The use of metaphors seems to be a thoroughly studied subject. However, when one tries to integrate results, coming from different domains as philosophy of language, philosophy and history of science and logic, they turn out to be quite incompatible. In the first part of this lecture, I shall solve this by formulating a view of metaphors, which explains the findings of philosophers and historians of science and which allows for a logical approach. This view is based on the interactionist theory of metaphors, as formulated originally by Max Black. His theory has some serious shortcomings. I shall solve them by combining Black's view with ideas Lawrence Barsalou, in confrontation with findings of philosophers and historians of science. In the second part of this lecture, I shall sketch the proof theory of a series of adaptive logics for metaphors, based on the model I presented in the first part. These logics give a profound insight in the mechanism of a metaphorical transfer, the main element of the interactionist view of metaphors. The first logic, M1, captures the very basic metaphorical transfer. M2, M3, M4 and M5 are all based on M1 and each of them focuses on a specific type of transfer. Finally, I shall discuss some open problems.