Normative implications
Logic
2025-03-18 v1
Abstract
We continue to develop a research line initiated in \cite{wollic22}, studying I/O logic from an algebraic approach based on subordination algebras. We introduce the classes of slanted (co-)Heyting algebras as equivalent presentations of distributive lattices with subordination relations. Interpreting subordination relations as the algebraic counterparts of input/output relations on formulas yields (slanted) modal operations with interesting deontic interpretations. We study the theory of slanted and co-slanted Heyting algebras, develop algorithmic correspondence and inverse correspondence, and present some deontically meaningful axiomatic extensions and examples.
Cite
@article{arxiv.2503.12965,
title = {Normative implications},
author = {Andrea De Domenico and Ali Farjami and Krishna Manoorkar and Alessandra Palmigiano and Mattia Panettiere and Apostolos Tzimoulis and Xiaolong Wang},
journal= {arXiv preprint arXiv:2503.12965},
year = {2025}
}