In valid-time indeterminacy it is known that an event stored in a database did in fact occur, but it is not known exactly when. In this paper we extend the SQL data model and query language to support valid-time indeterminacy. We represent the occurrence time of an event with a set of possible instants, delimiting when the event might have occurred, and a probability distribution over that set. We also describe query language constructs to retrieve information in the presence of indeterminacy. These constructs enable users to specify their credibility in the underlying data and their plausibility in the relationships among that data. A denotational semantics for SQL’s select statement with optional credibility and plausibility constructs is given. We show that this semantics is reliable, in that it never produces incorrect information, is maximal, in that if it were extended to be more informative, the results may not be reliable, and reduces to the previous semantics when there is no indeterminacy. Although the extended data model and query language provide needed modeling capabilities, these extensions appear initially to carry a significant execution cost. A contribution of this paper is to demonstrate that our approach is useful and practical. An efficient representation of valid-time indeterminacy and efficient query processing algorithms are provided. The cost of

Knowledge-base (KB) systems must typically deal with imperfection in knowledge, e.g. in the form of imcompleteness, inconsistency, uncertainty, to name a few. Currently KB system development is mainly based on the expert system technology. Expert systems, through their support for rule-based programming, uncertainty, etc., offer a convenient framework for KB system development. But they require the user to be well versed with the low level details of system implementation. The manner in which uncertainty is handled has little mathematical basis. There is no decent notion of query optimization, forcing the user to take the responsibility for an efficient implementation of the KB system. We contend KB system development can and should take advantage of the deductive database technology, which overcomes most of the above limitations. An important problem here is to extend deductive databases into providing a systematic basis for rule-based programming with imperfect knowledge. In this paper, we are interested in an exension handling probabilistic knowledge.

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.

Abstract. We discuss, compare and relate some old and some new models for incomplete and probabilistic databases. We characterize the expressive power of c-tables over infinite domains and we introduce a new kind of result, algebraic completion, for studying less expressive models. By viewing probabilistic models as incompleteness models with additional probability information, we define completeness and closure under query languages of general probabilistic database models and we introduce a new such model, probabilistic c-tables, that is shown to be complete and closed under the relational algebra. 1

This paper surveys methods for representing and reasoning with imperfect information. It opens with an attempt to classify the different types of imperfection that may pervade data, and a discussion of the sources of such imperfections. The classification is then used as a framework for considering work that explicitly concerns the representation of imperfect information, and related work on how imperfect information may be used as a basis for reasoning. The work that is surveyed is drawn from both the field of databases and the field of artificial intelligence. Both of these areas have long been concerned with the problems caused by imperfect information, and this paper stresses the relationships between the approaches developed in each.

This paper describes a generalization of the relational model in order to capture and manipulate a type of probabilistic information. Probabilistic databases are formalized by means of logic theories based on a probabilistic first-order language proposed by Halpern. A sound a complete method is described for evaluating queries in probabilistic theories. The generalization proposed can be incorporated into existing relational systems with the addition of a component for manipulating propositional formulas. 1

We define a new fixpoint semantics for rule-based reasoning in the presence of imprecise information. We first demonstrate the need to have such a rule-based semantics by showing a real-world application requiring such reasoning. We then define this semantics. Optimizations and approximations of the semantics are shown so as to make the semantics amenable to very large scale real-world applications. We finally prove that the semantics is probabilistic and reduces to the usual fixpoint semantics of stratified Datalog if all information is certain. 2 Index Terms axiomatic probability theory, incomplete information, knowledge discovery in databases, logic programming, query optimization and approximation, stratified Datalog 3 1 Introduction Many real world problems cannot be described or solved by deterministic information because of inherent vagueness (e.g., see [4, 10]). We demonstrate the truth of this statement in a real-world application to which we have successfully applied th...

In historical indeterminacy, it is known that an event stored in a temporal database did in fact occur, but it is not known exactly when the event occurred. We present the possible tuples data model, in which each indeterminate event is represented with a set of possible events that delimits when the event might have occurred, and a probability distribution over that set. We extend the TQuel query language with constructs that specify the user's credibility in the underlying historical data and in the user's plausibility in the relationships among that data. We provide a formal tuple calculus semantics, and show that this semantics reduces to the determinate semantics. We outline an efficient representation of historical indeterminacy, and efficient query processing algorithms, demonstrating the practicality of our proposed approach. 1 Department of Computer Science University of Arizona Tucson, AZ 85721 fcurtis,rtsg@cs.arizona.edu Historical Indeterminacy 1 Copyright c...

This is a draft of a manuscript of a postgraduate course taught at the Hong Kong University of Science and Technology in Spring 94. The course gives an introduction into the young and fascinating field of knowledge discovery in databases. The manuscript is suited for beginners who can leave out the more advanced sections, as well as people who would like to do research in this area. This manuscript is partly incomplete. Especially, the last section discussing approaches to learn knowledge involving time is missing. Contents 1 Introduction 2 1.1 Course Outline : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 1.2 Basic Notions : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 3 1.3 A Case Study : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 6 1.4 Outlook : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 9 LIST OF FIGURES 2 2 Rule Languages 15 2.1 Proposit...

1 We define a new query language for data and knowledge bases. This language is able to deal with weighted or uncertain base and derived information and reduces to a known query language in case that all information is deterministic. We show that this language is probabilistic in the sense of axiomatic probability theory. The novelty is that this language is non-propositional, able to deal with function symbols and offering extensibility through user defined built-in functions. Issues of knowledge acquisition are also addressed. We show where weighted base information can come from and how uncertain derived information might be assimilated. 1 Introduction Companies all over the world use databases to store a variety of information in large quantities. Information is most often certain and deterministic. In some application domains, however, part of the available information is uncertain or weighted. A particular business application could for example require storing weighted facts rep...