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A partition u of [k] = f1; 2; : : : ; kg is contained in another partition v of [l] if [l] has a k-subset on which v induces u. We are interested in counting partitions v not containing a given partition u or a given set of partitions R. This concept is related to that of forbidden permutations. A strengthening of Stanley{Wilf conjecture is proposed. We prove that the GF counting v is rational ...

This paper develops the first parts of a logical framework for the empirical sciences, by means of a redefinition of theory structuralism as originally developed by Joseph Sneed, Wolfgang Stegmüller, and others, in the context of a ‘rigid’ logic as based on a fixed (therefore rigid) ontology. The paper defends a formal conception of the empirical sciences that has an irreducible ontological bas...

Argumentation Frameworks

1 The medical staff might not have to be represented here since they only enter what factors that should be monitored and so they can be seen as the same entity as the nurses' station.

In this paper, we describe an open problem in abstract argumentation theory: the precise conditions under which semi-stable extensions exist. Although each finite argumentation framework can be shown to have at least one semi-stable extension, this is no longer the case when infinite argumentation frameworks are considered. This puts semi-stable semantics between stable and preferred semantics....