Paradigms for Non-classical Substitutions

Lawrence N. Stout, P. Eklund, M. A. Galan, J. Kortelainen

Research output: Chapter in Book/Report/Conference proceedingChapter


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.
Original languageAmerican English
Title of host publication39th International Symposium on Multiple-Valued Logic
StatePublished - May 2009


  • Mathematics

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