A structured argumentation framework for detaching conditional obligations

We present a general formal argumentation system for dealing with the detachment of conditional obligations. Given a set of facts, constraints, and conditional obligations, we answer the question whether an unconditional obligation is detachable by considering reasons for and against its detachment. For the evaluation of arguments in favor of detaching obligations we use a Dung-style argumentation-theoretical semantics. We illustrate the modularity of the general framework by considering some extensions, and we compare the framework to some related approaches from the literature.Comment: This is our submission to DEON 2016, including the technical appendi

Deontic logic as a study of conditions of rationality in norm-related activities

The program put forward in von Wright's last works defines deontic logic as ``a study of conditions which must be satisfied in rational norm-giving activity'' and thus introduces the perspective of logical pragmatics. In this paper a formal explication for von Wright's program is proposed within the framework of set-theoretic approach and extended to a two-sets model which allows for the separate treatment of obligation-norms and permission norms. The three translation functions connecting the language of deontic logic with the language of the extended set-theoretical approach are introduced, and used in proving the correspondence between the deontic theorems, on one side, and the perfection properties of the norm-set and the ``counter-set'', on the other side. In this way the possibility of reinterpretation of standard deontic logic as the theory of perfection properties that ought to be achieved in norm-giving activity has been formally proved. The extended set-theoretic approach is applied to the problem of rationality of principles of completion of normative systems. The paper concludes with a plaidoyer for logical pragmatics turn envisaged in the late phase of Von Wright's work in deontic logic

Enriching deontic logic with typicality

Legal reasoning is a method that is applied by legal practitioners to make legal decisions. For a scenario, legal reasoning requires not only the facts of the scenario but also the legal rules to be enforced within it. Formal logic has long been used for reasoning tasks in many domains. Deontic logic is a logic which is often used to formalise legal scenarios with its built-in notions of obligation, permission and prohibition. Within the legal domain, it is important to recognise that 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 which is based on defeasibility. KLM-style defeasible reasoning introduced by Kraus, Lehmann and Magidor (KLM), is a logic system that employs defeasibility while a logic that serves the same role for the stronger notion of typicality is Propositional Typicality Logic (PTL). Deontic paradoxes are often used to examine deontic logic systems as the scenarios arising from the paradoxes' structures produce undesirable results when desirable deontic properties are applied to the scenarios. This is despite the various scenarios themselves seeming intuitive. This dissertation shows that KLM-style defeasible reasoning and PTL are both effective when applied to the analysis of the deontic paradoxes. We first present the background information which comprises propositional logic, which forms the foundation for the other logic systems, as well as the background of KLM-style defeasible reasoning, deontic logic and PTL. We outline the paradoxes along with their issues within the presentation of deontic logic. We then show that for each of the two logic systems we can intuitively translate the paradoxes, satisfy many of the desirable deontic properties and produce reasonable solutions to the issues resulting from the paradoxes

Computing Strong and Weak Permissions in Defeasible Logic

In this paper we propose an extension of Defeasible Logic to represent and compute three concepts of defeasible permission. In particular, we discuss different types of explicit permissive norms that work as exceptions to opposite obligations. Moreover, we show how strong permissions can be represented both with, and without introducing a new consequence relation for inferring conclusions from explicit permissive norms. Finally, we illustrate how a preference operator applicable to contrary-to-duty obligations can be combined with a new operator representing ordered sequences of strong permissions which derogate from prohibitions. The logical system is studied from a computational standpoint and is shown to have liner computational complexity

Giving permission implies giving choice

When we want to examine different kinds of forms of acts within the framework of the description of the Dutch criminal law, whether an act is permitted or not permitted, we can encounter a difference. On the one hand, it could be the case that a certain act is permitted by a competent normative authority. On the other hand, it could be the case that in the Dutch criminal law a certain act is weak permitted without a competent normative authority having enacted that permission. The article presents the formalisation of the weak and strong permission in deontic logic based on the logic of enactment. A permission that follows from the absence of a prohibition, we call a weak permission; this permission is not enacted. A strong permission is always enacted (implicitly or explicitly), and implies a giving choice. The distinction between these two types of permission is a consequence of the universality of a normative system by the closure rule: 'whatever is not forbidden, is permitted'

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

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