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In this paper we explore possible foundations for reasoning about knowledge discovered from incomplete information. The basic idea is to employ Kripke's classical definitions of semantic structure and truth in a semantic structure, but to make the notion of structure more specific. Namely, we intend to present structures that are derived directly from data provided by a user and to develop logical systems for reasoning about these structures. We assume that the user's data consist of descriptions of some objects in terms of their properties, and we refer to the collection of these descriptions as explicit information. It happens that this kind of information is very often provided in application domains, and is a basis for a great variety of knowledge representation and processing methods. From explicit information we derive relationships among objects. They constitute implicit information contained in users' data. These relationships have the form of binary relations in a set of objects such that each of the relations is determined by a subset of properties of the respective objects. These relations reflect some aspects of incompleteness of explicit information. We consider relational structures, referred to as frames, that consist of a set of objects and a family of (accessibility) relations that are parameterised with subsets of a set, with the intuition that these subsets consist of properties of objects. These relations are referred to as information relations.

DOI: 10.1007/978-94-011-5108-5_23

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