?. Preuve and . Pour-qu, une séquence de vecteurs de vérité satisfasse l'assertion p i , il faut et il suffit qu'elle se termine par un

U. Objet and O. Vérifie, H) D'après le théorème 10.E, cela revient à vérifier que S ? (O) est un mot du langage décrit par R(H) Vérifier une assertion historique pour un objet revient donc à vérifier qu'un mot appartient au langage décrit par une expression régulière

L. Traqueurs-permettent-de-contourner-cette-mesure, Reprenons l'exemple précédent Du fait du facteur de requête, il n'est plus possible d'obtenir le résultat de la requête count(C AND X) Supposons alors que l'on arrive à décomposer la condition C AND X sous la forme A AND B telle que count(A)? k et count(A AND (NOT B))? k. A AND (NOT B) est le traqueur de C AND X pour l'état courant de BDS. On a alors count(C AND X)= count(A)-count(A AND (NOT B)). Or, les deux termes de la soustraction sont calculables puisque chacun

M. Abadi and L. Cardelli, A Theory of Objects, Monographs in Computer Science, 1996.
DOI : 10.1007/978-1-4419-8598-9

S. Abiteboul, Querying semi-structured data, Proc. Int. Conf. ICDT, 1997.
DOI : 10.1007/3-540-62222-5_33

S. Abiteboul, L. Herr, and J. Van-den-bussche, Temporal versus First-Order Logic to Query Temporal Databases, Int, Conf. Principles of Database Systems, 1996.

S. Abiteboul and V. Vianu, Transactions and integrity constraints, Proceedings of the fourth ACM SIGACT-SIGMOD symposium on Principles of database systems , PODS '85, 1985.
DOI : 10.1145/325405.325439

A. Aho and J. Ullman, The Theory of Parsing, Translation and Compiling, 1972.

M. Aigner, Combinatorial Theory, Grundlehren der mathematischen Wissenschaften 234, 1979.

A. Aiken, J. Widom, and J. Hellerstein, Behaviour of Database Production Rules : Termination, Confluence, and Observable Determinism, Proc. Int. Conf. ACM SIGMOD, pp.59-68, 1992.

A. Albano, M. Diotallevi, and G. Ghelli, Extensible Objects for Database Evolution: Language Features and Implementation Issues, Proc. Int. Work. on Database Programming Languages, pp.203-223, 1995.
DOI : 10.1007/978-3-642-59623-0_17

A. Corp, The NewtonScript Programming Language, Newton System Group, 1996.

A. Corp, Newton's Programmers Guide : System Software, 1996.

E. Audureau, P. Enjalbert, and L. Farinas-del-cerro, Logique Temporelle : sémantique et validation de programmes parallèles, collection études et recherches en informatique, 1990.

F. Bancilhon and N. Spyratos, Protection of Information in Relational Databases, Proc. Int. Conf. VLDB, 1977.

C. Bassolet, A. Simonet, and M. Simonet, Probabilistic classification in Osiris, a view-based OO DBMS and KBMS, Proceedings of 7th International Conference and Workshop on Database and Expert Systems Applications: DEXA 96, 1996.
DOI : 10.1109/DEXA.1996.558273

D. Bell and L. Lapaluda, Secure Computer Systems : Unified Exposition and Multics Interpretation, MITRE, 1975.

P. Bernstein, B. Blaustein, and E. M. Clarke, Fast Maintenance of Semantic Integrity Assertions Using Redundant Aggregate Data, Proc. Int. Conf. VLDB, 1980.

E. Bertino and H. Weigand, An Approach to Authorisation Modelling in Object Oriented Database Systems, Data & Knowledge Engineering, vol.12, issue.1, 1994.

N. Bourbaki, Théorie des Ensembles. Chap. I et II, Actualités scientifiques et industrielles, 1954.

F. Bry, H. Decker, and R. Manthey, A Uniform Approach to Constraint Satisfiability in Deductive Databases, Proc. Int. Conf. on Extending Database Technology, 1988.

