# A many-sorted polyadic modal logic

arXiv: https://arxiv.org/abs/1803.09709 · HTML: https://mlsanity.com/paper/1803.09709/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Mar 2018.

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

- [A Modal Logic for Possibilistic Reasoning with Fuzzy Formal Contexts](https://mlsanity.com/paper/2512.24980/) (2025)

## Abstract (arXiv)

This paper presents a many-sorted polyadic modal logic that generalizes some of the existing approaches. The algebraic semantics has led us to a many-sorted generalization of boolean algebras with operators, for which we prove the analogue of the J'onsson-Tarski theorem. While the transition from the mono-sorted logic to many-sorted one is a smooth process, we see our system as a step towards deepening the connection between modal logic and program verification, since our system can be seen as the propositional fragment of Matching logic, a first-order logic for specifying and reasoning about programs.