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Paradigms for Non-classical Substitutions

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4 Author(s)
Eklund, P. ; Dept. of Comput. Sci., Umea Univ., Umea ; Galan, M.A. ; Kortelainen, J. ; Stout, L.N.

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.

Published in:

Multiple-Valued Logic, 2009. ISMVL '09. 39th International Symposium on

Date of Conference:

21-23 May 2009