F. Bry and R. Manthey, Checking Consistency of Database Constraints : a Logical Basis, Proc. Int. Conf.VLDB, 1986.

P. Buneman, Semistructured Data, Int. Conf. On Principles of Database Systems, 1997.
DOI : 10.1145/263661.263675

P. Buneman, S. B. Davidson, and D. Suciu, Programming Constructs for Unstrucured Data, Int. Work. on Database Programming Languages, 1996.

U. Bussolati, M. G. Fugini, and G. Martella, A Conceptual Framework for Security System Design, Proc. IFIP World Conf., Septembre, 1983.

M. Casanova, L. Tucherman, and A. L. Furtado, Enforcing Inclusion Dependencies and Referential Integrity, Proc. Int. Conf. VLDB, 1988.

S. Ceri and J. Widom, Deriving Production Rules for Constraint Maintenance, Proc. Int. Conf. VLDB, 1990.

J. Chomicki, History-less checking of dynamic integrity constraints, [1992] Eighth International Conference on Data Engineering, pp.557-564, 1992.
DOI : 10.1109/ICDE.1992.213153

J. Chomicki, History-less Checking of Temporal Integrity Constraints, non publié, 1994.

J. Chomicki and D. Niwinski, On the Feasibility of Checking Temporal Integrity Constraints, Jour. of Computer and System Sciences, 1995.

C. Collet, Bases de Données Actives : des Systèmes Relationnels aux Systèmes à Objets, Thèse d'Habilitation à Diriger les Recherches, Laboratoire Logiciels, Systèmes et Réseaux ? IMAG, 1996.

A. B. Cremers and G. Domann, AIM-An Integrity Monitor for the Database System Ingres, Proc. Int. Conf. VLDB, 1983.

C. J. Date, An Introduction to Database Systems, 1990.

U. Dayal, E. Hanson, and J. Widom, Active Database systems, dans Modern Database systems: The Object Model, Interoperability, and Beyond, édité par Won Kim, 1994.

X. Delannoy, Understanding the tension between transition rules and confidentiality, Proc. British Nat. Conf. On Databases (BNCOD), pp.92-106, 1996.
DOI : 10.1007/3-540-61442-7_6

X. Delannoy, Typing Persistent Objects a posteriori to Manage Semi-Structured Data, Exposé donné à Ibex Object Systems Corp, www.ibex.ch), 1997.

X. Delannoy, D. Vigna, and C. , Binary integrity constraints against confidentiality, Proc. Int. Conf. on Database and Expert Systems Applications (DEXA), pp.264-275, 1996.
DOI : 10.1007/BFb0034687

X. Delannoy, D. Vigna, and C. , Secret Data Exactly Unveiled with 2 -ary Constraints : the Manicheistic Situations, Int. Work. on Database Theory, en conjonction avec la European Summer School in Logic, Language and Information (ESSLI), 1997.

X. Delannoy, D. Vigna, and C. , Secrets, Unveilings and Fraud : a General Framework and the Study of a Special Case, 1998.

X. Delannoy, La Cohérence dans les Bases de Données, Rapport de recherche RR-936I, 1994.

X. Delannoy, A. Simonet, and M. Simonet, Database Views wtih Dynamic Assertions, Proc. Int. Conf. on Object Oriented Information Systems (OOIS), 1996.
DOI : 10.1007/978-1-4471-0973-0_23
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.48.9343

C. Delobel, Contributions théoriques à la conception d'un système d'information, Thèse de Doctorat d'Etat, 1973.

D. Denning and P. Denning, Certification of programs for secure information flow, Communications of the ACM, vol.20, issue.7, 1977.
DOI : 10.1145/359636.359712

K. Dittrich, S. Gatziu, and A. Geppert, The Active Database Management System Manifesto: A Rule-base of ADBMS Features, Proc. Int. Work. on Rules In Database Systems, 1995.

. Dod, Connu aussi sous le nom de « Orange Book, 1985.

D. Menjívar and M. , Expression de Contraintes d'Intégrité dans un SGBD Temporel à Objets, 1997.

H. D. Ehrich, U. W. Lipeck, and M. Gogolla, Specification, Semantics, and Enforcement of Dynamic Database Constraints, Proc. Int. Conf. VLDB, 1984.

