# Hypertableau Reasoning for Description Logics

arXiv: https://arxiv.org/abs/1401.3485 · HTML: https://mlsanity.com/paper/1401.3485/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jan 2014.

## Built on by (most cited first, 2 of 2)

- [FALCON: Scalable Reasoning over Inconsistent ALC Ontologies](https://mlsanity.com/paper/2208.07628/) (2022)
- [A New Tractable Description Logic under Categorical Semantics](https://mlsanity.com/paper/2505.08916/) (2025)

## Abstract (arXiv)

We present a novel reasoning calculus for the description logic SHOIQ^+---a knowledge representation formalism with applications in areas such as the Semantic Web. Unnecessary nondeterminism and the construction of large models are two primary sources of inefficiency in the tableau-based reasoning calculi used in state-of-the-art reasoners. In order to reduce nondeterminism, we base our calculus on hypertableau and hyperresolution calculi, which we extend with a blocking condition to ensure termination. In order to reduce the size of the constructed models, we introduce anywhere pairwise blocking. We also present an improved nominal introduction rule that ensures termination in the presence of nominals, inverse roles, and number restrictions---a combination of DL constructs that has proven notoriously difficult to handle. Our implementation shows significant performance improvements over state-of-the-art reasoners on several well-known ontologies.