Proceedings of the 1999 International Workshop on Description Logics
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(2) International Workshop on Description Logics Linkoping, Sweden July 30 - August 1, 1999 Patrick Lambrix. Department of Computer and Information Science Linkopings universitet Linkoping, Sweden patla@ida.liu.se. Alex Borgida. Department of Computer Science Rutgers University New Brunswick, NJ, USA borgida@cs.rutgers.edu. Maurizio Lenzerini. Dipartimento di Informatica e Sistemistica Universita degli Studi di Roma "La Sapienza" Roma, Italy lenzerini@dis.uniroma1.it. Ralf Moller. Computer Science Department University of Hamburg Hamburg, Germany moeller@informatik.uni-hamburg.de. Peter Patel-Schneider. Bell Labs Research Murray Hill, NJ, USA pfps@research.bell-labs.com.
(3) Preface The 1999 International Workshop on Description Logics was held in Linkoping, Sweden from July 30 to August 1. It was an a liate event with the Sixteenth International Joint Conference on Articial Intelligence (IJCAI'99, Stockholm, July 31 - August 6) and with the Sixth International Workshop on Knowledge Representation meets Databases (KRDB'99, Linkoping, July 29-30). The workshop was organized in sessions on theoretical advances in description logics (2 sessions), applications of description logics (2 sessions), description logic systems (2 sessions) and extensions of description logics (1 session). Further, there was a joint session with the Sixth International Workshop on Knowledge Representation Meets Databases. There were two invited talks. Natasha Alechina gave a tutorial on logics for semi-structured data. Robert MacGregor and Deborah McGuinness gave a presentation on DARPA's High Performance Knowledge Base project. The workshop was sponsored by the Swedish Research Council for Engineering Sciences (TFR), Telefonaktiebolaget LM Ericssons Stiftelse for framjande av elektroteknisk forskning, Linkopings kommun, Erda AB and the Laboratory for Intelligent Information Systems, Linkopings universitet. Thanks go also to Lotta Nissen, Yelena Turetskaya and a number of students for their contribution to the organization..
(4) Invited talks. Contents. (Modal) Logics for Semistructured Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Natasha Alechina DARPA's High Performance Knowledge Base (HPKB) Program . . . . . . . . . 2 Robert MacGregor, Deborah McGuinness. Joint session with KRDB99. Reasoning with enhanced Temporal Entity-Relationship Models . . . . . . . . . 4 Alessandro Artale, Enrico Franconi Answering Queries Using Views in Description Logics . . . . . . . . . . . . . . . . . . . 9 Diego Calvanese, Giuseppe De Giacomo, Maurizio Lenzerini Theory-driven Logical Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Susanne Prediger, Gerd Stumme Backward Reasoning in Aboxes for Query Answering . . . . . . . . . . . . . . . . . . 18 Marie-Christine Rousset. Applications. Spatial Reasoning for Image Retrieval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Marco Aiello, Carlos Areces, Maarten de Rijke Description Logics and Feature Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Carlos Areces, Wiet Bouma, Maarten de Rijke A Proposal for a Description Logic Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Sean Bechhofer, Ian Horrocks, Peter Patel-Schneider, Sergio Tessaris Explaining ALC Subsumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Alex Borgida, Enrico Franconi, Ian Horrocks, Deborah McGuinness, Peter Patel-Schneider Description Logics for Image Recognition: a preliminary proposal . . . . . . 41 Eugenio Di Sciascio, Francesco M. Donini ICARUS: Intelligent Classication And Retrieval of Unlabelled Scenes . 46 Emilio Domenicucci, Francesco Donini, Marco Schaerf i.
(5) Applying DLs for Retrieval in Case-Based Reasoning . . . . . . . . . . . . . . . . . . 51 Pedro A. Gonzales-Calero, Belen Diaz-Agudo, Mercedes Gomez-Albarran A New Application for Description Logics: Disaster Management . . . . . . 56 Martina Grathwohl, Francois de Bertrand de Beuvron, Francois Rousselot Feature-Based Learners for Description Logics . . . . . . . . . . . . . . . . . . . . . . . . . 61 Daniel Kudenko, Haym Hirsh Integrating Concept-Based Knowledge Bases . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 Aida Vitoria, Margarida Mamede. Theory. Matching in Description Logics with Existential Restrictions . . . . . . . . . . . 71 Franz Baader, Ralf Kusters Rewriting in Description Logics Using Terminologies . . . . . . . . . . . . . . . . . . . 76 Franz Baader, Ralf Molitor A Suggestion for an n-ary Description Logic . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 Carsten Lutz, Ulrike Sattler, Stephan Tobies Computing Least Common Subsumers in Expressive Description Logics 86 Thomas Mantay Set Description Languages and Reasoning about Numerical Features of Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 Hans Jurgen Ohlbach Reasoning in a Closed Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 Francois Rousselot, Francois de Beuvron, Michael Schlick, David Rudlo ABox Reasoning with Transitive Roles and Axioms . . . . . . . . . . . . . . . . . . . 101 Sergio Tessaris, Graham Gough On the Complexity of Counting in Description Logics . . . . . . . . . . . . . . . . . 105 Stephan Tobies. ii.
