Normative implications

Andrea De Domenico; Ali Farjami; Krishna Manoorkar; Alessandra Palmigiano; Mattia Panettiere; Apostolos Tzimoulis; Xiaolong Wang

arXiv · 2503.12965

Normative implications

Andrea De Domenico·Ali Farjami·Krishna Manoorkar·Alessandra Palmigiano·Mattia Panettiere·Apostolos Tzimoulis·Xiaolong Wang

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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.

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BibTeX RIS

Andrea De Domenico, Ali Farjami, Krishna Manoorkar, Alessandra Palmigiano, Mattia Panettiere, Apostolos Tzimoulis, Xiaolong Wang. 2025-03-17. Normative implications. https://arxiv.org/abs/2503.12965

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