A Kelsenian Deontic Logic

Inspired by Kelsen’s view that norms establish causal-like connections between facts and sanctions, we develop a deontic logic in which a proposition is obligatory iff its complement causes a violation. We provide a logic for normative causality, define non-contextual and contextual notions of illicit and duty, and show that the logic of such duties is well-behaved and solves the main deontic paradoxes.

Defeasibility applied to Forrester’s paradox

Deontic logic is a logic often used to formalise scenarios in the legal domain. Within the legal domain there are many exceptions and conflicting obligations. This motivates the enrichment of deontic logic with not only the notion of defeasibility, which allows for reasoning about exceptions, but a stronger notion of typicality that is based on defeasibility. KLM-style defeasible reasoning is a logic system that employs defeasibility while Propositional Typicality Logic (PTL) is a logic that does the same for the notion of typicality. Deontic paradoxes are often used to examine logic systems as the paradoxes provide undesirable results even if the scenarios seem intuitive. Forrester’s paradox is one of the most famous of these paradoxes. This paper shows that KLM-style defeasible reasoning and PTL can be used to represent and reason with Forrester’s paradox in such a way as to block undesirable conclusions without completely sacrificing desirable deontic properties.

Deontic Paradoxes and Tableau System for Kalinowski’s Deontic Logic K1

In 1953, Jerzy Kalinowski published his paper on the logic of normative sentences. The paper is recognized as one of the first publications on the formal system of deontic logic. The aim of this paper is to present a tableau system for Kalinowski’s deontic logic and to discuss some of the topics related to the paradoxes of deontic logic.

The Robbery Paradox

James E. Tomberlin [6] has recently argued that the logical systems of conditional obligation proposed by Azizah al-Hibri [1] and Peter Mott [5] are incapable of resolving at least one variant of the notorious contrary to duty imperative paradox, formulated originally by Chisholm [2]. Tomberlin concedes that these systems offer the very best of the' “conditional obligation approach” to deontic logic and concludes his critical discussion with the pessimistic remark that “the best of this approach is simply not good enough. Deontic logic … is obliged to turn elsewhere for its proper formulation and resolution of the deontic paradoxes” ([6], 373). Below I argue that Tomberlin's three central arguments against al-Hibri and Mott are fallacious.