(6) Systems - performance *SAT, KSATC, DLP and TA: a comparative analysis . . . . . . . . . . . . . . . . . 110 Enrico Giunchiglia, Fausto Giunchiglia, Armando Tacchella An Empirical Evaluation of Optimization Strategies for ABox Reasoning in Expressive Description Logics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Volker Haarslev, Ralf Moller Performance of DLP on Random Modal Formulae . . . . . . . . . . . . . . . . . . . . 120 Ian Horrocks, Peter Patel- Schneider. Systems - descriptions. Systems Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 Peter Patel- Schneider CICLOP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Francois de Bertrand de Beuvron, Francois Rousselot, Martina Grathwohl, David Rudlo, Michael Schlick RACE System Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 Volker Haarslev, Ralf Moller FaCT and iFaCT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 Ian Horrocks MSPASS: Subsumption Testing with SPASS . . . . . . . . . . . . . . . . . . . . . . . . . . 136 Ullrich Hustadt, Renate Schmidt, Christoph Weidenbach Integrating Descriptions and Classication into a Predicate Calculus Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 Robert MacGregor DLP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 Peter Patel-Schneider *SAT System Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 Armando Tacchella. iii.
(7) Extensions A Correspondence between Temporal Description Logics . . . . . . . . . . . . . . 145 Alessandro Artale, Carsten Lutz DFL - A Dialog Based Integration of Concept and Rule Reasoners . . . . 150 Mira Balaban, Adi Eyal On Terminological Default Reasoning about Spatial Information: Extended Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 Volker Haarslev, Ralf Moller, Anni-Yasmin Turhan, Michael Wessel Towards expressive KR systems integrating datalog and description logics: preliminary report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 Riccardo Rosati. Short papers. Information Integration through Unication of Feature Structures . . . . 165 Antonio Badia Analysis of Semantic Networks By Means of Description Logics . . . . . . . 167 Anna Dorofeyeva Classication problems in object-based representation systems . . . . . . . . 169 Amedeo Napoli Description Logic and Faceted Knowledge Representation . . . . . . . . . . . . . 172 Uta Priss. iv.
(8) (Modal) Logics for Semistructured Data Natasha Alechina. School of Computer Science and IT University of Nottingham Nottingham, NG7 2RD, UK email: nza@cs.nott.ac.uk The area of semistructured data includes collections of data items which have in some ways similar but not identical structure. Examples of semistructured data range from heterogeneous databases to the World Wide Web Abi97]. The area is obviously quite heterogeneous itself. However there are some important features common to all kinds of semistructured data, namely: data is represented as an edge labelled graph. querying data involves traversing paths in a graph. Both features suggest that modal logic techniques can be successfully used for analysing logical properties of semistructured data. The reason for believing this is that modal logics were successfully applied to express similar properties over similar graphs, for example transition systems and feature structures. Logical issues involved in working with semistructured data (the list below contains mutually dependent items!) are: which operations should a query language have. expressive power and complexity of query evaluation. how precisely do we want to describe structures (what is the right notion of equivalence). how do we express information available about the format of data (what is the right description language). The talk will contain an overview of work on semistructured data and advocate the use of `modal fragments' of transitive closure logic Imm87] as a formal basis for query and description languages for semistructured data. By a modal fragment of some language containing rst order quantiers 8 and 9 we mean a fragment where the range of quantiers is restricted to elements which are `accessible' from the parameters of the quantied formula Ale95]. In the context of rst order logic extended with transitive closure operator, accessibility means existence of a path. We believe that this. restriction reects the spirit of navigational query languages such as Lorel AQM97].. References. Abi97] S. Abiteboul. Querying semi-structured data. In Proceedings ICDT'97, 1997. AQM97] S. Abiteboul, D. Quass, J. McHugh, J. Widom, and J.L. Wiener. The Lorel query language for semistructured data. Journal of Digital Libraries, 1(1):68-88, 1997. Ale95] N. Alechina. Modal Quantiers. PhD thesis, ILLC, University of Amsterdam, 1995. Imm87] N. Immerman. Languages that capture complexity classes. SIAM Journal of Computing, 16(4):760-778, 1987..
