Towards Collaborative Conceptual Exploration

In domains with high knowledge distribution a natural objective is to create principle foundations for collaborative interactive learning environments. We present a first mathematical characterization of a collaborative learning group, a consortium, based on closure systems of attribute sets and the well-known attribute exploration algorithm from formal concept analysis. To this end, we introduce (weak) local experts for subdomains of a given knowledge domain. These entities are able to refute and potentially accept a given (implicational) query for some closure system that is a restriction of the whole domain. On this we build up a consortial expert and show first insights about the ability of such an expert to answer queries. Furthermore, we depict techniques on how to cope with falsely accepted implications and on combining counterexamples. Using notions from combinatorial design theory we further expand those insights as far as providing first results on the decidability problem if a given consortium is able to explore some target domain. Applications in conceptual knowledge acquisition as well as in collaborative interactive ontology learning are at hand.Comment: 15 pages, 2 figure

On the Usability of Probably Approximately Correct Implication Bases

We revisit the notion of probably approximately correct implication bases from the literature and present a first formulation in the language of formal concept analysis, with the goal to investigate whether such bases represent a suitable substitute for exact implication bases in practical use-cases. To this end, we quantitatively examine the behavior of probably approximately correct implication bases on artificial and real-world data sets and compare their precision and recall with respect to their corresponding exact implication bases. Using a small example, we also provide qualitative insight that implications from probably approximately correct bases can still represent meaningful knowledge from a given data set.Comment: 17 pages, 8 figures; typos added, corrected x-label on graph

NEXAFS Study of the Composite Materials MWCNTs—Pyrolytic Metals by Synchrotron Radiation

New composite material—multi-walled carbon nanotubes (MWCNTs) coated with thin iron films—have been prepared by MOCVD growth technique using iron pentacarbonyl as the iron source. Their structures and morphologies were characterized by X-ray diffraction, scanning electron microscopy, transmission electron microscopy, and thermal gravimetric analysis. The NEXAFS C1s- and Fe2p-spectra of the composite materials MWCNTs-pyrolytic Fe were studied by total electron yield mode with using synchrotron radiation Russian-Germany beamline at BESSY-II. The study has shown that top layers of the MWCNTs in composite do not have essential destruction, coating of MWCNT's-surface is $Fe_{3}O_{4}$ and this coating is continuous. The iron oxide adhesion is provided by chemical binding between the carbon atoms of the MWCNT's top layer and the oxygen atoms of the coating

Some Computational Problems Related to Pseudo-intents

Abstract. We investigate the computational complexity of several deci-sion, enumeration and counting problems related to pseudo-intents. We show that given a formal context and a subset of its set of pseudo-intents, checking whether this context has an additional pseudo-intent is in conp, and it is at least as hard as checking whether a given simple hypergraph is not saturated. We also show that recognizing the set of pseudo-intents is also in conp, and it is at least as hard as identifying the minimal transver-sals of a given hypergraph. Moreover, we show that if any of these two problems turns out to be conp-hard, then unless p = np, pseudo-intents cannot be enumerated in output polynomial time. We also investigate the complexity of finding subsets of a given Duquenne-Guigues Base from which a given implication follows. We show that checking the existence of such a subset within a specified cardinality bound is np-complete, and counting all such minimal subsets is #p-complete.