Taming Jörmungandr: The Logical Foundations of Circularity
The project is devoted to developing new techniques for the formal analysis of cyclic phenomena in mathematical, philosophical and computational contexts. Although a variety of formalisms will be employed, the concept of cyclic and ill-founded proofs will play an important role. Cyclic proofs are formal arguments/deductions following the local constraints of a given calculus but where possibly infinite deduction trees are allowed provided they exhibit uniformity and satisfy a decidable correctness criterion. Informal examples of cyclic proofs are the irrationality of √2 by the method of infinite descent and Fermat’s ‘Last Theorem’ for the fourth power.