Paradigms for many-sorted non-classical substitutions
2011 (English)In: 2011 41st IEEE International Symposium on Multiple-Valued Logic (ISMVL 2011), IEEE Computer Society, 2011, 318-321 p.Conference paper (Refereed)
We present three paradigms for non-classical substitution in a many-sorted context. Such an exposition has previously been demonstrated in the unsorted case but its extension is far from trivial. The first paradigm, classical many-sorted substitution taking variables to terms, is traditionally presented in a rather informal and "verbal" manner but we find that a strict categorical formulation is necessary to pave the way for non-classical extensions. The second paradigm provides substitution of variables for many-valued sets of terms and relies heavily on functors and monads over the category of indexed sets. Finally, in the third paradigm, we establish full non-classical substitution of many-valued sets of variables by many-valued sets of terms. The third paradigm has the category of many-valued indexed sets as its underlying category. These paradigms ensures transparency of the underlying categories and also makes a clear distinction between set-theoretic operation in the meta language and operations on sets and many-valued sets as found within respective underlying categories.
Place, publisher, year, edition, pages
IEEE Computer Society, 2011. 318-321 p.
Computer and Information Science
IdentifiersURN: urn:nbn:se:umu:diva-52248DOI: 10.1109/ISMVL.2011.10ISBN: 978-1-4577-0112-2ISBN: 978-0-7695-4405-2OAI: oai:DiVA.org:umu-52248DiVA: diva2:501611
41st IEEE International Symposium on Multiple-Valued Logic (ISMVL), 23-25 May 2011, Tuusula, Finland