Logical Approaches to Incomplete Information: A Survey

The observation that it is frequently impossible to obtain complete information in the context of database applications has motivated a substantial literature seeking to extend the relational model. The paper surveys the literature on the modelling and processing of incomplete information (also known as indefinite information) using tools derived from classical logic and modal logic. The focus of the paper is on models in which query processing is decidable. Theories dealing with the quantification of indefiniteness, such as probabilistic or fuzzy models of uncertainty, are not discussed.

[1]  Billie S. Goldstein Constraints on Null Values in Relational Databases , 1981, VLDB.

[2]  Paolo Atzeni,et al.  Functional Dependencies and Constraints on Null Values in Database Relations , 1986, Inf. Control..

[3]  Joachim Biskup,et al.  A Formal Approach to Null Values in Database Relations , 1979, Advances in Data Base Theory.

[4]  Mihalis Yannakakis,et al.  On the Complexity of Database Queries , 1999, J. Comput. Syst. Sci..

[5]  Shashi K. Gadia,et al.  Incomplete Information in Relational Temporal Databases , 1992, VLDB.

[6]  Tomasz Imielinski,et al.  Complexity Tailored Design: A New Design Methodology for Databases With Incomplete Information , 1995, J. Comput. Syst. Sci..

[7]  Georg Gottlob,et al.  The Complexity of Nested Counterfactuals and Iterated Knowledge Base Revisions , 1993, IJCAI.

[8]  C. E. Alchourrón,et al.  On the logic of theory change: Partial meet contraction and revision functions , 1985 .

[9]  Joxan Jaffar,et al.  Constraint logic programming , 1987, POPL '87.

[10]  George Loizou,et al.  The Nested Relation Type Model: An Application of Domain Theory to Databases , 1990, Comput. J..

[11]  Moshe Y. Vardi Querying Logical Databases , 1986, J. Comput. Syst. Sci..

[12]  Witold Lipski,et al.  On semantic issues connected with incomplete information databases , 1979, ACM Trans. Database Syst..

[13]  Alberto O. Mendelzon,et al.  Knowledgebase Transformations , 1997, J. Comput. Syst. Sci..

[14]  Paolo Atzeni,et al.  Approaches to Updates over Weak Instances , 1989, MFDBS.

[15]  Marianne Winslett,et al.  Updating logical databases , 1990, Cambridge tracts in theoretical computer science.

[16]  Moshe Y. Vardi On the integrity of databases with incomplete information , 1985, PODS.

[17]  E. F. Codd,et al.  Extending the database relational model to capture more meaning , 1979, ACM Trans. Database Syst..

[18]  C.E. Dyreson,et al.  Valid-time indeterminacy , 1993, Proceedings of IEEE 9th International Conference on Data Engineering.

[19]  L. Thorne McCarty,et al.  Reasoning About Indefinite Actions , 1992, KR.

[20]  Chiaki Sakama,et al.  Possible Model Semantics for Disjunctive Databases , 1989, DOOD.

[21]  V. S. Subrahmanian Paraconsistent disjunctive deductive databases , 1990, Proceedings of the Twentieth International Symposium on Multiple-Valued Logic.

[22]  Yannis Vassiliou Functional Dependencies and Incomplete Information , 1980, VLDB.

[23]  John W. Lloyd,et al.  A Basis for Deductive Database Systems II , 1986, J. Log. Program..

[24]  Peter Z. Revesz On the semantics of theory change: arbitration between old and new information , 1993, PODS '93.

[25]  John Grant,et al.  Null Values in a Relational Data Base , 1977, Inf. Process. Lett..

[26]  Victor W. Marek,et al.  Autoepistemic logic , 1991, JACM.

[27]  Valeria De Antonellis,et al.  Relational Database Theory , 1993 .

[28]  C. J. Date A guide to INGRES : a user's guide to the INGRES product (a relational database management system with built-in application development facilities) from Relational Technology Inc. , 1987 .

[29]  Karen L. Kwast,et al.  The Incomplete Database , 1991, IJCAI.

[30]  Michael Adamowicz,et al.  Data base systems , 1976 .

[31]  Jack Minker,et al.  Bottom-Up Evaluation of Hierarchical Disjunctive Deductive Databases , 1991, ICLP.

[32]  Stephen J. Hegner Specification and implementation of programs for updating incomplete information databases , 1987, PODS '87.

[33]  Ron van der Meyden The Complexity of Querying Indefinite Data about Linearly Ordered Domains , 1997, J. Comput. Syst. Sci..

