# Horn Fragments of the Halpern-Shoham Interval Temporal Logic (Technical Report)

arXiv: https://arxiv.org/abs/1604.03515 · HTML: https://mlsanity.com/paper/1604.03515/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Apr 2016.

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

- [The Horn Non-Clausal Class and its Polynomiality](https://mlsanity.com/paper/2108.13744/) (2021)
- [Decision Tree Learning with Spatial Modal Logics](https://mlsanity.com/paper/2109.08325/) (2021)

## Abstract (arXiv)

We investigate the satisfiability problem for Horn fragments of the Halpern-Shoham interval temporal logic depending on the type (box or diamond) of the interval modal operators, the type of the underlying linear order (discrete or dense), and the type of semantics for the interval relations (reflexive or irreflexive). For example, we show that satisfiability of Horn formulas with diamonds is undecidable for any type of linear orders and semantics. On the contrary, satisfiability of Horn formulas with boxes is tractable over both discrete and dense orders under the reflexive semantics and over dense orders under the irreflexive semantics, but becomes undecidable over discrete orders under the irreflexive semantics. Satisfiability of binary Horn formulas with both boxes and diamonds is always undecidable under the irreflexive semantics.