Multiple-conclusion logic

Ordinary arguments can have any number of premises but only one conclusion. Multiple-conclusion logic also allows for any number of conclusions in an argument, regarding them as setting out the field of possibilities among which the truth must lie if the premises are true. Such an argument counts as valid if it is impossible for all the premises to be true and all the conclusions false. Anything that can be said about premises can now be said, mutatis mutandis, about conclusions, and much of the interest of the subject comes from exploiting this duality. Putting conclusions on a par with premises reflects the idea that truth and falsity, and likewise acceptance and rejection, are polar notions standing on a par with one another.