Continuous t-norm based fuzzy predicate logic is surveyed as a generalization of classical predicate logic; then a kind of fuzzy description logic based on our fuzzy predicate logic is briefly described as a powerful but still decidable formal system of description logic dealing with vague (imprecise) concepts.

With the increasing number of applications that base searching on similarity rather than on exact matching, novel index structures are needed to speedup execution of similarity queries. An important stream of research in this direction uses the metric space as a model of similarity. We explain the principles and survey the most important representatives of index structures. We put most emphasis on distributed similarity search architectures which try to solve the difficult problem of scalability of similarity searching. The actual achievements are demonstrated by practical experiments. Future research directions are outlined in the conclusions.