之 踌躇满志。依稀闻老板低声对他人云：“小儿科。”主编大惭。 ▲005.《GAME集中营》第一期出版后，闯关族来信甚多。编辑老D负责回信， 龙哥不甚留意。一日老D拆信后眼睛一闪光，大呼：“龙哥，空姐来信！”龙哥扑 上，急将信收入衣袋曰：“此信我回。”老D忿然曰：“不行，你字太赖。”二人扭 打一处。最后订协议如下：龙哥写，老D抄。 ▲006.老D一天不玩游戏机就便秘，据说有医生诊断书 ▲007.龙哥玩游戏，总把一只脚放在桌子上，直指电视，据他说是“第三只手”。 ▲008.龙哥逢人便说他是中国玩游戏第一人，十年前就开始玩 智力宝游戏机（据可靠消息，十年前中国还没有智力宝）？！ 当时只有一盘从左向右打的横卷轴射击游戏卡。玩得无聊，便 把电视机竖起来，变成由下向上打；把电视机倒过来，变成从 右向左打；再竖起来，变成由上向下打。据其说，“回”字有四种写法，射击游戏 也必有四种打法。
细数史上最佳十大游戏系列你可能全部玩过
第十名魔兽世界 这款暴雪出品的网络游戏是在最早出现于1994年的《魔兽争霸》系列所衍生出来的。《魔兽世界》允许玩家在《魔兽争霸》的世界，也就是艾泽拉斯大陆中扮演一名奇幻角色，并按自己的意愿发展至高等级。这是一款彻头彻尾的网络游戏，玩家之间可以互动，协作，并与伙伴们一起完成任务，获取经验和金钱。全世界有数百万玩家沉迷于此难以自拔。整个系列拥有无数拥趸，而且提升到了文化高度，这往往体现在那些电视里的山寨节目当中。在未来，还会有更多的资料片等待放出，以迎合那些持续增加并等待上线进行任务的玩家们。 第九名生化危机 卡普空最著名的生存类恐怖游戏“生化危机”的第一部出品于1996年。以邪恶的安布雷拉公司为线索，玩家逐渐揭开了一个关于可将死人变为僵尸并吃人血肉的致命病毒的故事。黑暗压抑的恐怖气氛与面对无尽僵尸极力求生的操作完美结合，为玩家带来一场极尽刺激疯狂的游戏体验。忠实的玩家们无止尽地购买着一部又一部的系列新作，而整个一系列的好莱坞电影也应运而生。生化危机成为了有史以来最成功的恐怖游戏系列，并为众多同类游戏争相效仿。 第八名口袋妖怪 如果你没听说过口袋妖怪的鼎鼎大名，那么过去十五年里你一定过着与世隔绝的生活。这是一款在全球各个角落都有着无数拥趸和话题的真真正正的重量级系列游戏。口袋妖怪于1996年在GB平台上发布了一对相互联系的RPG作品，并在这之后发展为全球最大的系列性游戏，并带来了数量庞大的周边营销。这其中包括了动画，漫画，集换式卡牌，手办，书籍，电影和电视节目及无数其他周边。游戏允许玩家搜寻并捕获各种不同的口袋妖怪，并将其用于战斗之中。游戏的一个重要元素就是“全搜集”，即搜集游戏中的每一种口袋妖怪角色，包括标志性的“皮卡丘”。口袋妖怪成为了一款极受欢迎的系列游戏，至今仍不断从各个年轻吸收着新的粉丝。 第七名塞尔达传说 作为任天堂的旗舰性游戏，塞尔达传说是一款高奇幻类的动作冒险游戏，所有故事都围绕着大名鼎鼎的核心主角“林克”展开。玩家总是要控制林克，从各种恶魔手中解救塞尔达公主。全系列的十五款官方游戏和无数外传为其营造了来自世界各地的无数粉丝，其数量还在以难以估计的速度增加。林克也成为了有史以来最具标志性的电视游戏人物。塞尔达传说系列打造了许多经典游戏，例如著名的“塞尔达传说：时空隧道”、“塞尔达传说：黄昏的公主”以及最受欢迎的“塞尔达传说：时之笛”。塞尔达传说系列被证实为有史以来最好的系列游戏之一。 第六名GT赛车