R. Elmasri and S. Navathe, Fundamentals of Database Systems, 1989.

R. Fagin, Multivalued dependencies and a new normal form for relational databases, ACM Transactions on Database Systems, vol.2, issue.3, 1977.
DOI : 10.1145/320557.320571

M. Fauvet, J. Canavaggio, and P. Scholl, Tempos : un Modèle d'Historiques pour un SGBD Temporel à Objets, Proc. Nat. Conf. Bases de Données Avancées, 1997.

M. Fernandez, L. Popa, and D. Suciu, A structure-based approach to querying semi-structured data, Int. Workshop on Database Programming Languages, 1997.
DOI : 10.1007/3-540-64823-2_9

M. G. Fugini and G. Martella, ACTEN : A Conceptual Model for Security System Design, Computers and Security, 1984.

D. Gabbay and P. Mc-brien, Temporal Logic and Historical Databases, Proc. Int

G. Gardarin and M. Melkanoff, Proving Consistency Of Database Transactions, Fifth International Conference on Very Large Data Bases, 1979., 1979.
DOI : 10.1109/VLDB.1979.718144

M. Gertz and U. Lipeck, Deriving integrity maintaining triggers from transition graphs, Proceedings of IEEE 9th International Conference on Data Engineering, pp.22-29, 1993.
DOI : 10.1109/ICDE.1993.344081

M. Gertz and U. Lipeck, Temporal" Integrity Constraints in Temporal Databases. Recent Advances in Temporal Databases, Proc. Int. Work. on Temporal Databases, pp.77-92, 1995.

P. Griffiths and W. Bradford, An authorization mechanism for a relational database system, ACM Transactions on Database Systems, vol.1, issue.3, pp.242-255, 1976.
DOI : 10.1145/320473.320482

A. Guénoche, Construction du Treillis de Galois d'une Relation Binaire, Mathématiques, Informatique et Sciences Humaines, pp.41-53, 1990.

A. Gupta and J. Widom, Local Verification of Global Integrity Constraints in Distributed Databases, Proc. Int. Conf. ACM SIGMOD, Mai, 1993.

J. Guttag and J. Horning, The Algebraic Specification of Abstract Data Types, Acta Informatica, 1978.

V. Harinarayan and A. Gupta, Optimization using tuple subsumption, Proc. Int. Conf. on Database Theory (ICDT), pp.338-352, 1995.
DOI : 10.1007/3-540-58907-4_26

J. He and V. Gligor, Formal methods and automated tool for timing-channel identification in tcb source code, Second European Symp. on Research in Computer Security, 1992.
DOI : 10.1007/BFb0013892

J. Hoare, An Axiomatic Basis for, Computer Programming, CACM, vol.12, issue.10, pp.576-580, 1969.

J. Hopcroft and J. Ullman, Introduction to Automata Theory, Languages and Computation, 1979.

A. Hsu and T. Imielinski, Integrity Checking for Multiple Updates, Proc. ACM SIGMOD Int. Conf. on Management of Data, 1985.
DOI : 10.1145/318898.318914

S. Jajodia and R. Sandhu, Toward a Multilevel Secure Relational Data Model

M. Jarke, S. Mazumdar, E. Simon, and D. Stemple, Assuring Database Integrity, Jour. of Database Administration, vol.1, issue.1, pp.391-400, 1990.

M. Jeusfeld and M. Jarke, From relational to object-oriented integrity simplification, Proc. Int. Conf. on Deductive and Object Oriented Databases, 1991.
DOI : 10.1007/3-540-55015-1_25

R. Kowalski, F. Sadri, and P. Soper, Integrity Checking in Deductive Databases, Proc. Int. Conf. VLDB, 1987.

V. Küchenhoff, On the efficient computation of the difference between consecutive database states, Proc. Int. Conf. on Deductive and Object Oriented Databases (DOOD), 1991.
DOI : 10.1007/3-540-55015-1_26

C. Kung, A Temporal Framework for Database Specification and Verification, Proc. Int. Conf. VLDB, 1984.

B. Lampson, A note on the confinement problem, Communications of the ACM, vol.16, issue.10, 1973.
DOI : 10.1145/362375.362389

U. Lipeck and D. Feng, Construction of Deterninistic Transition Graphs from Dynamic Integrity Constraints, Proc. Int. Work. on Graph Theoric Concepts in Computer Science, 1988.

