We provide a conceptual description of the field of nonmonotonic reasoning as comprising two essentially different theories, preferential and explanatory nonmonotonic reasoning. The relationship between the two constitutes the main theoretical problem of nonmonotonic reasoning, and its solution should hopefully provide an impetus for the future development of the field.

In recent years, there has been a large amount of disparate work concerning the representation and reasoning with qualitative preferential information by means of approaches to nonmonotonic reasoning. Given the variety of underlying systems, assumptions, motivations, and intuitions, it is difficult to compare or relate one approach with another. Here, we present an overview and classification f...

This paper studies the survival of fixed exchange rate regimes. The probability of an exit from a fixed exchange rate regime depends on the time spent within this regime. In such a context durations models are appropriate, in particular because of the possible non-monotonic pattern of duration dependence. Non-parametric estimates show that the pattern of duration dependence exhibits non-monoton...

As in the cases of freeness and monotonic independence, the notion of conditional freeness is meaningful when complex-valued states are replaced by positive conditional expectations. In this framework, the paper presents several positivity results, a version of the central limit theorem and an analogue of the conditionally free R-transform constructed by means of multilinear function series.

A logical concept of representation independence is developed for nonmonotonic logics , including probabilistic inference systems. The general framework then is applied to several nonmonotonic logics, particularly propo-sitional probabilistic logics. For these logics our investigation leads us to modiied inference rules with greater representation independence .

Two ex ante identically informed agents play an alternating offer bargaining game with endogenous information acquisition and common values. This paper shows that perfect Bayesian equilibria may have the following properties. (i) No agreement exists in ultimatum bargaining although both agents maintain symmetric information in equilibrium and the gain from trade is common knowledge. (ii) The ag...

Multi-context systems (MCSs) define a versatile framework for integrating and reasoning about knowledge from different (heterogeneous) sources. In MCSs, different types of nonmonotonic reasoning are characterized by different semantics such as equilibrium semantics and grounded equilibrium semantics [Brewka and Eiter, 2007]. We introduce a novel semantics of MCSs, a supported equilibrium semant...

An equitable risk allocation between contracting parties plays a vital role in enhancing the performance of the project. This research presents a new quantitative risk allocation approach by integrating fuzzy logic and bargaining game theory. Owing to the imprecise and uncertain nature of players’ payoffs at different risk allocation strategies, fuzzy logic is implemented to determine the value...

For many years, the non-monotonic reasoning community has focussed on highly expressive logics. Such logics have turned out to be computationally expensive, and have given little support to the practical use of non-monotonic reasoning. In this work we discuss defeasible logic, a less-expressive but more efficient non-monotonic logic. We report on two new implemented systems for defeasible logic...