A semantics for open normal defaults via a modified preferential approach

We present a new approach for handling open normal defaults that makes it possible 1. to derive existentially quantified formulae from other existentially quantified formulae by default, 2. to derive universally quantified formulae by default, and 3. to treat cardinality formulae analogously to other formulae. This was not the case for previous approaches. Reiter uses Skolemization in his treatment of open defaults to achieve the first goal, but this has the unpleasant side-effect that logically equivalent facts may lead to different default consequences. In addition, Reiter\u27s approach does not comply with our second requirement. Lifschitz\u27s main motivation for his approach was to satisfy this second demand. However, to achieve this goal he has to violate the third requirement, and the first condition is also not observed. Differing from these two previous approaches, we will not view open defaults as schemata for certain instantiated defaults. Instead they will be used to define a preference relation on models. But unlike the usual approaches to preferential semantics we shall not always take the minimal models to construct our semantics. Due to this new treatment of preference relations the resulting nonmonotonic consequence operator has nice proof-theoretic properties such as cumulativity

A semantics for open normal defaults via a modified preferential approach

We present a new approach for handling open normal defaults that makes it possible 1. to derive existentially quantified formulae from other existentially quantified formulae by default, 2. to derive universally quantified formulae by default, and 3. to treat cardinality formulae analogously to other formulae. This was not the case for previous approaches. Reiter uses Skolemization in his treatment of open defaults to achieve the first goal, but this has the unpleasant side-effect that logically equivalent facts may lead to different default consequences. In addition, Reiter's approach does not comply with our second requirement. Lifschitz's main motivation for his approach was to satisfy this second demand. However, to achieve this goal he has to violate the third requirement, and the first condition is also not observed. Differing from these two previous approaches, we will not view open defaults as schemata for certain instantiated defaults. Instead they will be used to define a preference relation on models. But unlike the usual approaches to preferential semantics we shall not always take the minimal models to construct our semantics. Due to this new treatment of preference relations the resulting nonmonotonic consequence operator has nice proof-theoretic properties such as cumulativity

Graph theoretical structures in logic programs and default theories

In this paper we present a graph representation of logic programs and default theories. We show that many of the semantics proposed for logic programs can be expressed in terms of notions emerging from graph theory, establishing in this way a link between the fields. Namely the stable models, the partial stable models, and the well-founded semantics correspond respectively to the kernels, semikernels and the initial acyclic part of the associated graph. This link allows us to consider both theoretical problems (existence, uniqueness) and computational problems (tractability, algorithms, approximations) from a more abstract and rather combinatorial point of view. It also provides a clear and intuitive understanding about how conflicts between rules are resolved within the different semantics. Furthermore, we extend the basic framework developed for logic programs to the case of Default Logic by introducing the notions of partial, deterministic and well-founded extensions for default theories. These semantics capture different ways of reasoning with a default theory

Model-based reconfiguration: Diagnosis and recovery

We extend Reiter's general theory of model-based diagnosis to a theory of fault detection, identification, and reconfiguration (FDIR). The generality of Reiter's theory readily supports an extension in which the problem of reconfiguration is viewed as a close analog of the problem of diagnosis. Using a reconfiguration predicate 'rcfg' analogous to the abnormality predicate 'ab,' we derive a strategy for reconfiguration by transforming the corresponding strategy for diagnosis. There are two obvious benefits of this approach: algorithms for diagnosis can be exploited as algorithms for reconfiguration and we have a theoretical framework for an integrated approach to FDIR. As a first step toward realizing these benefits we show that a class of diagnosis engines can be used for reconfiguration and we discuss algorithms for integrated FDIR. We argue that integrating recovery and diagnosis is an essential next step if this technology is to be useful for practical applications

Well-Founded Semantics for Extended Logic Programs with Dynamic Preferences

The paper describes an extension of well-founded semantics for logic programs with two types of negation. In this extension information about preferences between rules can be expressed in the logical language and derived dynamically. This is achieved by using a reserved predicate symbol and a naming technique. Conflicts among rules are resolved whenever possible on the basis of derived preference information. The well-founded conclusions of prioritized logic programs can be computed in polynomial time. A legal reasoning example illustrates the usefulness of the approach.Comment: See http://www.jair.org/ for any accompanying file