The project aims at establishing an adequate logical bases for real life applications, especially expert systems in medical diagnostics, covering the following topics: (A) Investigation of first-order t-norms based fuzzy logics and their important fragments, (B) Studies on paraconsistent fuzzy logic, (C) Adding non-standard quantifiers to paraconsistent fuzzy logic, (D) Investigation of the usefulness of the obtained theoretical results for applications.The motivation arose through the fellow’s experiences as a mathematical expert in several real life modeling projects. Firstly, the use of classical two valued logic induces a huge loss of information. Secondly, there is the problem of degeneration of formal reasoning systems in presence of inconsistencies.Despite of important results, sound mathematical basis that allow fuzzy logic to be adapted to concrete applications are still lacking. The key concept is t-norms, which combine flexibility with mathematical rigor and of logics whose 'and' connective is interpreted as a t-norm. Real life applications call for first-order logics which are still under developed. There should be a theory of suitable and application-driven fragments of these logics, developed according to relevant syntactic and semantics closure conditions.The fellow is a specialist in algebraic approach to BL logics and Lukasiewicz logic, while the host masters proof theoretical, automated deduction and model building approach to first-order fuzzy logics, in particular Gödel logics. The fellow's goal is to learn to manage this other approach to logic and solve the above mentioned problems by such methods. There is also another MC Fellow in Vienna working on paraconsistent logics. Moreover, the host group has joint projects on medical expert system applications with Medical University of Vienna; the fellow is involved in similar projects in Finland.Completing this project enables the fellow's intention to gain full professorship.