A probabilistic learning model for vague queries and missing or imprecise information in databases is described. Instead of retrieving only a set of answers, our approach yields a ranking of objects from the database in response to a query. By using relevance judgements from the user about the objects retrieved, the ranking for the actual query as well as the overall retrieval quality of the system can be further improved. For specifying different kinds of conditions in vague queries, the notion of vague pred-icates is introduced. Based on the underlying probabilistic model, also imprecise or missing attribute values can be treated easily. In addition, the corresponding formulas can be applied in combination with standard predicates (from two-valued logic), thus extending standard database systems for coping with missing or imprecise data.

Much recent work has focussed on using views to evaluate queries. More specifically, queries are rewritten to refer to views instead of the base relations over which the queries were originally written. The motivation is that the views represent the only ways in which some information source may be accessed. Another use of views that has been overlooked becomes important especially when no equivalent rewriting of a query in terms of views is possible: even though we cannot use the views to get all the answers to the query, we can still use them to deduce as many answers as possible. In many global information applications, the notion of equivalence used is often too restrictive. We propose a notion of pseudo-equivalence that allows more queries to be rewritten usefully: we show that if a query has an equivalent rewriting, the query also has a pseudo-equivalent rewriting. The converse is not true in general. In particular, when the views are conjunctive, we show that all Datalog queries...

In order to extend the ability to handle incomplete information in a definite deductive database, a Horn clause based system representing incomplete information as incomplete constants is proposed. By using the notion of incomplete constants the deductive database system handles incomplete information in the form of sets of possible values, thereby giving more information than null values. The resulting system extends Horn logic to express a restricted form of indefiniteness. Although a deductive database with this kind of incomplete information is, in fact, a subset of an indefinite deductive database system, it represents indefiniteness in terms of value incompleteness and therefore it can make use of the existing Horn logic computation rules. The inference rules for such a system are presented, its model theory discussed and an indefinite model theory proposed. The indefinite model theory is consistent with minimal model theory and extends its expressive power. Categories and Subje...

We propose a database model that allows users to annotate data with belief statements. Our motivation comes from scientific database applications where a community of users is working together to assemble, revise, and curate a shared data repository. As the community accumulates knowledge and the database content evolves over time, it may contain conflicting information and members can disagree on the information it should store. For example, Alice may believe that a tuple should be in the database, whereas Bob disagrees. He may also insert the reason why he thinks Alice believes the tuple should be in the database, and explain what he thinks the correct tuple should be instead. We propose a formal model for Belief Databases that interprets users ’ annotations as belief statements. These annotations can refer both to the base data and to other annotations. We give a formal semantics based on a fragment of multi-agent epistemic logic and define a query language over belief databases. We then prove a key technical result, stating that every belief database can be encoded as a canonical Kripke structure. We use this structure to describe a relational representation of belief databases, and give an algorithm for translating queries over the belief database into standard relational queries. Finally, we report early experimental results with our prototype implementation on synthetic data. 1.

We propose a database model that allows users to annotate a database with belief statements. Our motivation comes from scientific database applications, where a community of users is working together to assemble, revise, and curate a shared data repository. As the community accumulates knowledge and the database content evolves over time, it may contain conflicting information and members can disagree on the information it should store. For example, Alice believes that a tuple should be in the database; Bob disagrees and believes the tuple should not be in the database. He may also insert the reason why he thinks Alice believes the tuple should be in the database. In this paper, we propose a formal model for Belief Databases that allows users to annotate data with belief statements. The annotations can refer both to the base data and to other annotations. We give a formal semantics based on a fragment of multi-agent epistemic logic, and define a query language over belief databases. We then prove a key technical result, stating that every belief database can be encoded as a canonical Kripke structure. We use this structure to describe a relational implementation of a belief database, and give an algorithm for translating queries over the belief database into standard relational queries. Finally, we report first experimental results with our prototype implementation on synthetic belief databases. 1