U. Lipeck and G. Saake, Monitoring dynamic integrity constraints based on temporal logic, Information Systems, vol.12, issue.3, pp.255-269, 1987.
DOI : 10.1016/0306-4379(87)90004-4

K. Loepere, The Covert Channel Limiter Revisited, Operating System Review, 1989.

W. Mccune and L. Henschen, Maintaining state constraints in relational databases: a proof theoretic basis, Journal of the ACM, vol.36, issue.1, 1989.
DOI : 10.1145/58562.59302

Z. Manna and A. Pnueli, The Temporal Logic of Reactive and Concurrent Systems - Specification, 1991.

H. Mannila and K. Räihä, The design of Relational Databases, 1992.

V. Markowitz, Referential Integrity Revisited: An Object Oriented Approach, Proc. Int. Conf. VLDB, 1990.

V. Markowitz, Safe Referential Integrity Structures in Relational Databases, Proc. Int. Conf. VLDB, 1991.

H. Martin, M. Adiba, and B. Defude, Consistency checking in object oriented databases: A behavioral approach, Proc. Int. Conf. CIKM, 1992.
DOI : 10.1007/3-540-57419-0_4

S. Mazumdar, D. Stemple, and T. Shread, Resolving the Tension between Integrity and Security Using a Theorem Prover, Proc. Int. Conf. on Management of Data, pp.233-275, 1988.

C. B. Medeiros, G. Jomier, and W. Cellary, Maintaining Integrity Constraints across Versions in a Database, 1992.

C. B. Medeiros and P. Pfeffer, Object integrity using rules, Proc. Europ. Conf. on Object Oriented Programming, 1991.
DOI : 10.1007/BFb0057024

J. Melton and J. Melton, Senior Architect of Standards for Sybase Corp. and Editor of the ISO SQL-92 and emerging SQL-3 standards, 1995.

J. Melton and A. Simon, Understanding the new SQL Standard -A complete Guide, 1993.

M. Morgenstern, Constraint Equation: Declarative Expression of Constraints With Automatic Enforcement, Proc. Int. Conf. VLDB, 1984.

J. M. Nicolas, Logic for Improving Checking in Relational Databases, Acta Informatica, vol.18, issue.3, 1982.

A. Olivé, Integrity Constraint Checking In Deductive Databases, Proc. Int. Conf. VLDB, 1991.

M. T. Ozsu and P. Valduriez, Distributed Database Design : Fragmentation (Chap

P. Picouet and J. P. Cheiney, SGBD et Triggers: produits d'aujourd'hui et de demain, Les bases de données avancées : du modèle relationnel au modèle orienté objet, 1992.

E. Pipard, Détections d'Incohérences et d'Incomplétudes dans les Bases de Règles: le Système INDE, 1988.

D. Plexousakis, Compilation and simplification of temporal integrity constraints, Proc. Int. Work. on Rules in Database Systems, 1995.
DOI : 10.1007/3-540-60365-4_132

D. Plexousakis, Integrity Constraint and Rule Maintenance in Temporal Deductive Knowledge Bases, Proc. Int. Conf. VLDB, 1993.

X. Qian and D. R. Smith, Integrity Constraints Reformulation for Efficient Validation, Proc. Int. Conf. VLDB, 1987.

X. Qian and G. Wiederhold, Knowledge Based Integrity Constraint Validation, Proc. Int. Conf. VLDB, 1986.

A. Sales, Types Abstraits et Bases de Données: Formalisation de la Notion de Partage et Analyse Statique des Contraintes d'Intégrité, Thèse, 1984.

J. Schlörer, Disclosure from Statistical Databases : Quantitative Aspects of Trackers, ACM Transactions on Database Systems, vol.6, issue.1, 1980.