[34]  C. J. Date A Guide to the SQL Standard , 1987 .

[35]  Donald Perlis,et al.  Computing Protected Circumscription , 1985, J. Log. Program..

[36]  Jack Minker,et al.  Logic and Data Bases , 1978, Springer US.

[37]  Peter Gärdenfors,et al.  Belief Revision , 1995 .

[38]  Tomasz Imielinski,et al.  Incomplete Information in Relational Databases , 1984, JACM.

[39]  Michael L. Brodie On conceptual modelling - perspectives from artificial intelligence, databases and programming languages , 1984, Topics in information systems.

[40]  Antonio L. Furtado,et al.  Updating Relational Views , 1985, Query Processing in Database Systems.

[41]  Georg Gottlob,et al.  Disjunctive datalog , 1997, TODS.

[42]  Teodor C. Przymusinski On the Declarative Semantics of Deductive Databases and Logic Programs , 1988, Foundations of Deductive Databases and Logic Programming..

[43]  E. F. Codd,et al.  A relational model of data for large shared data banks , 1970, CACM.

[44]  Serge Abiteboul,et al.  On the Representation and Querying of Sets of Possible Worlds , 1991, Theor. Comput. Sci..

[45]  Hirofumi Katsuno,et al.  On the Difference between Updating a Knowledge Base and Revising It , 1991, KR.

[46]  Raymond Reiter On Closed World Data Bases , 1977, Logic and Data Bases.

[47]  Tomasz Imielinski,et al.  Incomplete object—a data model for design and planning applications , 1991, SIGMOD '91.

[48]  Michael Kifer,et al.  A Logic for Programming Database Transactions , 1998, Logics for Databases and Information Systems.

[49]  John C. Shepherdson,et al.  Negation in Logic Programming , 1988, Foundations of Deductive Databases and Logic Programming..

[50]  Sushil Jajodia,et al.  Temporal Databases: Theory, Design, and Implementation , 1993 .

[51]  John Grant,et al.  Integrity Constraints: Semantics and Applications , 1998, Logics for Databases and Information Systems.

[52]  Georg Gottlob,et al.  Closed World Databases Opened Through Null Values , 1988, VLDB.

[53]  Achim Jung,et al.  Types, logic and semantics for nested databases , 1995, MFPS.

[54]  Krzysztof R. Apt,et al.  Logic Programming and Negation: A Survey , 1994, The Journal of Logic Programming.

[55]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[56]  Gösta Grahne,et al.  The Problem of Incomplete Information in Relational Databases , 1991, Lecture Notes in Computer Science.

[57]  Gabriel M. Kuper,et al.  Constraint Query Languages , 1995, J. Comput. Syst. Sci..

[58]  Witold Lipski,et al.  Nonapplicable Nulls , 1986, Theor. Comput. Sci..

[59]  Ron van der Meyden Recursively Indefinite Databases , 1993, Theor. Comput. Sci..

[60]  Atsushi Ohori,et al.  Semantics of Types for Database Objects , 1988, Theor. Comput. Sci..

[61]  Jorge Lobo,et al.  Foundations of disjunctive logic programming , 1992, Logic Programming.

[62]  G. H. Gessert Handling missing data by using stored truth values , 1991, SGMD.

[63]  Robert C. Moore Semantical Considerations on Nonmonotonic Logic , 1985, IJCAI.

[64]  Leonid Libkin,et al.  Aspects of partial information in databases , 1995 .

[65]  Arthur M. Keller,et al.  Approaches for updating databases with incomplete information and nulls , 1984, 1984 IEEE First International Conference on Data Engineering.

[66]  Ashok K. Chandra,et al.  Optimal implementation of conjunctive queries in relational data bases , 1977, STOC '77.

[67]  Witold Lipski On relational algebra with marked nulls preliminary version , 1984, PODS '84.

[68]  Gunter Saake,et al.  Logics for databases and information systems , 1998 .

[69]  Divesh Srivastava,et al.  Constraint , 2020, Encyclopedia of Personality and Individual Differences.

[70]  Tomasz Imielinski,et al.  Incomplete information and dependencies in relational databases , 1983, SIGMOD '83.

[71]  Robert A. Kowalski,et al.  Predicate Logic as Programming Language , 1974, IFIP Congress.

[72]  Raymond Reiter,et al.  Towards a Logical Reconstruction of Relational Database Theory , 1982, On Conceptual Modelling.