(9) DA RP A’ s High Perf orm an ce Kn owled ge Ba s e (H P KB ) Progr am R o b ert Ma cGre g o r USC /Info rmati on Sc ience s Ins titut e mac grego r@isi .edu. The goal of DAR P A’ s HP K B pro gram is to demo nstra te the prac tical ity and ut ility of constr uctin g and reas oning wit h ver y lar ge kn owled ge ba ses [C ohen et al 98] . Th e con tract ors partic ipati ng in this init iativ e wer e tas ked to con struc t con vinci ng ap plica tions in specif ic mi litar y dom ains. The appl icati ons were and are constr ucted arou nd ontol ogie s and know ledge base s man aged by ge neral pur pose knowl edge repre senta tion (KR ) syste ms. The KR syste ms in use are C yc (C yc orp), Onto lingu a and ATP (S ta nford ), Oc elot and S NAR K (S R I) , Loo m and P ow erLoo m (US C /IS I ) and SME (NWU) . Th ese KR sys tems all suppor t ver y exp ressi ve la nguag es, and th ey hav e sim ilar conte xt me chani sms for su bdivi ding knowledg e. A ll of the syste ms ex cept Loom have been exten ded during the progr am by spec ial-p urpos e rea soner s des igned to accele rate and/o r bro aden the scope of th eir ded uctiv e pro cesso rs. A var iety of tr ansla tors exist for tra nslat ing betwee n differ ent pairs among thes e system s. A high percen tage of th e pro gram is de voted to manual con struc tion of kn owled ge ba ses. Addi tiona l fac tual kno wledg e has been acqu ired using text extr actio n, “kn owled ge sl urpin g”, and ex tract ion from struct ured tex tual sourc es su ch as the CIA World Fact Book. Ori ginal ly, the pr ogram was inten ded to sup port resea rch into probab ilist ic re asoni ng as well as deduct ive rea sonin g. T he di fficu lty of con struc ting sizab le ba ses of pro babil istic know ledge caus ed mo st of thes e eff orts to mig rate elsew here. How ever, othe r kin ds of reas oners are bei ng em ploye d in vario us ap plica tions , inc ludin g ana logic al re asoni ng an d geo spati al re asoni ng (N WU), the EXP E C T sy stem (IS I) , whi ch re asons with quas idec larat ive proced ures, case -base d rea sonin g (IS I), and qua litat ive simula tion (S tan ford and NWU). The guid ing force behin d the appl icati ons are ch allen ge pro blems that spec ify the do main of ap plica tion, know ledg e sou rces, exam ple questi ons, and at tes ting time, test que stion s. An innov ation of this progra m is the use of “pa ramet erize d que stion s” (P Qs ). A PQ is a struct ured Eng lish quest ion that contai ns ph rases that will be alter ed at test ing time along pre-s pecif ied dimensio ns. Thu s, ea ch PQ repr esent s a set of ques tions . F o r exa mple , the gene ral questi on: How is <te rm1> {diff erent fro m/lik e} <t erm2> was insta ntiat ed as “How is a terror-. D eb o ra h L. McG u in n e s s Sta nford Univ ersit y dlm @ksl. stanf ord.e du. ist grou p’s intere st in incr ease prest ige and in fluen ce di ffer ent from a crim inal organ izati on’s inter est in incre ase pre stige and influ ence? (The answ er is they have diff erent goa ls an d tar gets – ter roris ts se ek to incr ease prest ige amo ng th eir suppor ters to bo lster thei r cau se wh ile cri minal orga nizat ions targe t oth er cr imina l organ izati ons in order to increa se th eir chance s of monop olizi ng th eir pow er an d con trol in th e ill icit secto r. ) Each appli catio n bui lder has adopte d a number of P Qs , and is tailor ing the ir kn owled ge ba ses and so metim es ex tendi ng th eir und erlyi ng re asoni ng sy stems to reason comp etent ly wi th any ques tions gen erabl e by those P Qs . At the end of Year one, vari ous develo pers had produc ed ap plica tions that exhi bited impr essiv e rea sonin g cap abili ties. How ever, ther e was litt le in the way of instr ument ation for measu ring or ev aluat ing how th e kno wledg e in the KB s co ntrib uted to ea ch sy stem’ s perfor mance . Th is wa s par tiall y rem edied by post-h oc ana lysis of the ap plica tions . F o r Yea r 2, more caref ul mec hanis ms ha ve be en est ablis hed for ev aluat ing the appli catio ns an d ext ensiv e met rics are being colle cted. The manu al ef fort expen ded to pro duce the ontolo gies and know ledge base s has been cons idera ble. To the exten t tha t thi s kno wledg e is reu sable , this effort migh t be con sider ed ju stifi able. S om e of the instru menta tion intro duced into the syste ms du ring Year 2 is aimed at trying to quanti fy th e amo unt of Yea r 1 knowle dge that is reu sed in the Year 2 ap plica tions . S o me ex perim ents att empt to me asure use of kn owled ge hi gh up in an ontol ogy relati ve to the use of mor e spe cific know ledge low er do wn in the hiera rchie s; a demon strab le us e of hig her-l evel (more abst ract, more gene ral) knowl edge is see n as anoth er de monst ratio n of reuse . In Year 2 som e add ition al “c ritic al co mpone nt exper imen ts” were introd uced as we ll. These were aime d at ext racti ng kn owled ge an d als o at mergi ng kn owled ge bas es. The text extr actio n cri tical comp onent expe rimen t aim s to build fram es fr om te xt in put. The mergi ng exp erime nt ta kes two kn owled ge ba ses and us es St anfor d’s tools to su pport a kn owled ge en ginee r in a tas k of com binin g kno wledg e bas es – thus helpi ng id entif y whe n two term s sho uld be mer ged into one or have link s rel ating the two object s..
