Helmut Thöne

New direction for uncertainty reasoning in deductive databases

This paper contributes a novel approach to nonmonotonic uncertainty reasoning, which is ubiquitous in many real-life applications. Founded on the paradigm of conditional probabilities we develop a rule-based calculus and prove that it is sound, even in the presence of incomplete information. Thus the merits of doing consistent judgments in uncertain domains and the advantages of modularity and incrementality of rulebased application development come together. We also can offer mechanisms to trace down inconsistencies that may be hidden in very large collections of uncertain rules. As next-generation applications will have to handle vast amounts of uncertain data, an integration into databases is mandatory. We give a direct implementation of our calculus on top of a database system with a DATALOG-interface. In this way we extend current database technology towards providing new applications with new suitable primitives and with a database platform for coping with uncertainty.

Towards precision of probabilistic bounds propagation

The DUCK-calculus presented here is a recent approach to cope with probabilistic uncertainty in a sound and efficient way. Uncertain rules with bounds for probabilities and explicit conditional independences can be maintained incrementally. The basic inference mechanism relies on local bounds propagation, implementable by deductive databases with a bottom-up fixpoint evaluation. In situations, where no precise bounds are deducible, it can be combined with simple operations research techniques on a local scope. In particular, we provide new precise analytical bounds for probabilistic entailment.

Fixpoint iteration with subsumption in deductive databases

Declarative languages for deductive and object-oriented databases require some high-level mechanism for specifying semantic control knowledge. This paper proposes user-supplied subsumption information as a paradigm to specify desired, prefered or useful deductions at the meta level. For this purpose we augment logic programming by subsumption relations and succeed to extend the classical theorems for least models, fixpoints and bottom-up evaluation accordingly. Moreover, we provide a differential fixpoint operator for efficient query evaluation in deductive databases. This operator discards subsumed tuples on the fly. We also exemplify the ease of use of this programming methodology. In particular, we demonstrate how heuristic AI search procedures can be integrated into deductive databases in this way.

Database Support for Problematic Knowledge

Recently substantial research efforts have been spent on extending database technology in various ways towards a better support of applications of the nineties. In contrast, the tough problems of adding the right uncertainty reasoning capabilities have received relatively modest attention despite evident importance. Among the many faces of uncertainty we focus on what we call problematic knowledge, which is — e. g. — inherent in what-if decision scenarios. Based on a rule calculus with probability intervals introduced lately [GKT 91] we show how to do rule chaining under independence and how to add comparative probability. Also a method for reasoning with uncertain facts, founded on the notions of maximal context and detachment, is given. Full database support can be given to the calculus. We discuss some aspects of the optimization problem and how to deliver uncertainty reasoning to the users application by interoperability in a heterogeneous database environment.

On cautious probabilistic inference and default detachment

Conditional probabilities are one promising and widely used approach to model uncertainty in information systems. This paper discusses the DUCK-calculus, which is founded on the cautious approach to uncertain probabilistic inference. Based on a set of sound inference rules, derived probabilistic information is gained by local bounds propagation techniques. Precision being always a central point of criticism to such systems, we demonstrate that DUCK need not necessarily suffer from these problems. We can show that the popular Bayesian networks are subsumed by DUCK, implying that precise probabilities can be deduced by local propagation techniques, even in the multiply connected case. A comparative study with INFERNO and with inference techniques based on global operations-research techniques yields quite favorable results for our approach. Since conditional probabilities are also suited to model nonmonotonic situations by considering different contexts, we investigate the problems of maximal and relevant contexts, needed to draw default conclusions about individuals.

The differential fixpoint operator with subsumption

Declarative languages for deductive and object-oriented databases require some high-level mechanism for specifying semantic control knowledge. This paper proposes user-supplied subsumption information as a paradigm to specify desired, prefered or useful deductions at the meta level. For this purpose we augment logic programming by subsumption relations and succeed to extend the classical theorems for least models, fixpoints and bottom-up evaluation accordingly. Moreover, we provide a differential fixpoint operator for efficient query evaluation. This operator discards subsumed tuples on the fly. We also exemplify the ease of use of this programming methodology. In particular, we demonstrate how heuristic AI search procedures can be integrated into logic programming in this way.

Increased robustness of Bayesian networks through probability intervals

Abstract We present an extension of Bayesian networks to probability intervals, aiming at a more realistic and flexible modeling of applications with uncertain and imprecise knowledge. Within the logical framework of causal programs we provide a model-theoretic foundation for a formal treatment of consistency and of logical consequences. A set of local inference rules is developed, which is proved to be sound and—in the absence of loops—also to be complete; i.e., tightest probability bounds can be computed incrementally by bounds propagation. These inference rules can be evaluated very efficiently in linear time and space. An important feature of this approach is that sensitivity analyses can be carried out systematically, unveiling portions of the network that are prone to chaotic behavior. Such investigations can be employed for improving network design towards more robust and reliable decision analysis.

Probabilistic Reasoning With Facts And Rules In Deductive Databases

In this paper we present a new method for probabilistic reasoning with true facts and uncertain rules within a deductive database. Besides a cautious approach to inferences on uncertain rules, we show a default approach for uncertainty reasoning including factual knowledge, based on the ideas of maximal context and detachment. Integrated into a database these approaches support many important applications with probabilistic value dependencies. One sample application will be provided: Lead qualification within a marketing database.

An application of disjunctive logic programming with incomplete information

Despite their different perspectives, probabilistic reasoning and disjunctive logic programming strive for similar goals. Both address the problem of representing incomplete information and providing conclusions under reasonable assumptions such as independencies or closed world assumptions. This paper investigates the evaluation of independence assumptions which can be characterized by graphs (MARKOV and BAYESIAN networks). The underlying independence axioms are well-known/spl minus/they correspond to a set of disjunctive clauses. Based on a compact representation of disjunctive clauses, called clause trees, we provide an efficient /spl Delta/-iteration technique with subsumption, which allows us to compute the least fixpoint of the program or alternatively the verification of particular independences. Experimental results revealed that our approach is much more efficient than the conventional evaluation techniques.<<ETX>>