Powersets of terms and composite monads

Authors:
P. Eklund;M. A. Galán;J. Medina;M. Ojeda-Aciego;A. Valverde
Affiliations:
Department of Computing Science, UmeÅ University, SE-901 87 UmeÅ, Sweden;Department of Applied Mathematics, University of Málaga, E-29071 Málaga, Spain;Department of Applied Mathematics, University of Málaga, E-29071 Málaga, Spain;Department of Applied Mathematics, University of Málaga, E-29071 Málaga, Spain;Department of Applied Mathematics, University of Málaga, E-29071 Málaga, Spain
Venue:
Fuzzy Sets and Systems
Year:
2007

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Abstract

Composing various powerset functors with the term monad gives rise to the concept of generalized terms. This in turn provides a technique for handling many-valued sets of terms in a framework of variable substitutions, thus being the prerequisite for categorical unification in many-valued logic programming using an extended notion of terms. As constructions of monads involve complicated calculations with natural transformations, proofs are supported by a graphical approach that provides a useful tool for handling various conditions, such as those well known for distributive laws.