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Similarities between powersets of terms
Umeå University, Faculty of Science and Technology, Department of Computing Science.
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2004 (English)In: Fuzzy sets and systems (Print), ISSN 0165-0114, E-ISSN 1872-6801, Vol. 144, no 1, 213-225 p.Article in journal (Refereed) Published
Abstract [en]

Generalisation of the foundational basis for many-valued logic programming builds upon generalised terms in the form of powersets of terms. A categorical approach involving set and term functors as monads allows for a study of monad compositions that provide variable substitutions and compositions thereof. In this paper, substitutions and unifiers appear as constructs in Kleisli categories related to particular composed powerset term monads. Specifically, we show that a frequently used similarity-based approach to fuzzy unification is compatible with the categorical approach, and can be adequately extended in this setting; also some examples are included in order to illuminate the definitions.

Place, publisher, year, edition, pages
Elsevier, 2004. Vol. 144, no 1, 213-225 p.
Keyword [en]
Similarities, Fuzzy unification, Category theory and unification, Generalised terms
National Category
Computer and Information Science
Identifiers
URN: urn:nbn:se:umu:diva-3902DOI: 10.1016/j.fss.2003.10.021OAI: oai:DiVA.org:umu-3902DiVA: diva2:142801
Available from: 2004-04-22 Created: 2004-04-22 Last updated: 2017-12-14Bibliographically 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.

Publisher
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 from: 2004-04-22 Created: 2004-04-22Bibliographically approved

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