Information technologies - synergy of theory and application

In this lecture we give several examples and lessons learned from research, development and experiments in the area of theory and applications of information technology. We will try to describe a possible synergy of theory and application too. Namely, to describe where practical needs bring new problems for theory and where theory helps to formulate methods, which should be verified in practice. In the theoretical part we will mention research on correctness and completeness of fuzzy logic programming [1,2] and various measures for evaluating success. In applications we mention acquaintance with development and experiments of preferential querying and user dependent top-k answers [3]. In all of these it also depends on whether our task is deductive (querying), inductive (learning) or abductive. In practice, it is important to have a user behavior model (for many different users). To see what is (can be, must be) done automatically (trained, assisted, unsupervised, . . . ) and what by human, what is domain dependent and what is generic. Our fuzzy model is not a mere generalization from two values to many values. The key point of our study here is our understanding of fuzzy value as preference degree. Using fuzzy as preferences enlightens phenomena which in a two valued world are not visible at all. From mathematical point of view one can generalize LP to many valued logic. Also here we face several challenges. Should our rules be implications or clauses, should our computation be refutation or query answering, is unification touched by this or not? In two valued logic these are equivalents, in [1] we have developed a model of ([0,1] valued) fuzzy logic programming FLP with implicative rules and computation based on backward usage of modus pones (and possible extension with fuzzy similarity in [4]). Concerning implementation of this system, M. Lieskovsky has constructed in [5] a fuzzy Warren abstract machine. Our system enables new form of cuts for threshold queries (see [1]). Further development went in two directions. (First) What happens in finitely valued case when different attributes take different number of truth val-