(10) The foll ow-on prog ram to HP K B wil l be calle d the R ap id Kn owled ge Fo rmula tion (R KF ) prog ram. That pro gram will targe t the cons truct ion of too ls th at en able dom ain expert s who are not versed in logic or ot her KR rel ated techn ology to constr uct usable know ledge base s. If RKF is suc cessf ul, the co st of cons truct ing knowle dge bas es wi ll be redu ced signif icant ly, enabli ng th e rou tine con struc tion of la rge knowle dge based appli catio ns.. R e f e r e n ce s [C o hen et al 98] P . Coh en, R . S ch rag, E. Jo nes, A. P ea se, A. Lin , B. S ta rr, D. Gun ning, M. B urke. , The DAR P A Hig h-P er forma nce Knowle dge B ases proje ct, in AI Magaz ine, 19 (4)..
(11) Reasoning with enhanced Temporal Entity-Relationship Models Alessandro Artale Department of Computation UMIST, Manchester, UK artale@co.umist.ac.uk Abstract Recent efforts in the Conceptual Modelling community have been devoted to properly capturing time-varying information, and several proposals of temporally enhanced Entity-Relationship (ER) exist. This work gives a logical formalisation of the various properties that characterise and extend different temporal ER models which are found in literature. The formalisation we propose is based on Description Logics (DL), which have been proved useful for a logical reconstruction of the most popular conceptual data modelling formalisms. The proposed DL has the ability to express both enhanced temporal ER schemas and integrity constraints in the form of complex inclusion dependencies. Reasoning in the devised logic is decidable, thus allowing for automated deductions over the whole conceptual representation, which includes both the ER schema and the integrity constraints over it.. 1. Introduction. In the temporal ER community two different main modelling approaches have been devised to provide support for the conceptualisation of valid time. The implicit approach hides the temporal dimension in the interpretation structure of the ER constructs. Thus, a temporal ER model does not include any new specific temporal construct with respect to a standard ER model. Each ER construct is always interpreted with a temporal semantics, so that instances of temporal entities or relationships are always potentially timevarying objects. The explicit approach, on the other hand, retains the non-temporal semantics for the conventional ER constructs, while adding new syntactical constructs for representing temporal entities and relationships and their temporal interdependencies. The advantage of the explicit approach is the so called upward compatibility: the meaning of conventional (legacy) ER diagrams when used inside a temporal model remains unchanged. This is crucial, for example, in modelling data warehouses or federated databases, where sources may be a collection of both temporal and legacy databases. A logical formalisation is introduced in this paper that can cover both the implicit and the explicit approaches. The. Enrico Franconi Department of Computer Science University of Manchester, UK franconi@cs.man.ac.uk idea is to provide a formalisation for implicit temporal ER models, enriched with the ability to express a powerful class of temporal integrity constraints. While instances of ER entities or relationships are potentially time-varying objects, integrity constraints can impose restrictions in the temporal validity of such objects. The formalisation is powerful enough that it is possible to explicitly state as integrity constraints the distinction between time-varying and snapshot (i.e., time invariant) constructs. In this way, an ER diagram may contain both temporal and non-temporal information, providing the ability to capture the explicit approach. The formalisation presented in this paper is based on the expressive temporal Description Logic (DL) ALCQIT DL, which is able to capture conventional ER models and has the ability to express a powerful class of temporal inclusion dependency constraints. Advantages of ALCQIT is its high expressivity combined with desirable computational properties – such as decidability, soundness and completeness of deduction procedures, allowing for a complete calculus for temporal integrity constraints. The paper is organised as follows. Section 2 introduces the temporally enhanced ER model, in both the implicit and explicit approaches. Section 3 briefly introduces the adopted temporal DL. Section 4 will show how temporal ER schemas can be encoded into the temporal DL, how additional temporal integrity constraints can be imposed on schemas, and how it is possible to reason in this framework. The final section describes how integrity constraints can encode time-varying and snapshot constructs.. 2. The Temporal ER Model. In this Section we informally introduce the temporally enhanced ER model. Let us consider first a standard ER diagram, i.e., a diagram where no explicit temporal constructs appear. According to the implicit approach, a temporally enhanced ER diagram does not have any specific temporal construct, since it is intended that every construct has always a temporal interpretation. Thus, the syntax of the temporal model is the same as the standard one, and the temporal dimension is considered only at the semantical level. We have defined a first-order semantics for the temporally enhanced ER model – in the implicit approach –.
