1. The axiom of choice. The object of this paper is to consider the possibUity of setting up a logic in which the axiom of choice is false. The way of approach is through the second ordinal class, in connection with which there appear certain alternatives to the axiom of choice. But these alternatives have consequences not only with regard to the second ordinal class but also with regard to oth...

The assumption of linearity is tested using five statistical tests for the US and the Canadian unemployment rates. An AR(p) model was used to remove any linear structure from the series. Strong evidence in favour of non−linearity was found in the case of Canada. The result for the US is not so clear cut. The author would like to thank Chung−Ming Kuan, David Chappell, Chris Martin and Costas Mil...

Brandenburger, Friedenberg, and Keisler [Econometrica 76 (2008), 307352] show that rationality and common assumption of rationality (RCAR) is impossible in a complete and continuous type structure. We show, by inroducing an alternative notion of “weak assumption”, that rationality and common weak assumption of rationality (RCWAR) is possible in a complete and continuous type structure. This pos...

The proposals of the Basel Committee on Banking Supervision for the revision of minimum requirements for bank’s risk capital leave the quantification of lossgiven-default (LGD) parameter used for capital calculation unspecified. This paper proposes a new methodology for incorporating LGD parameter explicitly into the Basel risk weight function. Numerical examples based on the new methodology ar...

Battigalli and Siniscalchi’s [Journal of Economic Theory 106, 356-391 (2002)] notion of “strong belief”in conditional probability systems and Yang’s [Journal of Economic Theory, forthcoming] notion of “weak assumption”in lexicographic probability systems are unified by the same requirements on preferences. Our analysis, hence, reconciles the tension between Battigalli and Siniscalchi’s characte...

A concept for identification of candidates for outliers is presented, with a focus on nominal variables. The database concerned is searched for rules that are almost universally valid, with rare exceptions. In statistical terms, for these rules, the hypothesis that the rule is universally valid except for random faults cannot be rejected. Outlier candidates are those values that violate these r...

The purpose of this poster is to introduce a dialectical theory for plan synthesis based on a multiagent approach. This approach is a promising way to devise systems able to take into account partial knowledge and heterogeneous skills of agents. We propose to consider the planning problem as a defeasible reasoning where agents exchange proposals and counter-proposals and are able to conjecture ...

This document describes the historical and background information behind the removal of the "on-link assumption" from the conceptual host sending algorithm defined in Neighbor Discovery for IP Version 6 (IPv6). According to the algorithm as originally described, when a host’s default router list is empty, the host assumes that all destinations are on-link. This is particularly problematic with ...

Today, different formalisms exist to solve reasoning problems under uncertainty. For most of the known formalisms, corresponding computer implementations are available. The problem is that each of the existing systems has its own user interface and an individual language to model the knowledge and the queries. This paper proposes ABEL, a new and general language to express uncertain knowledge a...

In Eurocrypt 2003, Boneh et al. presented a novel cryptographic primitive called aggregate signatures. An aggregate signature scheme is a digital signature that supports aggregation: i.e. given k signatures on k distinct messages from k different users it is possible to aggregate all these signatures into a single short signature. Applying the above concept to verifiably encrypted signatures, B...