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Powersets of Terms and Composite Monads
Umeå University, Faculty of Science and Technology, Department of Computing Science.
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2004 (English)In: Technical Report, UMINF, ISSN 0348-0542, no 7Article in journal (Refereed) Published
Abstract [en]

Composing various powerset functors with the term monad gives rise to the concept of generalised 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.

Place, publisher, year, edition, pages
Umeå: Department of Computing Science , 2004. no 7
Keyword [en]
Composite monads, generalised terms, many-valued logic
URN: urn:nbn:se:umu:diva-3900OAI: diva2:142799
Available from: 2004-04-22 Created: 2004-04-22 Last updated: 2011-04-08Bibliographically 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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