We introduce the notion of strongly distributed multi-agent systems and present a uniform approach to incremental problem solving on them. The approach is based on the systematic use of two logical reduction techniques: Feferman-Vaught reductions and syntactically defined translation schemes. The multi-agent systems are presented as logical structures A. The problems are represented as boolean or quantitative formulae on them. We propose a uniform template for methods, which allow for a certain cost evaluation of formulae of logic L over A from values of formulae over its components and values of formulae over the index structure I. We show that our approach works for very many of extensions of First Order Logic.