Left exact logic
Left exact logic is a fragment of coherent logic, which has coherent logic as a conservative extension. Left exact logic is interpretable in any category with all finite limits and left exact theories and their models correspond to the left exact sketches and their models as discussed by \textit{M. Barr} and \textit{C. Wells} [Toposes, triples, and theories (1985; Zbl 0567.18001)]. This paper outlines the rules of left exact logic and briefly discusses its relation with coherent logic as well as with universal Horn logic.
scientific article; zbMATH DE number 4021134