# A complete axiom set for Hansson's deontic logic DSDL2

@article{Parent2010ACA, title={A complete axiom set for Hansson's deontic logic DSDL2}, author={Xavier Parent}, journal={Log. J. IGPL}, year={2010}, volume={18}, pages={422-429} }

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].

## 8 Citations

### Axioms for Hansson’s Dyadic Deontic Logics

- Computer Science
- 2018

This paper presents axiomatic systems equivalent to Bengt Hansson’s semantically defined dyadic deontic logics, DSDL1, DSDL2 and DSDL3. Each axiomatic system is demonstrated to be sound and complete…

### Adaptive Deontic Logics: A Survey

- PhilosophyFLAP
- 2019

This paper motivate, explain, illustrate, and discuss the use of ALs in deontic logic, and indicates some of the possibilities that the adaptive logic framework creates for tackling other types of problems within deontics logic.

### Maximality vs optimality in dyadic deontic logic- Completeness results for systems in Hansson's tradition.

- Computer Science
- 2013

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.

### COMPLETENESS OF ÅQVIST’S SYSTEMS E AND F

- EconomicsThe Review of Symbolic Logic
- 2014

This paper tackles the problem of whether Åqvist's dyadic deontic systems E and F are complete with respect to their intended Hanssonian preference-based semantics, and establishes that, under either the maximality rule or the optimality rule, they are sound and complete.

### Normative Reasoning and Consequence

- Philosophy, LawNormative Multi-Agent Systems
- 2013

In this chapter, we first provide a general introduction to the research area methodology and relevance, then we discuss normative reasoning for multiagent systems, and finally we discuss current…

### Contrary-to-Duty Paradoxes and Counterfactual Deontic Logic

- PhilosophyPhilosophia
- 2019

In this paper, I will discuss some examples of the so-called contrary-to-duty (obligation) paradox, a well-known puzzle in deontic logic. A contrary-to-duty obligation is an obligation telling us…

### Norms and Deontic Logic

- Computer Science, Law
- 2020

This chapter will first present standard deontic logic, then it will analyze its drawbacks, and a synthesis of some problems tackled in normative systems is presented: conditional obligations, norms with exceptions, violations, norm with deadlines and collective obligations.

### Maximality vs. Optimality in Dyadic Deontic Logic

- Computer ScienceJ. Philos. Log.
- 2014

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.

## References

SHOWING 1-10 OF 32 REFERENCES

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

- Computer ScienceDEON
- 2008

Aqvist's dyadic deontic logic G , which aims at providing an axiomatic characterization of Hansson's seminal system DSDL3 for conditional obligation, is shown to be strongly complete with respect to…

### An analysis of some deontic logics

- Philosophy
- 1969

The purpose of this article is to investigate the structure and to discuss the applications of deontic logics of von Wright’s type as presented in [15] and [19]. The ‘paradoxes’ which arise in these…

### Preference semantics for deontic logic part I — Simple models

- Computer Science
- 2003

Determination results for some deontic logics with respect to a simple preference-based semantics, in which possible worlds are ranked by comparative value but none need be best or top-ranked among alternatives, are presented.

### Defeasible Deontic Logic

- Philosophy
- 2010

Relevant to philosophy, law, management, and artificial intelligence, these papers explore the applicability of nonmonotonic or defeasible logic to normative reasoning. The resulting systems purport…

### On some questions of L. Åqvist

- PhilosophyLog. J. IGPL
- 2006

The question raised in [7] which the authors will answer positively is about the representability of Åqvist’s system G in a hierarchy of alethic modal logics Hm, m = 1, 2, · · ·.

### Reactive Kripke Models and Contrary to Duty Obligations

- PhilosophyDEON
- 2008

This is an intuitive description of the approach to modelling contrary to duty obligations through the analysis of typical problematic examples taken from Carmo and Jones, L. van der Torre and Prakken and Sergot.

### Dyadic Deontic Logic and Contrary-to-Duty Obligations

- Philosophy
- 1997

One of the main issues in the discussion on standard deontic logic (SDL) is the representation of contrary-to-duty (CTD) obligations. A well-known example is Forrester’s (1984) paradox of the gentle…

### Modal logic

- PhilosophyArtificial Intelligence Review
- 2004

This paper shows how the tree or tableau method provides a simple and easily comprehensible decision procedure for systems such as K, T, S4 and S5 and how the formal techniques of modal logic can be used to analyse several informal problems involving modal concepts, including cases combining modality with quantification.

### Handbook of Philosophical Logic

- Philosophy
- 2002

This paper presents a meta-mathematicalPrinciples of Deductive Systems: Foundations to Meta-mathematicics Murdoch J. Gabbay, with a focus on the role of formal semantics in the development of deterministic systems.

### Deontic Logic in Computer Science

- Computer ScienceLecture Notes in Computer Science
- 2012

The approach which is proposed is an extension to several agents of the ”bringing it about” operators of the STIT operators which holds the property of non monotonicity with respect to sets of agents.