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Setfunctors, L-fuzzysetcategories, and generalizedterms
Umeå University, Faculty of Science and Technology, Department of Computing Science.
Umeå University, Faculty of Science and Technology, Department of Computing Science.
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2002 (English)In: Computers and Mathematics with Applications, ISSN 0898-1221, Vol. 43, no 6-7, 693-705 p.Article in journal (Refereed) Published
Abstract [en]

In this work, we generalize previous constructions of fuzzysetcategories, introduced in [1], by consideringL-fuzzysets in which the values of the characteristic functions run on a completely distributive lattice, rather than in the unit real interval. Later, these L-fuzzysets are used to define the L-fuzzycategories, which are proven to be rational. In the final part of the paper, the L-fuzzyfunctors given by the extension principles are provided with a structure of monad which is used, together with the functorial definition of theterm monad, to provide monad compositions as a basis for a notion of generalisedterms.

Place, publisher, year, edition, pages
Elsevier, 2002. Vol. 43, no 6-7, 693-705 p.
Keyword [en]
Extension principles, Generalised terms, Monad compositions
National Category
Computer Science
URN: urn:nbn:se:umu:diva-3898DOI: 10.1016/S0898-1221(01)00314-5OAI: diva2:142797
Available from: 2004-04-22 Created: 2004-04-22 Last updated: 2012-05-14Bibliographically approved
In thesis
1. Categorical Unification
Open this publication in new window or tab >>Categorical Unification
2004 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis deals with different aspects towards many-valued unification which have been studied in the scope of category theory. The main motivation of this investigation comes from the fact that in logic programming, classical unification has been identified as the provision of coequalizers in Kleisli categories of term monads. Continuing in that direction, we have used categorical instrumentations to generalise the classical concept of a term. It is expected that this approach will provide an appropriate formal framework for useful developments of generalised terms as a basis for many-valued logic programming involving an extended notion of terms.

As a first step a concept for generalised terms has been studied. A generalised term is given by a composition of monads that again yields a monad, i.e. compositions of powerset monads with the term monad provide definitions for generalised terms. A composition of monads does, however, not always produce a monad. In this sense, techniques for monads composition provide a helpful tool for our concerns and therefore the study of these techniques has been a focus of this research.

The composition of monads make use of a lot of equations. Proofs become complicated, not to mention the challenge of understanding different steps of the equations. In this respect, we have studied visual techniques and show how a graphical approach can provide the support we need.

For the purpose of many-valued unification, similarity relations, generalised substitutions and unifiers have been defined for generalised terms.

91 p.
Report / UMINF, ISSN 0348-0542 ; 04.09
Datalogi, Monad compositions, generalised terms, many-valued logic, Datalogi
National Category
Computer Science
Research subject
Computing Science
urn:nbn:se:umu:diva-245 (URN)91-7305-642-1 (ISBN)
Public defence
2004-05-24, MA121, MIT-huset, Umeå University, Umeå, 13:15
Available from: 2004-04-22 Created: 2004-04-22Bibliographically approved

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Eklund, PatrikGalán, M.A.
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