http://bcpw.bg.pw.edu.pl/Content/1717/information-systems-theopretical-found.pdf

Information systems theoretical foundations

Various 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 this 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.

On semantic issues connected with incomplete information databases

Semantic and logical problems arising in an incomplete information database are investigated. A simple query language is described, and its semantics, which refers the queries to the information about reality contained in a database, rather than to reality itself, is defined. This approach, called the internal interpretation, is shown to lead in a natural way to the notions of a topological Boolean algebra and a modal logic related to $4 in the same way as referring queries directly to reality (external interpretation) leads to Boolean algebras and classical logic. An axiom system is given for equivalent (with respect to the internal interpretation) transformation of queries, which is then exploited as a basic tool in a method for computing the internal interpretation for a broad class of queries. An interesting special case of the problem of determining the internal interpretation amounts to deciding whether an assertion about reality (a \"yes-no\" query) is consistent with the incomplete information about reality contained in a database. A solution to this problem, which relies on the classical combinatorial problem of distinct representatives of subsets, is given.

On Databases with Incomplete Information

Representation of nondeterministic information

The problem considered in this paper is how to approximate sets of objects that are qualitatively but not necessarily spatially near each other. The term qualitatively near is used here to mean closeness of descriptions or distinctive characteristics of objects. The solution to this problem is inspired by the work of Zdzislaw Pawlak during the early 1980s on the classification of objects by means of their attributes. This article introduces a special theory of the nearness of objects that are either static (do not change) or dynamic (change over time). The basic approach is to consider a link relation, which is defined relative to measurements associated with features shared by objects independent of their spatial relations. One of the outcomes of this work is the introduction of new forms of approximations of objects and sets of objects. The nearness of objects can be approximated using rough set methods. The proposed approach to approximation of objects is a straightforward extension of the rough set approach to approximating objects, where approximation can be considered in the context of information granules (neighborhoods). In addition, the usual rough set approach to concept approximation has been enriched by an increase in the number of granules (neighborhoods) associated with the classification of a concept as near to its approximation. A byproduct of the proposed approximation method is what we call a near set. It should also be observed that what is presented in this paper is considered a special (not a general) theory about nearness of objects. The contribution of this article is an approach to nearness as a vague concept which can be approximated from the state of objects and domain knowledge.

http://www.m-hikari.com/ams/ams-password-2007/ams-password53-56-2007/petersAMS53-56-2007.pdf

Near Sets. Special Theory about Nearness of Objects

Information storage and retrieval systems: Mathematical foundations

In the paper we propose certain methods of economizing the storage space of a computer while storing there a system of information storage and retrieval.

V. Wiktor Marek

Papers

Information storage and retrieval systems: Mathematical foundations

File Organization, An Application of Graph Theory