| 1. |
- Eklund, Patrik, 1958-, et al.
(author)
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A categorical approach to unication of generalised terms
- 2002
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In: Electronic Notes in Theoretical Computer Science. - : Elsevier. - 1571-0661. ; 66:5, s. 41-45
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Journal article (peer-reviewed)abstract
- Unification of generalised terms in a many-valued setting involves considerations for equalities in the sense of similarity degrees between operators and thus similarities between terms. Further, allowing for substitutions of variables with powersets of terms requires ‘flattening’ operators for handling composition of variable substitutions. These techniques are available when using powerset functors composed with the term functor so that this composition of functors is extendable to a monad. In this paper we provide a framework for unification of such generalised terms.
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| 2. |
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| 3. |
- Eklund, Patrik, 1958-, et al.
(author)
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A framework for unication using powersets of terms
- 2002
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In: Proc. 9th Information Processing and Management of Uncertainty in Knowledge Based Systems Conference (IPMU 2002). ; , s. 1095-1098
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Conference paper (peer-reviewed)
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| 4. |
- Eklund, Patrik, 1958-, et al.
(author)
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A graphical approach to monad composition
- 2001
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In: Electronic Notes in Theoretical Computer Science. - 1571-0661. ; 40, s. 145-160
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Journal article (peer-reviewed)abstract
- In this paper we show how composite expressions involving natural transformations can be pictorially represented in order to provide graphical proof support for providing monad compositions. Examples are drawn using powerset monads composed with the term monad.
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| 5. |
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| 6. |
- Eklund, Patrik, 1958-, et al.
(author)
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Composing submonads
- 2001
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In: 31st IEEE International Symposium on Multiple-Valued Logic, 2001. Proceedings.. - Warsaw, Poland : IEEE Computer Society. - 0769510833 ; , s. 367-372
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Conference paper (peer-reviewed)abstract
- In this paper we use the concept of subfunctors and submonads in order to provide a technique for constructing new monads from given ones. We study some properties of these constructions and provide more examples on monad compositions
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| 7. |
- Eklund, Patrik, et al.
(author)
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Powersets of Terms and Composite Monads
- 2004
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In: Technical Report, UMINF. - Umeå : Department of Computing Science. - 0348-0542. ; :7
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Journal article (peer-reviewed)abstract
- 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.
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| 8. |
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| 9. |
- Eklund, Patrik, et al.
(author)
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Setfunctors, L-fuzzysetcategories, and generalizedterms
- 2002
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In: Computers and Mathematics with Applications. - : Elsevier. - 0898-1221 .- 1873-7668. ; 43:6-7, s. 693-705
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Journal article (peer-reviewed)abstract
- 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.
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| 10. |
- Eklund, P., et al.
(author)
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Similarities between powersets of terms
- 2004
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In: Fuzzy sets and systems (Print). - : Elsevier. - 0165-0114 .- 1872-6801. ; 144:1, s. 213-225
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Journal article (peer-reviewed)abstract
- 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.
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