# Functorial Question Answering

## TL;DR

This paper reveals that distributional compositional models in natural language processing are mathematically equivalent to relational databases, leading to complexity results and defining question answering as NP-complete.

## Contribution

It establishes a formal correspondence between DisCo models and relational databases, connecting natural language semantics to database theory and complexity.

## Key findings

- DisCo models correspond to relational databases
- Semantic evaluation reduces to conjunctive query evaluation
- Question answering is NP-complete

## Abstract

Distributional compositional (DisCo) models are functors that compute the meaning of a sentence from the meaning of its words. We show that DisCo models in the category of sets and relations correspond precisely to relational databases. As a consequence, we get complexity-theoretic reductions from semantics and entailment of a fragment of natural language to evaluation and containment of conjunctive queries, respectively. Finally, we define question answering as an NP-complete problem.