Let us investigate! Dynamic Conjecture-Making as the Formal Logic of Abduction

We present a dynamic approach to Peirce's original construal of abductive logic as a logic of conjecture making, and provide a new decidable, contraction-free and cut-free proof system for the dynamic logic of abductive inferences with neighbourhood semantics. Our formulation of the dynamic logic of abduction follows the philosophical and scientific track that led Peirce to his late, post-1903 characterization of abductive conclusions as "investigands", namely invitations to investigate propositions conjectured at the level of pre-beliefs.