The talk will consist of two loosely connected parts: set-theoretic and computer science. We give an overview (no technical details) of our results on Galois-Tukey connections as a general framework for problem reduction. Boolean structure of absolutely divergent series gives rise to several Boolean-like asymptotic structures. Second part deals with applications of many valued logic to preference modeling, querying top-k answers and learning each individual user preferences from behaviour data (especially we mention lack of real world benchmarks).