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Setfunctors, L-fuzzysetcategories, and generalizedterms
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.ORCID-id: 0000-0003-3965-2834
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för datavetenskap.
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2002 (Engelska)Ingår i: Computers and Mathematics with Applications, ISSN 0898-1221, E-ISSN 1873-7668, Vol. 43, nr 6-7, s. 693-705Artikel i tidskrift (Refereegranskat) 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.

Ort, förlag, år, upplaga, sidor
Elsevier, 2002. Vol. 43, nr 6-7, s. 693-705
Nyckelord [en]
Extension principles, Generalised terms, Monad compositions
Nationell ämneskategori
Datavetenskap (datalogi)
Identifikatorer
URN: urn:nbn:se:umu:diva-3898DOI: 10.1016/S0898-1221(01)00314-5Scopus ID: 2-s2.0-0036498585OAI: oai:DiVA.org:umu-3898DiVA, id: diva2:142797
Tillgänglig från: 2004-04-22 Skapad: 2004-04-22 Senast uppdaterad: 2024-04-11Bibliografiskt granskad
Ingår i avhandling
1. Categorical Unification
Öppna denna publikation i ny flik eller fönster >>Categorical Unification
2004 (Engelska)Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
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.

Förlag
s. 91
Serie
Report / UMINF, ISSN 0348-0542 ; 04.09
Nyckelord
Datalogi, Monad compositions, generalised terms, many-valued logic, Datalogi
Nationell ämneskategori
Datavetenskap (datalogi)
Forskningsämne
administrativ databehandling
Identifikatorer
urn:nbn:se:umu:diva-245 (URN)91-7305-642-1 (ISBN)
Disputation
2004-05-24, MA121, MIT-huset, Umeå University, Umeå, 13:15
Opponent
Handledare
Tillgänglig från: 2004-04-22 Skapad: 2004-04-22 Senast uppdaterad: 2018-01-13Bibliografiskt granskad

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