[73]  Joachim Biskup,et al.  Extending the Relational Algebra for Relations with Maybe Tuples and Existential and Universal Null Values , 1984, Fundam. Inform..

[74]  Leonid Libkin A Relational Algebra for Complex Objects Based on Partial Information , 1991, MFDBS.

[75]  Edward P. F. Chan A Possible World Semantics for Disjunctive Databases , 1993, IEEE Trans. Knowl. Data Eng..

[76]  Adrian Walker,et al.  Towards a Theory of Declarative Knowledge , 1988, Foundations of Deductive Databases and Logic Programming..

[77]  Witold Lipski,et al.  On Databases with Incomplete Information , 1981, JACM.

[78]  John Grant,et al.  Answering Queries in Indefinite Databases and the Null Value Problem , 1986, Adv. Comput. Res..

[79]  Atsushi Ohori,et al.  Orderings and Types in Databases , 1990, DBPL.

[80]  Tomasz Imielinski Abstraction in query processing , 1991, JACM.

[81]  Alexander Borgida,et al.  Description Logics in Data Management , 1995, IEEE Trans. Knowl. Data Eng..

[82]  Manolis Koubarakis,et al.  Database models for infinite and indefinite temporal information , 1994, Inf. Syst..

[83]  Nicole Bidoit,et al.  Negation in Rule-Based Database Languages: A Survey , 1991, Theor. Comput. Sci..

[84]  Raymond Reiter,et al.  Deductive Question-Answering on Relational Data Bases , 1977, Logic and Data Bases.

[85]  Manolis Koubarakis Foundations of Indefinite Constraint Databases , 1994, PPCP.

[86]  Leonid Libkin,et al.  OR-SML: A Functional Database Programming Language for Disjunctive Information and Its Applications , 1994, DEXA.

[87]  G. H. Gessert,et al.  Four valued logic for relational database systems , 1990, SGMD.

[88]  Peter Buneman,et al.  Using Powerdomains to Generalize Relational Databases , 1991, Theor. Comput. Sci..

[89]  Kenneth A. Ross,et al.  The well-founded semantics for general logic programs , 1991, JACM.

[90]  Roberto V. Zicari,et al.  Incomplete information in object-oriented databases , 1990, SGMD.

[91]  Edward Sciore,et al.  The universal instance and database design , 1980 .

[92]  Leonid Libkin,et al.  Decomposition of Domains , 1991, MFPS.

[93]  Jean-Marie Nicolas,et al.  Data Base: Theory vs. Interpretation , 1977, Logic and Data Bases.

[94]  Ch Chen,et al.  Pattern recognition and artificial intelligence , 1976 .

[95]  Raymond Reiter,et al.  On Integrity Constraints , 1988, TARK.

[96]  Alberto O. Mendelzon,et al.  Updates and Subjunctive Queries , 1995, Inf. Comput..

[97]  Georg Gottlob,et al.  On the Complexity of Propositional Knowledge Base Revision, Updates, and Counterfactuals , 1992, Artif. Intell..

[98]  Donald Perlis,et al.  Applications of Protected Circumscription , 1984, CADE.

[99]  John Wylie Lloyd,et al.  Foundations of Logic Programming , 1987, Symbolic Computation.

[100]  Laks V. S. Lakshmanan,et al.  Intuitionistic Interpretation of Deductive Databases with Incomplete Information , 1992, Theor. Comput. Sci..

[101]  Moshe Y. Vardi The complexity of relational query languages (Extended Abstract) , 1982, STOC '82.

[102]  Michael Stonebraker The INGRES Papers: Anatomy of a Relational Database System , 1986 .

[103]  Véronique Royer,et al.  The Semantics of Incomplete Databases as an Expression of Preferences , 1991, Theor. Comput. Sci..

[104]  Alon Y. Levy Obtaining Complete Answers from Incomplete Databases , 1996, VLDB 1996.

[105]  Michael Kifer,et al.  An Overview of Transaction Logic , 1994, Theor. Comput. Sci..

[106]  Jack Minker,et al.  Advances in Data Base Theory , 1981, Springer US.

[107]  Moshe Y. Vardi On the complexity of bounded-variable queries (extended abstract) , 1995, PODS '95.

[108]  Hector J. Levesque,et al.  The Logic of Incomplete Knowledge Bases , 1982, On Conceptual Modelling.

[109]  Witold Lipski On Relational Algebra with Marked Nulls. , 1984, PODS 1984.

