Some people believe that if there is any reasoning process that cannot be captured by logic, it should be our apprehension of humour. Incongruity-based humour, however, has been analysed, especially by cognitive linguists, as something which can be regimented straightforwardly. In this talk, I assess several fairly recent incongruity-resolution theories of humour, point to some overall vices and virtues and wonder what logical tools should be added to the toolkit of the cognitive linguist, so that we can arrive at an adequate theory of incongruity-based humour.