The project, planned as a continuation of project LOGFAC (TIC2001-1577-C03-01), has three basic objectives. The first one is to continue the logic and algebraic study of t-norm based many-valued logics in the frame of both residuated and substructural logics. The second one is the formalization, within the framework of the above logics, of several deductive soft computing mechanisms, based on fuzzy logic, to deal with fuzziness and imprecision. The last one is to continue theoretical and experimental research on algorithms for the satisfiability problem in many-valued logics and their application to computational problems, in particular to constraint satisfaction problems with hard and soft constraints problems.