In Gentzen's proof theory for classical logic, a notion of consequence is defined to hold between multiple premises and multiple conclusions.
While in Kraus et al. (1990) the standard of deduction was classical propositional logic, in Arieli and Avron (2000) also nonclassical monotonic core logics and variants with multiple conclusions are considered.
If we opted to use sequent rules, we would have to decide whether or not to allow "substructure" (see the entry on substructural logics) and whether to allow multiple conclusions in the sequents.
and the inferential framework taken into account (single antecedents (i.e., premises) and conclusions, multiple antecedents or multiple conclusions, sets, multisets, or sequences of formulas in antecedent or succedent position).
At this stage of development, well into the 21st century, it seems fair to say that paraconsistency is not any particular approach to logic, but is rather a property that some logics have and others do not (like, say, compactness, or multiple conclusions).
Other cases are less clear but show the multiple conclusions cases of retrograde amnesia tend to offer.
Despite multiple conclusions by the US Justice Department that police forces systematically use force against the mentally ill, there remains no national standard for crisis intervention.
Multiple studies of blood flow present multiple conclusions.
One could try to develop an appropriate intuition by arguing that reasoning towards multiple conclusions delineates the area in which truth lies rather than establishing a single proposition as true.
(However, see Restall (2005) for a defence of multiple conclusion consequence for Anti-realists; and see Beall (2011) for a defence of certain sub-classical multiple-conclusion logics in the service of non-classical solutions to paradox).
