# Propositional dynamic logic with Belnapian truth values

arXiv: https://arxiv.org/abs/1608.06084 · HTML: https://mlsanity.com/paper/1608.06084/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Aug 2016.

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

- [Abductive Reasoning in a Paraconsistent Framework](https://mlsanity.com/paper/2408.07287/) (2024)

## Abstract (arXiv)

We introduce BPDL, a combination of propositional dynamic logic PDL with the basic four-valued modal logic BK studied by Odintsov and Wansing (`Modal logics with Belnapian truth values', J. Appl. Non-Class. Log. 20, 279--301 (2010)). We modify the standard arguments based on canonical models and filtration to suit the four-valued context and prove weak completeness and decidability of BPDL.