# General Interpolation by Polynomial Functions of Distributive Lattices

2 ORPAILLEUR - Knowledge representation, reasonning
Inria Nancy - Grand Est, LORIA - NLPKD - Department of Natural Language Processing & Knowledge Discovery
Abstract : 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}
Document type :
Conference papers
Domain :
Complete list of metadatas

Cited literature [14 references]

https://hal.archives-ouvertes.fr/hal-01093655
Contributor : Miguel Couceiro <>
Submitted on : Saturday, February 18, 2017 - 10:13:22 AM
Last modification on : Thursday, October 17, 2019 - 8:54:15 AM
Long-term archiving on : Friday, May 19, 2017 - 12:15:37 PM

### File

int-gen-revised.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : hal-01093655, version 1

### Citation

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. ⟨hal-01093655⟩

Record views