(12) ID. C D ! A j. #. join_date. Name (1,N). Belongs_to. First_name Name. Department. Employee. Last_name. (1,N). Profit. (1,N). (1,1). hours/week Amount. (0,N). (1,N). period. Works_for (1,N). Birth_date. Responsible for. (1,N) (1,N). Start_date. End_date. (1,1). Salary. work_period. Amount. Project. (1,N). Start_date. Salary_period Start_date. End_date. Manager. End_date. (1,1). ID. Budget. (1,1). Manages Rank Start_date. Type. >j ?j :C j CuDj CtDj 8R. C j 9R. C j f "j f :Cj n R. C j n R. C j CU D j CSD j 3 Cj 3; C j 2 Cj 2; C R S ! P j fj R; j RjC j RS +. Figure 1. The temporal ER diagram. by extending the non temporal semantics introduced in [3]. Interpretations of a temporal ER diagram are called legal database states. Intuitively, a legal database state is a temporally dependent database – i.e., a finite relational structure whose tuples depend on time – which conforms to the constraints imposed by the schema. Let us consider the example ER diagram of Figure 1; this diagram is the running example considered in the survey paper [6]. As we have noticed before, the implicit approach does not consider the temporal constructs related to the validity time of entities and relationships (see, e.g., the TEER model in [4]). Thus, the example diagram should be modified, since there are some of those disallowed constructs. The Profit relationship becomes an attribute of the entity Department, the Salary relationship becomes an attribute of the entity Employee, the Work-period entity disappears, since it just denotes the validity time of the relationship Works-for. The resulting diagram is such that every construct has its own implicit validity time. We consider now an enhancement of the temporal ER model by means of integrity constraints. The following constraints may be imposed over the example ER diagram: managers are the only employees who do not work for a project (she/he just manages it);. . a manager becomes qualified after a period when she/he was just an employee. The presence of the above constraints limits the number of legal database states, since not all the unconstrained databases conform to the newly introduced constraints. The enriched schema, which includes both the ER diagram and the integrity constraints, logically implies the following:. . for every project, there is at least an employee who is not a manager,. each manager worked in a project before managing some (possibly different) project. Please note that these deductions are not trivial, since from the ER schema the cardinality constraints do not impose that employees necessarily work in a project.. +. 1. I. I. n C I(t) C I(t) \ DI(t) C I(t) DI(t) fi 2 II j 8j . RII((tt)) (ij ) ) CII(t()t) (j )g fiI2 j 9jI.(Rt) (ij ) ^ C (j )g n dom fI(t) I(t) I(t) fi 2 dom f j C (f (i))g fi 2 II j ]fj 2 II j RII((tt)) (ij ) ^ C II((tt)) (j )g ng fi 2 j ]fj 2 j R (ij ) ^ C (j )g ng fi 2 I j 9v. v > t ^ DI (v) (i) ^I (w) 8w. (t < w < v) ! C (i)g fi 2 I j 9v. v < t ^ DI (v) (i) ^I (w) 8w. (v < w < t) ! C (i)g fi 2 II j 9v. v > t ^ CII ((vv)) (i)g fi 2 I j 9v. v < t ^ C I(v()i)g fi 2 I j 8v. v > t ! CI(v) (i)g fi 2 j 8v. v < t ! C (i)g f(Iijt ) 2 II II jt RI t (ji)g R \( C ) It It ( ). R. ( ) ( ). S. ( ). ( ). Figure 2. ALCQIT and its semantics.. In the case where an explicit approach to provide temporal support is adopted, new constructs are usually added to represent the temporal dimension of the model. At the cost of adding new constructs, this approach has the advantage of preserving the atemporal meaning of conventional (legacy) ER schemas when embedded into temporal ER diagrams: this property is called upward compatibility. This crucial property is not realizable within the standard implicit temporal approach. According to our approach, both entities and relationships in the explicit temporal ER model can be either unmarked, in what case they are considered snapshot constructs (i.e., each of their instances has a global lifetime, as in the case they derive from a legacy diagram), or explicitly temporary marked (i.e., each of their instances has a temporary lifetime).. 3. The Temporal Description Logic. We introduce very briefly in this section the ALCQIT temporal DL, which is obtained by combining a standard tense logic and the standard non-temporal ALCQI DL [2]. The basic types of the DL are concepts, roles, and features. According to the syntax rules at the left of Figure 2, ALCQI concepts (denoted by the letters C and D) are built out of primitive concepts (denoted by the letter A), roles (denoted by the letter R S ), and primitive features (denoted by the letter f ); roles are built out of primitive roles (denoted by the letter P ) and primitive features. We define the meaning of concepts as sets of individuals and the meaning of roles as sets of pairs of individuals. A temporal structure T = (P <) is assumed, where P is a.
