Paradigms for Non-classical Substitutions
We will present three paradigms for non-classical substitution. Firstly, we have the classical substitution of variables with terms. This is written in a strict categorical form supporting presentation of the other two paradigms. The second paradigm is substitutions of variables with many-valued sets of terms. These two paradigms are based on functors and monads over the category of sets. The third paradigm is the substitution of many-valued sets of variables with terms over many-valued sets of variables. The latter is based on functors and monads over the category of many-valued sets. This provides a 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.
Lawrence N. Stout, P. Eklund, M. A. Galan, and J. Kortelainen. "Paradigms for Non-classical Substitutions" 39th International Symposium on Multiple-Valued Logic (2009 ed). Naha, Okinawaw, Japan: IEE Computer Society, 2009. 77-79.
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