S. Schwiderski, T. Hartmann, and G. Saake, Monitoring temporal preconditions in a behaviour oriented object model, Data & Knowledge Engineering, vol.14, issue.2, pp.143-186, 1994.
DOI : 10.1016/0169-023X(94)90042-6

A. Simonet and M. Simonet, Les classes d'équivalence induites par des dépendances interattributs: fondements pour une représentation des objets partagés dans les bases de connaissances, Rapport de Recherche, 769-I laboratoire Artemis, 1989.

A. Simonet and M. Simonet, Objects with Views and Constraints: from Databases to Knowledge bases, Proc. Int. Conf. on Object Oriented Information Systems (OOIS), 1994.
DOI : 10.1007/978-1-4471-3016-1_14

A. Simonet and M. Simonet, OSIRIS : an Object Oriented System unifying Databases and Knowledge Bases, KBKS, vol.95, 1995.

A. Simonet and M. Simonet, Classement d'Objets et Evaluation des Requêtes en Osiris, 12ièmes Journées Bases de Données Avancées, Publié sous la direction de P, Août, pp.27-30, 1996.

W. Smith, The Newton application architecture, Proceedings of COMPCON '94, 1994.
DOI : 10.1109/CMPCON.1994.282931

W. Smith, Using a Prototype-based Language for User Interface : The Newton Project's Experience, Proc. Int. Conf. on Object Oriented Programming Systems, Language and Application, 1995.

R. Smith, M. Lentczner, W. Smith, A. Taivalsaari, and D. Ungar, Prototype-Based Languages : Object Lessons from Class-Free Programming, Proc. Int. Conf. OOPSLA, 1987.

J. Stein, T. L. Anderson, and D. Maier, Mistaking Identity, Proc. Int. Work. on Database Programming Languages, 1989.

L. Stein, H. Lieberman, and D. Ungar, A shared View of Sharing : the Treaty of Orlando, Object Oriented Concepts, Applications and Databases, 1988.

M. Stonebraker, Implementation of Integrity Constraints and Views by Query Modification, Proc. Int. Conf. ACM SIGMOD, 1975.

A. Thayse, P. Gribomont, G. Hulin, A. Pirotte, D. Roelants et al., Approche logique de l'intelligence artificielle, 1989.

T. Turner, Logiques pour l'Intelligence Artificielle, 1986.

J. D. Ullman, Principles of Database and Knowledge-Base Systems, 1989.

D. Ungar and R. Smith, Self : The Power of Simplicity, Proc. Int. Conf. OOPSLA, 1987.

S. D. Urban, A. P. Karadimce, and R. B. Nannapaneni, The implementation and evaluation of integrity maintenance rules in an object-oriented database, [1992] Eighth International Conference on Data Engineering, 1992.
DOI : 10.1109/ICDE.1992.213152

W. Weber, W. Stucky, and J. Karszt, Integrity Checking in Database Systems, Information Systems, vol.8, issue.2, 1983.

J. Widom, R. Cochran, and B. Lindsay, Implementing set-oriented production rules as an extension to Starburst, Proc. Int. Conf. VLDB, 1991.

J. Widom, The Starburst active database rule system, IEEE Transactions on Knowledge and Data Engineering, vol.8, issue.4, 1996.
DOI : 10.1109/69.536251

S. Wiseman, Control of confidentiality in databases, Computers & Security, vol.9, issue.6, 1990.
DOI : 10.1016/0167-4048(90)90131-C

S. Wiseman, On the Problem of Security in Databases, IFIP WG 11.3 Proc. Int. Work. on Database Security Database Security, III : Status and Prospects, pp.301-310, 1989.

P. Wolper, Temporal logic can be more expressive, 22nd Annual Symposium on Foundations of Computer Science (sfcs 1981), 1981.
DOI : 10.1109/SFCS.1981.44
URL : http://dx.doi.org/10.1016/s0019-9958(83)80051-5

A. Yahia, L. Lakhal, and R. Ciccheti, Building inheritance graphs in object database design, Proc. Int. Conf. on Database and Expert Systems Applications (DEXA), pp.11-28, 1996.
DOI : 10.1007/BFb0034666