On semantic issues connected with incomplete information databases

Abstract

1Various approaches to interpreting queries in a database with incomplete information are discussed. A simple model of a database is described, based on attributes which can take values in specified attribute domains. Information incompleteness means that instead of having a single value of an attribute, we have a subset of the attribute domain, which represents our knowledge that the actual value, though unknown, is one of the values in this subset. This extends the idea of Codd's null value, corresponding to the case when thii subset is the whole attribute domain. A simple query language to communicate with such a system is described and its various semantics are precisely defined. We emphasize the distinction between two different interpretations of the query language-the external one, which refers the queries directly to the real world modeled in an incomplete way by the system, and the internal one, under which the queries refer to the system's information about this world, rather than to the world itself. Both external and internal interpretations are provided with the corresponding sets of axioms which serve as a basis for equivalent transformations of queries. The technique of equivalent transformations of queries is then extensively exploited for evaluating the interpretation of (i.e. the response to) a query.

Data exchange and incomplete information

“…Query answering semantics. Indeed there is nothing sacred about the certain answers semantics; more than 25 years ago, Lipski [22] already suggested using both certain and maybe answers in the context of partial information, as providing lower and upper approximations to query results. Even more advanced forms of approximations were proposed [9,8,15,21] but here we use the basic lower and upper ones.…”

“…But it is well known that answering queries over databases with incomplete information must be done with care: not treating nulls as such leads to semantically incorrect answers [2,17,22,30]. Hence, we define the notions of solutions and query answering in data exchange treating solutions as databases with nulls.…”

Correctness of SQL Queries on Databases with Nulls

“…Intuitively, this means that such answers will be true no matter how we interpret incomplete information that is present in the database. This approach, first proposed in the late 1970s [13,26], is now dominant in the literature and it is standard in all applications where incomplete information appears (data integration, data exchange, ontology-based data access, data cleaning, etc. ).…”

An Application of Rough Non-Deterministic Information Analysis to Class Evaluation Data by Students

“…NISs were proposed by Pawlak, Orlowska and Lipski in order to handle information incompleteness in DISs, like null values, unknown values, missing values. From the beginning of the research on incomplete information, NISs have been recognized to be the most important framework for handling information incompleteness [5][6][7][8]. Therefore, rule generation in NISs will also be an important framework for rule generation in incomplete information.…”

“…However, very few work deals with rule generation from incomplete information on computers. Lipski showed a question-answering system besides the axiomatization of logic [6] . Grzymala-Busse developed a system named LERS, which depends upon LEM1 and LEM2 algorithms [7] .…”