# Two variable fragment of Term Modal Logic

arXiv: https://arxiv.org/abs/1904.10260 · HTML: https://mlsanity.com/paper/1904.10260/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Apr 2019.

## Built on by (most cited first, 1 of 1)

- [Common Knowledge of Abstract Groups](https://mlsanity.com/paper/2211.16284/) (2022)

## Abstract (arXiv)

Term modal logics (TML) are modal logics with unboundedly many modalities, with quantification over modal indices, so that we can have formulas of the form exists y. forall x. (Boxx P(x,y) supsetDiamondy P(y,x)). Like First order modal logic, TML is also "notoriously" undecidable, in the sense that even very simple fragments are undecidable. In this paper, we show the decidability of one interesting fragment, that of two variable TML. This is in contrast to two-variable First order modal logic, which is undecidable.