2025/03/17 by De Domenico, Andrea, Farjami, Ali, Manoorkar, Krishna +4
#FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.2503.12965
We continue to develop a research line initiated in \citewollic22, 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.