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Recently in Koshevoy (Math. Social Sci. 38 (1999) 35), it was established a connection between the theory of choice functions satisfying path-independence condition and closure operators with the anti-exchange property. Closure operators with the anti-exchange property are a combinatorial...
A well-known result is that the inference problem for propositional Horn formulae can be solved in linear time. We show that this remains true even in the presence of arbitrary (static) propositional background knowledge. Our main tool is the notion of a cumulated clause, a slight generalization...
On a very small surface, a chip, several thousands of oligonucleotides, having a length between 20 and 25 bases, can be synthesized. The actual technology to manufacture in parallel these high-density oligo-chips is photolithography using masks to select the oligos on which one base, among A, T,...
Some classical models of clustering (hierarchies, pyramids, etc.) are related to interval hypergraphs. In this paper we study clustering models related to hypertrees which are an extension of interval hypergraphs. We first prove that a hypertree can be characterized by an order on its vertices,...
We consider the problem of numerical representations of PQI interval orders. A preference structure on a finite set A with three relations P , Q , I standing for “strict preference”, “weak preference” and “indifference”, respectively, is defined as a PQI interval order iff there...
Because antimatroid closure spaces satisfy the anti-exchange axiom, it is easy to show that they are uniquely generated. That is, the minimal set of elements determining a closed set is unique. A prime example is a discrete convex geometry in Euclidean space where closed sets are uniquely...
In this paper we propose an empirical prediction method to retrieve, for a given ordinal criterion and a set of binary predictors, a series of nested sets of predictors, each set containing all singly necessary (and, if feasible, jointly sufficient) predictors for a particular criterion value....
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