1997: Probabilistically Reliable Default Reasoning

In Proceedings of the International Conference on the Principles of Knowledge Representation and Reasoning (KR 2004), 2004

This article provides an experimental analysis of the possibilistic handling of default rules. Three different nonmonotonic consequence relations are considered: minimum specificity inference (MSP), lexicographical closure (LC), and epsilon-belief functions (LCD). The latter was initially proposed within the belief function framework; it is rephrased here within a possibility theory framework. These three consequence relations share some properties but differ on others, which allows for an experimental test of their psychological ...

Machine Intelligence and Pattern Recognition, 1990

There is much interest in providing proba-• bilistic semantics for defaults but most ap proaches seem to suffer from one of two prob lems: either they require numbers, a problem defaults were intended to avoid, or they gen erate peculiar side effects. Rather than provide semantics to defaults, we address the original problem that defaults were intended to solve: that of reasoning un der uncertainty where numeric probability distributions are not available. We describe a non-numeric formalism called an inference graph based on standard probability theory, conditional independence and sentences of confirmation, where a confirms b = coni(a, b) = p(a!b) > p(a). The formalism seems to handle the exam ples from the nonmonotonic literature. Most importantly, the sentences of our system can be verified by performing an appropriate ex periment in the semantic domain.

Annals of Mathematics and Artificial Intelligence, 2008

We provide a description of generalized default logic as a unified formalism for nonmonotonic reasoning. Special attention will be paid to the role of the monotonic logic underlying default reasoning, as well as to the representation opportunities created by the use of assumptions (justifications) in the heads of default rules. On the other hand, it will be shown that even the generalized default logic can be simplified to a formal system that involves only monotonic rules and default assumptions.

1996

In this paper we present a novel approach to default reasoning, based on the concept of A- uncertainty, namely uncertainty concerning rule applicability. The paper first presents a focused analysis, based on some simple default reasoning examples, of the limitations of some well-known approaches to default reasoning. Then, the novel approach, based on the explicit representation of A-uncertainty is introduced. It is based on a concept of A-uncertainty intended as a property concerning both an inference rule and the individual to which it is applied, and it is shown to be appropriate to overcome most of the limitations found in classical approaches in a natural and effective way. A general default reasoning scheme is then proposed, which exploits the advantages of the introduced representation and sets up a promising background for efficient implementations of automated reasoning .

Lecture Notes in Computer Science, 2004

Statistical Default Logic (SDL) is an expansion of classical (i.e., Reiter) default logic that allows us to model common inference patterns found in standard inferential statistics, e.g., hypothesis testing and the estimation of a population's mean, variance and proportions. This paper presents an embedding of an important subset of SDL theories, called literal statistical default theories, into stable model semantics. The embedding is designed to compute the signature set of literals that uniquely distinguishes each extension on a statistical default theory at a pre-assigned error-bound probability.

1996

We apply logic program development technology to de ne abstract proof procedures, in the form of logic programs, for computing the admissibility semantics for default reasoning proposed in 2]. The proof procedures are derived from a formal speci cation. The derivation guarantees the soundness of the proof procedures. The completeness of the proof procedures is shown by employing a technique of symbolic execution of logic programs to compute (an instance of) a relation implied by the speci cation.

Artificial Intelligence, 1994

Reiter's default logic has proven to be an enduring and versatile approach to nonmonotonic reasoning. Subsequent work in default logic has concentrated in two major areas. First, modifications have been developed to extend and augment the approach. Second, there has been ongoing interest in semantic foundations for default logic. In this paper, a number of variants of default logic are developed to address differing intuitions arising from the original and subsequent formulations. First, we modify the manner in which consistency is used in the definition of a default extension. The idea is that a global rather than local notion of consistency is employed in the formation of a default extension. Second, we argue that in some situations the requirement of proving the antecedent of a default is too strong. A second variant of default logic is developed where this requirement is dropped; subsequently these approaches are combined, leading to a final variant. These variants then lead to default systems which conform to alternative intuitions regarding default reasoning. For all of these approaches, a fixed-point and a pseudo-iterative definition are given; as well a semantic characterisation of these approaches is provided. In the combined approach we argue also that one can now reason about a set of defaults and can determine, for example, if a particular default in a set is redundant. We show the relation of this work to that of Lukaszewicz and Brewka, and to the Theorist system.

Artificial intelligence, 1997

We present an abstract framework for default reasoning, which includes Theorist, default logic, logic programming, autoepistemic logic, non-monotonic modal logics, and certain instances of circumscription as special cases. The framework can be understood as a generalisation of Theorist. The generalisation allows any theory formulated in a monotonic logic to be extended by a defeasible set of assumptions.

Computational Intelligence, 2004

We present a general approach for representing and reasoning with sets of defaults in default logic, focussing on reasoning about preferences among sets of defaults. First, we consider how to control the application of a set of defaults so that either all apply (if possible) or none do (if not). From this, an approach to dealing with preferences among sets of default rules is developed. We begin with an ordered default theory, consisting of a standard default theory, but with possible preferences on sets of rules. This theory is transformed into a second, standard default theory wherein the preferences are respected. The approach differs from other work, in that we obtain standard default theories and do not rely on prioritised versions of default logic. In practical terms this means we can immediately use existing default logic theorem provers for an implementation. As well, we directly generate just those extensions containing the most preferred applied rules; in contrast, most previous approaches generate all extensions, then select the most preferred. In a major application of the approach, we show how semi-monotonic default theories can be encoded so that reasoning can be carried out at the object level. With this, we can reason about default extensions from within the framework of standard default logic. Hence one can encode notions such as skeptical and credulous conclusions, and can reason about such conclusions within a single extension.

Computational Intelligence, 1994

Default logic has been introduced for handling reasoning with incomplete knowledge. It has been widely studied, and various definitions have been proposed for it. Most of the variants have been defined by means of fixed points of some operator. We propose here another approach, which is based on a study of the way in which general rules with exceptions, used in a default reasoning process, can contradict one another. We then isolate sets of noncontradicting rules, as large as possible in order to exploit as much information as possible, and construct, for each of these sets of rules, the set of conclusions that can be deduced from it. We show that our framework encompasses most of the existing variants of default logic, allowing those variants to be compared from a knowledge representation point of view. Our approach also enables us to provide an operational definition of extensions in some interesting cases. Proof-theoretical and semantical aspects are investigated.