State-based Modal Logics for Free Choice
Logic
2025-01-13 v3 Logic in Computer Science
Abstract
We study the mathematical properties of bilateral state-based modal logic (BSML), a modal logic employing state-based semantics (also known as team semantics), which has been used to account for free choice inferences and related linguistic phenomena. This logic extends classical modal logic with a nonemptiness atom which is true in a state if and only if the state is nonempty. We introduce two extensions of BSML and show that the extensions are expressively complete, and develop natural deduction axiomatizations for the three logics.
Keywords
Cite
@article{arxiv.2305.11777,
title = {State-based Modal Logics for Free Choice},
author = {Maria Aloni and Aleksi Anttila and Fan Yang},
journal= {arXiv preprint arXiv:2305.11777},
year = {2025}
}
Comments
46 pages; corrected a typo in the truth conditions and cleaned up the references