Axiomatic Aspects of Default Inference

We view the syntax-based approaches to default reasoning as a model-based diagnosis problem, where each source giving a piece of information is considered as a component. It is formalized in the ATMS framework (each source corresponds to an assumption). We assume then that all sources are independent and "fail" with a very small probability. This leads to a probability assignment on the set of candidates, or equivalently on the set of consistent environments. This probability...

Prioritized Default Logic presents an optimal solution for addressing real-world problems characterized by incomplete information and the need to establish preferences among diverse scenarios. Although it has reached great success in the theoretical aspect, its practical implementation has received less attention. In this article, we introduce Borhan, a system designed and created for prioritized default logic reasoning. To create an effective system, we have refined existing...

System Z+ [Goldszmidt and Pearl, 1991, Goldszmidt, 1992] is a formalism for reasoning with normality defaults of the form "typically if phi then + (with strength cf)" where 6 is a positive integer. The system has a critical shortcoming in that it does not sanction inheritance across exceptional subclasses. In this paper we propose an extension to System Z+ that rectifies this shortcoming by extracting additional conditions between worlds from the defaults database. We show th...

In this paper we introduce a nonmonotonic framework for belief revision in which reasoning about the reliability of different pieces of information based on meta-knowledge about the information is possible, and where revision strategies can be described declaratively. The approach is based on a Poole-style system for default reasoning in which entrenchment information is represented in the logical language. A notion of inference based on the least fixed point of a monotone op...

This paper presents a logical approach to nonmonotonic reasoning based on the notion of a nonmonotonic consequence relation. A conditional knowledge base, consisting of a set of conditional assertions of the type "if ... then ...", represents the explicit defeasible knowledge an agent has about the way the world generally behaves. We look for a plausible definition of the set of all conditional assertions entailed by a conditional knowledge base. In a previous paper, S. Kraus...

Many writers have observed that default logics appear to contain the "lottery paradox" of probability theory. This arises when a default "proof by contradiction" lets us conclude that a typical X is not a Y where Y is an unusual subclass of X. We show that there is a similar problem with default "proof by cases" and construct a setting where we might draw a different conclusion knowing a disjunction than we would knowing any particular disjunct. Though Reiter's original forma...

Rational inference relations were introduced by Lehmann and Magidor as the ideal systems for drawing conclusions from a conditional base. However, there has been no simple characterization of these relations, other than its original representation by preferential models. In this paper, we shall characterize them with a class of total preorders of formulas by improving and extending Gardenfors and Makinson's results for expectation inference relations. A second representation ...

Tremendous research effort has been dedicated over the years to thoroughly investigate non-monotonic reasoning. With the abundance of non-monotonic logical formalisms, a unified theory that enables comparing the different approaches is much called for. In this paper, we present an algebraic graded logic we refer to as LogAG capable of encompassing a wide variety of non-monotonic formalisms. We build on Lin and Shoham's argument systems first developed to formalize non-monoton...

Description logic programs (dl-programs) under the answer set semantics formulated by Eiter {\em et al.} have been considered as a prominent formalism for integrating rules and ontology knowledge bases. A question of interest has been whether dl-programs can be captured in a general formalism of nonmonotonic logic. In this paper, we study the possibility of embedding dl-programs into default logic. We show that dl-programs under the strong and weak answer set semantics can be...

We introduce the operation of possibility qualification and show how. this modal-like operator can be used to represent "typical" or default knowledge in a theory of nonmonotonic reasoning. We investigate the representational power of this approach by looking at a number of prototypical problems from the nonmonotonic reasoning literature. In particular we look at the so called Yale shooting problem and its relation to priority in default reasoning.