(13) set of time points and < is a strict linear order on P . Formally, an ALCQIT temporal interpretation over T is a : triple I = hT I I (t)i, consisting of a set I of individuals (the domain of I ) and a function I (t) (the interpretation function of I ) mapping, for each t 2 P , every concept to a subset of I , every role to a subset of I I , and every feature to a partial function from I to I , such that the equations at the right of Figure 2 are satisfied. A knowledge base is a finite set of terminological axioms of the form C v D. An interpretation I over a temporal structure T = (P <) satisfies a terminological axiom C v D if C I (t) DI (t) for every t 2 P . A knowledge base is satisfiable in the temporal structure T if there is a temporal interpretation I over T which satisfies every axiom in ; in this case I is called a model over T of . Checking for KB satisfiability is deciding whether there is at least one model for the knowledge base. logically implies an axiom C v D in the temporal structure T (written j= C v D) if C v D is satisfied by every model over T of . In this latter case, the concept C is said to be subsumed by the concept D in the knowledge base and the temporal structure T . Concept subsumption can be reduced to concept satisfiability since C is subsumed by D in if and only if (C u :D) is unsatisfiable in . The tense-logical extension of ALCQI has been inspired by the works of [9, 12]. It is possible to show that reasoning in ALCQIT (i.e., deciding knowledge base satisfiability and deciding logical implication) is decidable; the proof is based on a reduction to the decidable language introduced in [12]. The computational complexity of reasoning in ALCQIT is EXPTIME-hard. As an example let us consider the axiom stating that any living mortal should live in some place, remains alive until it will die, and at some point in the past was born:. u. v (9 U 2; : S2 :. )u. Mortal LivingBeing LIVES-IN. Place + LivingBeing LivingBeing LivingBeing LivingBeing. ( (. 4. )u ). Encoding the Implicit Model. We show in this Section how an ER schema with implicit representation of time – as informally introduced in Section 2 – can be expressed as a ALCQIT knowledge base. Let us first consider the translation from an ER diagram (without considering the integrity constraints) to a ALCQIT knowledge base: an ER diagram D is translated according to table 3 into a corresponding knowledge base where each domain, entity or relationship symbol corresponds to a primitive concept, and each attribute or ER-role symbol corresponds to a primitive feature. Temporal integrity constraints are expressed by means of additional terminological axioms in . More precisely, an integrity constraint is any inclusion dependency which can be expressed by means of a terminological axiom of the kind C v D. It is important to emphasise the fact. D ISA. link between two enti-. ties E F attribute A with domain D of an entity E ISA link between two relationships R S attribute A with domain D of a relationship R relationship R relating n entities E1 : :: En by means of the ER-roles. PER1 :: : PERn. minimum cardinality constraint n = 0 in a ER-role PER relating a relationship R with and entity E maximum cardinality conin a ER-role straint n = PER relating a relationship R with and entity E. 6. 6 1. EvF EvA:D RvS RvA:D R v (PER1 : E1 ) u : :: u (PERn : En ) E v n (PER );1 . R E v n (PER );1 . R. Figure 3. The translation ER ! DL. that in this approach the integrity constraints are part of the schema, so that reasoning is carried on by taking in complete account all the information contained in the schema. Based on the results of [3], we have proved a theorem stating that the translation is correct, in the sense that there is a precise correspondence between legal database states of D and models of the derived knowledge base . The existence of this correspondence is such that, whenever the problem of checking an ER schema against a property has a specific solution, then the corresponding reasoning problem in the DL has a corresponding solution, and vice-versa. Thus, it is possible to exploit standard reasoning procedures in the DL for checking properties of the ER schema – for example, by using a temporal extension of a state-of-theart DL system such as iFaCT [7]. The reasoning problems we are mostly interested in are consistency of a ER schema – which is mapped to a satisfiability problem in the corresponding DL knowledge base – and logical implication within a ER schema – which is mapped to a logical implication problem in the corresponding DL knowledge base. As a final remark, it should be noted that the high expressivity of DL constructs can capture an extended version of the basic ER model, which includes not only taxonomic relationships, but also arbitrary boolean constructs to represent so called generalized hierarchies with disjoint unions; entity definitions by means of either necessary or sufficient conditions or both [3]. Example. Let us consider the example introduced in Section 2. We first translate the fragment of the ER diagram (Figure 1) involving the entities Project, Employee, Manager and the relationship Works-for in the DL knowledge base ER :. v v9 v. ;:. u. :. WORKS-FOR has-prj Project has-emp Employee Project has-prj 1 . WORKS-FOR Manager Employee.
