The use of adaptive logics for the practice and the philosophy of mathematics and the use of mathematical tools for the abstract analysis of adaptive logics

This project concerns an investigation into three aspects of the relation between mathematics and adaptive logics (AL's): it is investigated how (a) AL's can be used for the formal modeling of the mathematical practice, (b) AL's can solve problems of the foundations of mathematics, and © mathematical techniques can be used for the abstract study of AL's.