# A Formal Algebra for OLAP

**Authors:** Bart Kuijpers, Alejandro Vaisman  
**arXiv:** [1609.05020](https://arxiv.org/abs/1609.05020)  
**Date:** 2016-09-16  
**Summary page:** https://www.summarizepaper.com/en/paper/1609.05020v1/

## Key points

- The paper addresses the need for a standardized language in OLAP
- OLAP involves querying multidimensional databases
- There is no well-defined, accepted semantics for many operations in OLAP
- The authors present a set of operations that manipulate data cubes and define their semantics clearly
- These operations can be composed to create a powerful language for expressing complex OLAP queries
- Data is represented as a multidimensional cube with measures that can be aggregated along dimensions
- Operations are expressed as atomic transformations over a fixed multidimensional matrix
- Each transformation produces a new measure and generates a flag indicating input cells for the next operation
- The algebraic framework provides an effective way to manipulate data cubes
- The work offers formal proof of correctness for the operations, providing clear semantics for them
- This formal basis can serve as a foundation for developing more robust practical tools for data analysis in OLAP

## Summary

The paper "A Formal Algebra for OLAP" by Bart Kuijpers and Alejandro Vaisman addresses the need for a standardized language in Online Analytical Processing (OLAP). OLAP involves querying multidimensional databases and despite extensive research in this field, there is still no well-defined, accepted semantics for many of the usual operations. To tackle this problem, the authors present a set of operations that manipulate data cubes and define their semantics clearly. They prove that these operations can be composed to create a powerful language capable of expressing complex OLAP queries. In their approach, the authors represent data as a multidimensional cube where each cell contains one or more measures that can be aggregated along dimensions. The operations are expressed as a sequence of atomic transformations over a fixed multidimensional matrix. Each transformation produces a new measure and generates a flag indicating which cells should be considered as input for the next operation. This elegant algebraic framework provides an effective way to manipulate data cubes. What sets this work apart from previous efforts is its formal proof of correctness for the operations, offering clear semantics for them. By establishing this formal basis, the authors believe that their work will serve as a foundation to develop more robust practical tools for data analysis in OLAP. Overall, this paper contributes to bridging the gap in OLAP research by providing a standardized language and formal proof of correctness for its operations.