(14) We then encode the integrity constraints, which are expressed by means of terminological axioms in a knowledge base IC :. . . Managers are the only employees who do not work for a project: Employee u 8has-emp;1. :WORKS-FOR v Manager A manager becomes qualified after a period when she/he was just an employee: Manager. v Qualified S (Employee u :Manager). It turns out that the following integrity constraints are logically implied from ER IC :. . . For every project, there is at least an employee who is not a manager:. ER IC j= Project v 9(has-prj;1
(15) has-emp). :Manager. A manager worked in a project before managing some (possibly different) project:. ER IC j=; Manager v 3 9(has-emp;1
(16) has-prj). Project Moreover, if we change in ER the minimum cardinality. of the participation of employees to the Works-for relationship to one (i.e., we make it a mandatory participation):. v 9has-emp;1. WORKS-FOR then, even if ER is satisfiable, ER IC is an unsatEmployee. isfiable knowledge base, because of the first integrity constraint. For the abovementioned theorem, no legal DB state exists for the ER schema including the constraints.. 5. Encoding the Explicit Model. This Section shows how the proposed formalisation can encode explicit temporal ER models by simply imposing specific constraints defining snapshot and temporary constructs, thus maintaining upward compatibility.. 5.1. Snapshot Vs. Temporary Entities. The ALCQIT DL is able to capture explicit temporal ER models by first applying the translation given in the previous Section, and then adding precise axioms to distinguish between snapshot and temporal constructs. In the following, axioms for entities are illustrated. In the next Section, the analogous for relationships will be showed. A snapshot entity is axiomatised as follows:. E v (2+ E ) u (2; E ). (Snapshot axiom). expressing that whenever the entity is true it is necessarily true in every past and future time point. Indeed, instances of snapshot entities have necessarily a global lifetime. On the other hand, a temporary entity is axiomatised by the following constraint:. E v (3+ :E ) t (3; :E ). (Temporary axiom). asserting that there must be a past or future time point where the entity does not hold. Indeed, instances of temporary entities have necessarily a limited lifetime. Using the reasoning capabilities of ALCQIT it is possible to support the database designer to discover relevant schema properties. As an example of the logical implications holding in a diagram making use of both snapshot and temporary entities, let us consider the interaction between entities via ISA links. Let us suppose that there is an ISA link between a snapshot entity E 1 and a temporary entity E2. This temporal ER diagram is translated into the following unsatisfiable knowledge base:. E1 v (2+ E1) u (2; E1) E2 v (3+ :E2) t (3; :E2) E1 v E2. Thus, a snapshot entity can not be a subclass of a temporary entity, this is true also whenever such a kind of taxonomic relation is derived in the temporal ER model. From these considerations it is easy to understand why the following implications hold:. f E2 v (+3+ :E2) t (;3; :E2) E1 v E2 g j= E1 v (3 :E1) t (3 :E1) f E1 v (+2+ E1) u (;2; E1) E1 v E2 g j= E2 v (2 E2 ) u (2 :E2). i.e., necessarily, every subclass of a temporary entity must be temporary; and a superclass of a snapshot entity must be a snapshot entity. Conversely, nothing can be said with respect to subclasses of snapshot entities. For example, a schema where a temporary entity is a subclass of a snapshot entity is consistent. An incorrect ER schema can be the result of disjoint subclasses – i.e., a partitioning. A schema is inconsistent if exactly one of a whole set of snapshot disjoint subclasses is temporary [8]. Without loss of generality, let us illustrate the case where E1 E2 are disjoint subclasses of the entity E , with E1 snapshot and E2 temporary, then such an ER schema is inconsistent. Indeed, the corresponding knowledge base is unsatisfiable (note that the first set of axioms correspond to the disjoint subclass axioms):. E v E1 t E2 E1 v E u :E2 E2 v E E1 v (2+ E1) u (2; E1) E2 v (3+ :E2) t (3; :E2). The following is an immediate consequence of the above inconsistent schema:. f E v E1 t+ E2 E1 ;v E u :E2 E2 v E E1 v (2 E1 ) u (2 E1) g j= E2 v (2+ E2) u (2; E2). i.e., an ER schema with exactly one entity whose temporal behaviour is unknown among a whole set of snapshot disjoint subclasses, implies that this entity is snapshot..