[110]  Keith L. Clark,et al.  Negation as Failure , 1987, Logic and Data Bases.

[111]  Mirka Miller,et al.  A Multivalued Approach to Handle Nulls in RDB , 1992, Future Databases.

[112]  Serge Abiteboul,et al.  Update Semantics for Incomplete Databases , 1985, VLDB.

[113]  Robert A. Kowalski Logic for Data Description , 1977, Logic and Data Bases.

[114]  Arthur M. Keller,et al.  On the Use of an Extended Relational Model to Handle Changing Incomplete Information , 1985, IEEE Transactions on Software Engineering.

[115]  Jeffrey D. Ullman,et al.  Principles of database and knowledge-base systems, Vol. I , 1988 .

[116]  Charles W. Bachman Summary of current work ANSI/X3/SPARC/study group: database systems , 1974, SGMD.

[117]  Gabriel M. Kuper,et al.  Updating Logical Databases , 1986, Adv. Comput. Res..

[118]  Subrata Kumar Das,et al.  Deductive Databases and Logic Programming , 1992 .

[119]  Yannis Vassiliou,et al.  Null values in data base management a denotational semantics approach , 1979, SIGMOD '79.

[120]  Tomasz Imielinski,et al.  Querying Design and Planning Databases , 1991, DOOD.

[121]  J. Van Leeuwen,et al.  Handbook of theoretical computer science - Part A: Algorithms and complexity; Part B: Formal models and semantics , 1990 .

[122]  Carlo Zaniolo,et al.  Database relations with null values , 1982, J. Comput. Syst. Sci..

[123]  Mark Levene,et al.  The Nested Universal Relation Database Model , 1992, Lecture Notes in Computer Science.

[124]  David Maier,et al.  Discarding the Universal Instance Assumption: Preliminary Results , 1980, XP1 Workshop on Database Theory.

[125]  Raymond Reiter,et al.  A sound and sometimes complete query evaluation algorithm for relational databases with null values , 1986, JACM.

[126]  Christian Esculier,et al.  Non-Monotonic Knowledge Evolution in VLKDBs , 1990, VLDB.

[127]  Manolis Koubarakis,et al.  The Complexity of Query Evaluation in Indefinite Temporal Constraint Databases , 1997, Theor. Comput. Sci..

[128]  Joachim Biskup,et al.  A foundation of CODD's relational maybe-operations , 1983, TODS.

[129]  Amihai Motro,et al.  Integrity = validity + completeness , 1989, TODS.

[130]  Kwok-bun Yue A more general model for handling missing information in relational databases using a 3-valued logic , 1991, SGMD.

[131]  Ronald Fagin,et al.  On the semantics of updates in databases , 1983, PODS.

[132]  Amihai Motro,et al.  Uncertainty Management in Information Systems , 2011, Springer US.

[133]  Elliott Mendelson,et al.  Introduction to Mathematical Logic , 1979 .

[134]  Leonid Libkin Normalizing incomplete databases , 1995, PODS '95.

[135]  Dov M. Gabbay,et al.  Handbook of Logic in Artificial Intelligence and Logic Programming: Volume 3: Nonmonotonic Reasoning and Uncertain Reasoning , 1994 .

[136]  Arthur M. Keller Set-Theoretic Problems of Null Completion in Relational Databases , 1986, Inf. Process. Lett..

[137]  Frank Dignum,et al.  Addition and removal of information for a knowledge base with incomplete information , 1992, Data Knowl. Eng..

[138]  Paris C. Kanellakis,et al.  Elements of Relational Database Theory , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[139]  Paolo Atzeni,et al.  Functional Dependencies in Relations with Null Values , 1984, Inf. Process. Lett..

[140]  Jack Minker,et al.  On Indefinite Databases and the Closed World Assumption , 1987, CADE.

[141]  John Mylopoulos,et al.  Readings in Artificial Intelligence and Databases , 1988 .

[142]  Johann Eder,et al.  Logic and Databases , 1992, Advanced Topics in Artificial Intelligence.

[143]  Nadine Lerat Query Processing in Incomplete Logical Databases , 1986, ICDT.

[144]  Moshe Y. Vardi On the Complexity of Bounded-Variable Queries. , 1995, PODS 1995.

[145]  Pascal Ostermann Modal Logic and Incomplete Information , 1987, MFDBS.

[146]  Mihalis Yannakakis,et al.  On the complexity of database queries (extended abstract) , 1997, PODS.