Normal default logic, the fragment of default logic obtained by restricting defaults to rules of the form α:Mβ β , is the most important and widely studied part of default logic. In [MNR94], we proved a basis theorem for extensions of recursive propositional logic normal default theories and hence for finite predicate logic normal default theories. That is, we proved that every recursive propos...

Reiter’s default logic suffers the triviality, that is, a single contradiction in the premise of a default theory leads to the only trivial extension which everything follows from. In this paper, we propose a default logic based on fourvalued semantics, which endows default logic with the ability of handling inconsistency without leading to triviality. We define four-valued models for default t...

This paper develops a methodology for modeling and estimating expected loss over arbitrary horizons. We jointly model the probability of default and the recovery rate given default. Different model specifications are estimated using an extensive default and recovery data set that contains the majority of defaults between 1980–2004 of AMEX, NYSE and NASDAQ listed companies. We undertake extensiv...

The default ART MAP algorithm aud its parameter values specified here define a ready-to-usc gcncral-pm·posc neural nchvork system for supervised learning and recognition.

It is very important for bank to control the credit risk of guarantee loan or combinational loan by evaluating the joint default risk of different enterprises. Firstly we apply a combinational copula function to measure the joint default risk of two enterprises with credit rating information; secondly the default intensity model is intended to analyze the default time distribution; thirdly we u...

Default logic is an important and influential formalization of commonsense reasoning. Determining whether a given default theory has an extension is the main computational problem pertinent to default logic, the analog of testing for validity and finding deductions in more classical logics. Substantially generalizing a result by Etherington [5] we show that all default theories that have no odd...

Banks using either the Foundation or Advanced option of the Internal Ratings Based approach to credit risk under Basel II must estimate long-run annual average default probabilities for buckets of homogeneous assets. The one-factor model underlying the capital calculations in Basel II has implications for the distribution of average (across assets) default rates over time. One of these implicat...

Default logic is one of the best known and most studied of the approaches to nonmonotonic reasoning. Subsequently, several variants of default logic have been proposed to give systems with properties differing from the original. In this paper we show that these variants are in a sense superfluous, in that for any of these variants of default logic, we can exactly mimic the behaviour of a varian...

The problem how to control default reasoning is addressed. In earlier work it was described how selection functions (on default conclusions) added to default logic can be exploited to describe control. In this paper specific properties of selection functions are described. Moreover, we investigate under which conditions selection functions can be expressed in the form of declarative control kno...

Normal forms play an important role in computer science, for example in the areas of logic and databases. This paper provides a study of normal forms for some prominent logics for default reasoning. In particular we show that in Constrained and in Justiied Default Logic, semi{normal default theories can represent arbitrary default theories. The main result for Justiied Default Logic requires th...