umu.sePublications
ReferencesLink to record
Permanent link

Direct link
A categorical approach to unification of generalised terms
Show others...
2002 In: Electronic Notes in Theoretical Computer Science, Vol. 66, no 5, 11 pages-Article in journal (Refereed) Published
Place, publisher, year, pages
2002. Vol. 66, no 5, 11 pages-
Identifiers
urn:nbn:se:umu:diva-3901 (URN)oai:DiVA.org:umu-3901 (OAI)diva2:142800 (DiVA)
Available from2004-04-22 Created:2004-04-22Bibliographically 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.

Publisher, range
91 p.
Series
Report / UMINF, ISSN 0348-0542 ; 04.09
Keyword
Datalogi, Monad compositions, generalised terms, many-valued logic, Datalogi
National Category
Computer Science
Research subject
Computing Science
Identifiers
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
Opponent
Supervisors
Available from2004-04-22 Created:2004-04-22Bibliographically approved

Open Access in DiVA

No full text

Other links

http://www1.elsevier.com/gej-ng/31/29/23/120/52/26/66.5.004.pdf

Search in DiVA

By author/editor
Eklund, P.Galán, M.A.Medina, J.Ojeda-Aciego, M.Valverde, A.
By organisation
Computing Science

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Total: 20 hits
ReferencesLink to record
Permanent link

Direct link