Modal Extensions of CLoN with Bi-neighborhood Semantics
2026-06-29 • Logic in Computer Science
Logic in Computer Science
AI summaryⓘ
The authors explore a type of logic that is weaker than usual and involves tricky negation (saying something is not true in a limited sense). They develop a new way to understand these logics using neighborhood semantics, which involves looking at sets of possibilities around statements. Their work aims to handle moral rules and dilemmas in a way that avoids contradictions or making everything trivially true. By carefully defining how the negation works with modal operators, they show that interesting and meaningful logical rules can still apply.
non-normal modal logicneighborhood semanticsFDE logicweak negationmodal operatorsdeontic logicmoral dilemmaslogical axiomsrejection sets
Authors
Mahan Vaz, Daniel Skurt
Abstract
In this paper we will present neighborhood semantics for non-normal modal extensions of $\clon$, which is a sublogic of {\sf FDE}. Our framework is built upon earlier work on {\sf FDE}-based non-normal modal logics and employs two different neighborhood functions for each modal operator. Despite being a logic with a very weak negation operator, we will show that with the right definition of the rejection sets of the modal operators, we can validate non-trivial axioms that contain the weak negation operator. The philosophical aim of our approach is to construct the basis for deontic logics that are able to accommodate both the usual deontic principles and moral dilemmas, without resulting in trivialization of the system.