Logic of Violations: A Gentzen System for Reasoning with Contrary-To-Duty Obligations

Abstract
In this paper we present a Gentzen system for reasoning with contrary-to-duty obligations. The intuition behind the system is that a contrary-to-duty is a special kind of normative exception. The logical machinery to formalise this idea is taken from substructural logics and it is based on the definition of a new non-classical connective capturing the notion of reparational obligation. Then the system is tested against well-known contrary-to-duty paradoxes.
Keywords 440106 Logic  C1  780100 Non-oriented Research
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DOI 10.26686/ajl.v4i0.1780
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Toleration and the Design of Norms.Luciano Floridi - 2015 - Science and Engineering Ethics 21 (5):1095-1123.
Obligation as Optimal Goal Satisfaction.Robert Kowalski & Ken Satoh - 2018 - Journal of Philosophical Logic 47 (4):579-609.

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