Drawing somewhat on the techniques and culture of philosophy, but mostly on those of mathematics and computing, Pyn (U. of Bath) and Ritter (U. of Birmingham) introduce reductive logic and proof-search. They argue that the reductive view of logic is at least as fundamental as the deductive view; identify some of the problems that must be addressed in order to provide a semantics of proof-searches of comparable value to the corresponding semantics of proof; and explain how to solve these problems in intuitionistic logic, which adequately models not only the logical but also the operational aspects of the reductive system. Most of the chapters have been published separately.