We show that the arithmetical theory -INDx5, formalized in the language of Buss, i.e. with x/2 but without the MSP function x/2y, does not prove that every nontrivial divisor of a power of 2 is even. It follows that this theory proves neither NP=coNP nor.

We construct models of the integers, to yield: witnessing, independence and separation results for weak systems of bounded induction.

Nous montrons que: - la théorie T vérifée par la partie non-négative des anneaux ordonnés, discrets, dans lesquels le quotient euclidien par un entier standard quelconque existe, et la théorie IE0(2x) de l'induction pour les formules ouvertes dans le langage Lexp formé par les symboles d'addition, de multiplication, de relation d'ordre, d'exponentielle (2x) et des constantes 0 et 1, ont les mêmes conséquences universelles dans le langage de T. - la théorie IE0(2x) ne démontre pas - (3 divise 2x). - (...) la théorie IE0(2x) ne démontre pas que l'ensemble des nombres premiers est existentiellement définissable dans le langage Lexp. (shrink)

One of the major problems of intrusion detection concerns the large amount of alerts that intrusion detection systems (IDS) produce. Security operator who analyzes alerts and takes decisions, is often submerged by the high number of alerts to analyze. In this paper, we present a new alert correlation approach based on knowledge and preferences of security operators. This approach, which is complementary to existing ones, allows to rank-order produced alerts on the basis of a security operator knowledge about the system, (...) used IDS and his preferences about alerts that he wants to analyze or to ignore. Our approach is based on the development of a new non-classical logic for representing preferences, called FO-MQCL (First Order - Minimal Qualitative Choice Logic). Our logic extends a fragment of the first order logic by adding a new logical connective. The general idea is to present only alerts that fully fit security operator's preferences and knowledge. And if needed, less preferred alerts can also be presented. (shrink)

One of the major problems of intrusion detection concerns the large amount of alerts that intrusion detection systems (IDS) produce. Security operator who analyzes alerts and takes decisions, is often submerged by the high number of alerts to analyze. In this paper, we present a new alert correlation approach based on knowledge and preferences of security operators. This approach, which is complementary to existing ones, allows to rank-order produced alerts on the basis of a security operator knowledge about the system, (...) used IDS and his preferences about alerts that he wants to analyze or to ignore. Our approach is based on the development of a new non-classical logic for representing preferences, called FO-MQCL (First Order - Minimal Qualitative Choice Logic). Our logic extends a fragment of the first order logic by adding a new logical connective. The general idea is to present only alerts that fully fit security operator's preferences and knowledge. And if needed, less preferred alerts can also be presented. (shrink)

We completely characterize the logical hierarchy of subsystems of open induction introduced by Boughattas [1].