English

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.

Keywords

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}
}
R2 v1 2026-06-28T22:23:17.466Z