A paper on logic and factorisations MAPS I: RELATIVE TO A FACTORISATIONS SYSTEM by Dusko Pavlovic is available by anonymous ftp from triples.math.mcgill.ca. The file is called mapsI-A4.dvi.Z (or mapsI-US.dvi.Z). It is in the directory pub/pavlovic. Please let me know if you have problems fetching or printing this file. Regards, Dusko Pavlovic Abstract Originally, the categorical calculus of relations was developed using the canonical factorisation in regular categories. More recently, relations restricted to a proper factorisation system have been studied by several authors. In the present paper, we consider the general situation, in which relations are induced by an arbitrary stable factorisation. This extension of the calculus of relations is necessary for a categorical development of strongly constructive (and computational) logic, where non-monic relations come about naturally. In this setting, we analyze the correspondence of the maps, i.e. the total, single-valued relations, and the functions, as given by the arrows in the underlying category. ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++