On four noncommutative fuzzy connectives and their axiomatization

In most of the query languages, conjunctive and disjunctive combinations of conditions remain the usual way for aggregation. Fuzzy query languages also offer trade-off operators, such as means in order to compensate between elementary conditions. In this paper, we would like to introduce a new type of condition basically founded on the interaction between two predicates, thus enriching the panoply of tools the user is provided with and the power of query languages.