General Interpolation by Polynomial Functions of Distributive Lattices - Archive ouverte HAL
Communication Dans Un Congrès Année : 2012

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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Dates et versions

hal-01093655 , version 1 (18-02-2017)

Identifiants

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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