(17) 5.2. Snapshot Vs. Temporary Relationships. The case for relationships is more complex. Temporary relationships are captured by enforcing the temporary axiom on relationships – in a way analogous to the case of temporary entities:. R v (3+ :R) t (3; :R). (Temporary axiom). To capture snapshot relationships, in addition to the snapshot axiom, we need to force each ER-role to be time invariant. For this purpose, the so called global features are needed. They are features whose value does not depend on time: we will indicate such particular kind of feature by prefixing the feature name with a “?”. Atomic global features are interpreted as partial functions independent from time: 8t v 2 P . ?gI (t) = ?gI (v). Using global features instead of generic features for ERroles defining a relationship results in a homogeneous relationship – i.e., a relationship with tuples whose values are valid at the same time period. Homogeneous relationships are encoded by means of the following axiom:. R v (?PER : E1) u : : : u (?PERn : En) 1. (Homog. ax.). Snapshot relationships are necessarily global and homogeneous relationships. Thus, if R is a snapshot relationship involving the entities E 1 : : : En, the following axioms should be added to :. R v (2+ R) u (2; R) R v (?PER : E1) u : : : u (?PERn : En) 1. The two axioms are such that whenever a tuple belongs to a snapshot relationship, then the very same tuple is assumed to belong to the relationship at every time. The interaction between temporal and snapshot constructs can result in an inconsistent ER schema that can be checked and discarded automatically. This is case when a snapshot relationship R involves a temporary entity. Indeed, the following knowledge base is unsatisfiable:. R v (2+ R) u (2; R) R v (?PER : E1) u : : : u (?PERn : En) Ei v (3+ :Ei) t (3; :Ei ) 1. i.e., snapshot relationships cannot have temporary entities as participants. On the other hand, temporary relationships admit snapshot entities since the entity instances participate in the relationship only for a temporary time – i.e., during the validity time of the relationship.. 6. Conclusions. This preliminary work gives a logical formalisation of a temporal ER model, which has the ability to express both enhanced temporal ER schemas and (temporal) integrity constraints in the form of general axioms imposed on the schema itself. The formal language we have proposed is a. member of the family of Description Logics, and it has a decidable reasoning problem, thus allowing for automated deduction over the whole conceptual representation. We have also shown how the integrity contraints can encode the distinction between time-varying and snapshot constructs. This work is just at the beginning. The most promising research direction to be explored is to better characterise the expressivity of temporal integrity constraints in order to axiomatise several extensions as proposed in the literature of temporal ER models. Currently, we are exploring the possibility to axiomatise the difference between homogeneous and heterogeneous relationships [5, 10], and to express historical marks (H-marks) [11]. This work was partially supported by the “Foundations of Data Warehouse Quality” (DWQ) European ESPRIT IV Long Term Research (LTR) Project 22469.. References [1] A. Artale and E. Franconi. Temporal ER modeling with description logics. In Proc. of the 6 th International Workshop on Knowledge Representation meets Databases (KRDB’99), 1999. Also in Proc. of the 1999 International Workshop on Description Logics (DL’99). [2] D. Calvanese, G. De Giacomo, M. Lenzerini, and D. Nardi. Reasoning in expressive description logics. In A. Robinson and A. Voronkov, editors, Handbook of Automated Reasoning. Elsevier, 1999. To appear. [3] D. Calvanese, M. Lenzerini, and D. Nardi. Description logics for conceptual data modeling. In J. Chomicki and G. Saake, editors, Logics for Databases and Information Systems. Kluwer, 1998. [4] R. Elmasri and S. B. Navathe. Fundamentals of Database Systems. Benjamin/Cummings, 1994. [5] S. Gadia. A homogeneous relational model and query languages for temporal databases. ACM Transactions On Database Systems, 13:418–448, 1988. [6] H. Gregersen and J. S. Jensen. Temporal Entity-Relationship models - a survey. IEEE Transactions on Knowledge and Data Engineering, 1999. To appear. [7] I. Horrocks and U. Sattler. A description logic with transitive and inverse roles and role hierarchies. Journal of Logic and Computation, 1999. To appear. [8] P. McBrien, A. Seltveit, and B. Wangler. An EntityRelationship model extended to describe historical information. In Proc. of CISMOD’92, pages 244–260, 1992. [9] K. D. Schild. Combining terminological logics with tense logic. In Proc. of the 6 th Portuguese Conference on Artificial Intelligence (EPIA’93), 1993. [10] A. Tansel and E. Tin. Expressive power of temporal relational query languages and temporal completeness. In O. Etzion, S. Jajodia, and S. Sripada, editors, Temporal Databases - Research and Practice, pages 129–149. Springer-Verlag, 1998. [11] C. Theodoulidis, P. Loucopoulos, and B. Wangler. A conceptual modelling formalism for temporal database applications. Information Systems, 16(3):401–416, 1991. [12] F. Wolter and M. Zakharyaschev. Temporalizing description logics. In Proceedings of FroCoS’98, 1998..
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