  The pioneering work of Blok and J\'onsson and its further development by
Galatos and Tsinakis initiated an abstract study of consequence relations using
the tools of module theory, where consequence relations over all types of
syntactic objects are put on an equal footing. However, the assumption that in
a consequence relation the premises form merely a set, as opposed to a more
complicated structure, is still retained. An attempt to extend this framework
to account for inferentially substructural generalizations of consequence
relations, where the premises have the structure of a finite multiset, was
recently made by Cintula, Gil-F\'erez, Moraschini, and Paoli. In this paper, we
develop a different inferentially substructural generalization of the work of
Galatos and Tsinakis, where we instead assume that the premises have the
structure of a set of finite multisets. This leads a somewhat smoother
framework which, unlike that of Cintula et al., covers the original theory of
Galatos and Tsinakis as a special case.
