Xavier Parent

Moral particularism in the light of deontic logic

The aim of this paper is to strengthen the point made by Horty about the relationship between reason holism and moral particularism. In the literature prima facie obligations have been considered as the only source of reason holism. I strengthen Horty’s point in two ways. First, I show that contrary-to-duties provide another independent support for reason holism. Next I outline a formal theory that is able to capture these two sources of holism. While in simple settings the proposed account coincides with Horty’s one, this is not true in more complicated or “realistic” settings in which more than two norms collide. My chosen formalism is so-called input/output logic. A bottom-line example is introduced. It raises the issue of whether the conventional wisdom is right in assuming that normative reasons run parallel to epistemic ones.

Sing and Dance

Makinson and van der Torre [13] introduce a number of input/output (I/O) logics to reason about conditional norms. The key idea is to make obligations relative to a given set of conditional norms. The meaning of the normative concepts is, then, given in terms of a set of procedures yielding outputs for inputs. Using the same methodology, Stolpe[19,20] has developed some more I/O logics to include systems without the rule of weakening of the output (or principle of inheritance). We extend Stolpe’s account in two directions. First, we show how to make it support reasoning by cases−a common form of reasoning. Second, we show how to inject a new (as we call it, “aggregative”) form of cumulative transitivity, which we think is more suitable for normative reasoning. The main outcomes of the paper are soundness and completeness theorems for the proposed systems with respect to their intended semantics.

Intuitionistic Basis for Input/Output Logic

It is shown that I/O logic can be based on intuitionistic logic instead of classical logic. More specifically, it is established that, when going intuitionistic, a representation theorem is still available for three of the four (unconstrained) original I/O operations. The trick is to see a maximal consistent set as a saturated one. The axiomatic characterization is as in the classical case. Therefore, the choice between the two logics does not make any difference for the resulting framework.

On the Strong Completeness of Åqvist's Dyadic Deontic Logic G

Aqvists dyadic deontic logic G , which aims at providing an axiomatic characterization of Hanssons seminal system DSDL3 for conditional obligation, is shown to be strongly complete with respect to its intended modelling.

A complete axiom set for Hansson's deontic logic DSDL2

The main contribution of this paper is a (strong) completeness result for an axiomatization of Hansson [13]’s deontic system DSDL2, whose semantics involves a non-necessarily transitive betterness relation. Reference is made to a deductive system put forth by Åqvist [2, 3].

Two dimensional Standard Deontic Logic [including a detailed analysis of the 1985 Jones-Pörn deontic logic system]

This paper offers a two dimensional variation of Standard Deontic Logic SDL, which we call 2SDL. Using 2SDL we can show that we can overcome many of the difficulties that SDL has in representing linguistic sets of Contrary-to-Duties (known as paradoxes) including the Chisholm, Ross, Good Samaritan and Forrester paradoxes. We note that many dimensional logics have been around since 1947, and so 2SDL could have been presented already in the 1970s. Better late than never! As a detailed case study illustrating the power of 2SDL, we examine the system DL of Deontic Logic of Andrew Jones and Ingmar Pörn offered in 1985 to solve the Chisholm paradox of Contrary to Duties. The critical examination is done using logics and methods available in 1985 and solutions are proposed using what was available in 1985.

Maximality vs. Optimality in Dyadic Deontic Logic

This paper reports completeness results for dyadic deontic logics in the tradition of Hansson’s systems. There are two ways to understand the core notion of best antecedent-worlds, which underpins such systems. One is in terms of maximality, and the other in terms of optimality. Depending on the choice being made, one gets different evaluation rules for the deontic modalities, but also different versions of the so-called limit assumption. Four of them are disentangled, and compared. The main observation of this paper is that, even in the partial order case, the contrast between maximality and optimality is not as significant as one could expect, because the logic remains the same whatever notion of best is used. This is established by showing that, given analogous properties for the betterness relation, the same system is sound and complete with respect to its intended modelling. The chief result of this paper concerns Åqvist’s system F supplemented with the principle (CM) of cautious monotony. It is established that, under the maximality rule, F + (CM) is sound and complete with respect to the class of models in which the betterness relation is required be reflexive and smooth (for maximality). From this, a number of spin-off results are obtained. First and foremost, it is shown that a similar determination result holds for optimality; that is, under the optimality rule, F + (CM) is also sound and complete with respect to the class of models in which the betterness relation is reflexive and smooth (for optimality). Other spin-off results concern classes of models in which further constraints are placed on the betterness relation, like totalness and transitivity.

The pragmatic oddity in norm-based deontic logics

The ideal worlds of a possible worlds semantics may satisfy both a primary obligation and an associated secondary obligation, for example the obligation to keep a promise and the obligation to apologise for not keeping it. This is known as the pragmatic oddity introduced by Prakken and Sergot. We argue that an adequate treatment of the pragmatic oddity within a norm-based semantics can be obtained, by not allowing primary and secondary obligations to aggregate, because they are obligations of a different kind. On the basis of this conceptual analysis, we introduce two logics, depending on the stance taken on the representation of normative conflicts, and we present sound and complete proof systems for these logics. We then give a formal analysis, discuss extensions, and highlight various topics for further research.

A Model for Regulating of Ethical Preferences in Machine Ethics

Relying upon machine intelligence with reductions in the supervision of human beings, requires us to be able to count on a certain level of ethical behavior from it. Formalizing ethical theories is one of the plausible ways to add ethical dimensions to machines. Rule-based and consequence-based ethical theories are proper candidates for Machine Ethics. It is debatable that methodologies for each ethical theory separately might result in an action that is not always justifiable by human values. This inspires us to combine the reasoning procedure of two ethical theories, deontology and utilitarianism, in a utilitarian-based deontic logic which is an extension of STIT (Seeing To It That) logic. We keep the knowledge domain regarding the methodology in a knowledge base system called IDP. IDP supports inferences to examine and evaluate the process of ethical decision making in our formalization. To validate our proposed methodology we perform a Case Study for some real scenarios in the domain of robotics and automatous agents.

A Deontic Logic Reasoning Infrastructure

A flexible infrastructure for the automation of deontic and normative reasoning is presented. Our motivation is the development, study and provision of legal and moral reasoning competencies in future intelligent machines. Since there is no consensus on the “best” deontic logic formalisms and since the answer may be application specific, a flexible infrastructure is proposed in which candidate logic formalisms can be varied, assessed and compared in experimental ethics application studies. Our work thus links the historically rich research areas of classical higher-order logic, deontic logics, normative reasoning and formal ethics.