General Interpolation by Polynomial Functions of Distributive Lattices
Résumé
For a distributive lattice $L$, we consider the problem of interpolating functions $f\colon D\to L$ defined on a finite set $D\subseteq L^n$, by means of lattice polynomial functions of $L$. Two instances of this problem have already been solved. In the case when $L$ is a distributive lattice with least and greatest elements $0$ and $1$, Goodstein proved that a function $f\colon\{0,1\}^{n}\to L$ can be interpolated by a lattice polynomial function $p\colon L^{n}\to L$ if and only if $f$ is monotone; in this case, the interpolating polynomial $p$ was shown to be unique.The interpolation problem was also considered in the more general setting where $L$ is a distributive lattice, not necessarily bounded, and where$D\subseteq L^{n}$ is allowed to range over cuboids $D=\left\{ a_{1},b_{1}\right\} \times\cdots\times\left\{ a_{n},b_{n}\right\} $ with $a_{i},b_{i}\in L$ and $a_{i}
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https://hal.science/hal-01093655
Soumis le : samedi 18 février 2017-10:13:22
Dernière modification le : mercredi 20 novembre 2024-15:36:02
Archivage à long terme le : vendredi 19 mai 2017-12:15:37
Citer
Miguel Couceiro, Didier Dubois, Henri Prade, Agnès Rico, Tamas Waldhauser. General Interpolation by Polynomial Functions of Distributive Lattices. 14th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2012), Jul 2012, Catania, Italy. pp.347-355, ⟨10.1007/978-3-642-31718-7_36⟩. ⟨hal-01093655⟩
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