Premise Composition
There are numerous ways to compose premises (and in the multiple conclusion case, conclusions as well). One way is to collect them into a set. But since e.g. {a,a} = {a} we have contraction for free if premises are sets. We also have associativity and permutation (or commutativity) for free as well, among other properties. In substructural logics, typically premises are not composed into sets, but rather they are composed into more fine-grained structures, such as trees or multisets (sets that distinguish multiple occurrences of elements) or sequences of formulae. For example, in linear logic, since contraction fails, the premises must be composed in something at least as fine-grained as multisets.
Read more about this topic: Substructural Logic
Famous quotes containing the words premise and/or composition:
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—Anonymous Father. Ourselves and Our Children, by Boston Women’s Health Book Collective, ch. 3 (1978)
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—Derek Gjertsen, British scientist, author. Science and Philosophy: Past and Present, ch. 3, Penguin (1989)