A paraconsistent relational data model

Bagai, Rajiv; Sunderraman, Rajshekhar

doi:10.1080/00207169508804361

Cited by 24 publications

(4 citation statements)

References 19 publications

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“…Our logic is a generalization of Lukasiewicz's three-valued logic, with the intermediate value duplicated many times and ordered such that none of the copies of this value imply other ones, but it differs from Lukasiewicz's manyvalued logics as well as from logics based on bilattices [13,22,7,9,10,25] where the third value means "neither true nor false" and the fourth value means "both true and false" (and is designated as well).…”

Section: Overall Motivationmentioning

confidence: 99%

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A Paraconsistent Higher Order Logic

Villadsen

2004

Artificial Intelligence and Symbolic Computation

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Abstract. Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where an inconsistency does not lead to such an explosion, and since in practice consistency is difficult to achieve there are many potential applications of paraconsistent logics in knowledge-based systems, logical semantics of natural language, etc. Higher order logics have the advantages of being expressive and with several automated theorem provers available. Also the type system can be helpful. We present a concise description of a paraconsistent higher order logic with countable infinite indeterminacy, where each basic formula can get its own indeterminate truth value (or as we prefer: truth code). The meaning of the logical operators is new and rather different from traditional many-valued logics as well as from logics based on bilattices. The adequacy of the logic is examined by a case study in the domain of medicine. Thus we try to build a bridge between the HOL and MVL communities. A sequent calculus is proposed based on recent work by Muskens.Many non-classical logics are, at the propositional level, funny toys which work quite good, but when one wants to extend them to higher levels to get a real logic that would enable one to do mathematics or other more sophisticated reasonings, sometimes dramatic troubles appear.

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Section: Overall Motivationmentioning

confidence: 99%

“…We present a paraconsistent higher order logic ∇ based on the (simply) typed λ-calculus [18,4]. Although it is a generalization of Lukasiewicz's three-valued logic the meaning of the logical operators is new, but with relations to logics based on bilattices [13,22,7,9,10,25].…”

Section: Introductionmentioning

confidence: 99%

A Paraconsistent Higher Order Logic

Villadsen

2004

Artificial Intelligence and Symbolic Computation

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“…The model of flexible relations [1] considered the data inconsistencies obtained from integration the multiple autonomous relational databases. A paraconsisted relational model described in [4,17] and later on extended on paraconsistent object-oriented and semi-structured database models [15,14] defined a paraconsistent relation as a pair of two relational tables. A positive table represents all facts know to be true and negative table represents all facts known to be false.…”

Section: Introductionmentioning

confidence: 99%

Living with inconsistencies in a multidatabase system

Getta

2004

Proceedings. 15th International Workshop on Database and Expert Systems Applications, 2004.

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Integration of autonomous sources of information is one of the most important problems in implementation of the global information systems. This paper considers multidatabase systems as one of the typical architectures of global information services and addresses a problem of storing and processing inconsistent information in such systems. A new data model proposed in the paper separates sure from inconsistent information and introduces a system of elementary operations on the containers with sure and inconsistent information. A review of the implementation aspects in an environment of a typical relational database management system concludes the paper. Disciplines Physical Sciences and Mathematics Publication DetailsThis article was originally published as: Getta, JR, Living with inconsistencies in a multidatabase system, Proceedings

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“…The model of flexible relations [1] considered the data inconsistencies obtained from integration the multiple autonomous relational databases. A paraconsisted relational model described in [6], [14] and later on extended on paraconsistent object-oriented and semistructured database models [4], [12] defined a paraconsistent relation as a pair of two relational tables where a positive table represents all facts know to be true and negative table represents all facts known to be false. A nonempty intersection of the positive and negative tables represents the inconsistencies.…”

Section: Introductionmentioning

confidence: 99%

Efficient Processing of Databases with Inconsistent Information

Getta

2010

2010 International Conference on Computational Intelligence and Software Engineering

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Abstract-Representation and efficient processing of inconsistent information is a common problem for centralized and distributed database systems. While detection of inconsistencies through offline verification of the consistency constraints is a relatively easy task, a complete elimination of inconsistent information from a database as almost impossible. Therefore, database systems should enable the features that allow for the representation and processing of inconsistent information by the user applications. Implementation of such features require the conceptual extensions to both data model and data manipulation language used for the implementation of a database system. This work presents a formal model for the representation and processing of inconsistent information in a database system. Whenever, the contents of a database fails the evaluation of a consistency constraints then the minimal number valid states of the database is represented by the model. Such approach allows for the flexible representation of various sorts of inconsistencies through the relational tables with variants. The model defines a set of operations on the representation of inconsistent information. This work also reviews the implementation aspects of a database system with inconsistent information. Abstract-Representation and efficient processing of inconsistent information is a common problem for centralized and distributed database systems. While detection of inconsistencies through offline verification of the consistency constraints is a relatively easy task, a complete elimination of inconsistent information from a database as almost impossible. Therefore, database systems should enable the features that allow for the representation and processing of inconsistent information by the user applications. Implementation of such features require the conceptual extensions to both data model and data manipulation language used for the implementation of a database system. This work presents a formal model for the representation and processing of inconsistent information in a database system. Whenever, the contents of a database fails the evaluation of a consistency constraints then the minimal number valid states of the database is represented by the model. Such approach allows for the flexible representation of various sorts of inconsistencies through the relational tables with variants. The model defines a set of operations on the representation of inconsistent information. This work also reviews the implementation aspects of a database system with inconsistent information. Disciplines Physical Sciences and Mathematics

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A paraconsistent relational data model

Cited by 24 publications

References 19 publications

A Paraconsistent Higher Order Logic

A Paraconsistent Higher Order Logic

Living with inconsistencies in a multidatabase system

Efficient Processing of Databases with Inconsistent Information

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