Contrary-to-Duty Paradoxes and Counterfactual Deontic Logic

Philosophia - 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...     

Dynamic Deontic Logic and its Paradoxes

In Meyer’s promising account [7] deontic logic is reduced to a dynamic logic. Meyer claims that with his account “we get rid of most (if not all) of the nasty paradoxes that have plagued traditional deontic logic.” But as was shown by van der Meyden in [4], Meyer’s logic also contains a paradoxical formula. In this paper we will show that another paradox can be proven, one which also effects Meyer’s “solution” to contrary to duty obligations and his logic in general. Presented by Hannes Leitgeb     

A New Representation Theorem for Contranegative Deontic Logic

The logic of an ought operator O is contranegative with respect to an underlying preference relation if it satisfies the property Op & (¬p)(¬q) Oq. Here the condition that is interpolative ((p (pq) q) (q (pq) p)) is shown to be necessary and sufficient for all -contranegative preference relations to satisfy the plausible deontic postulates agglomeration (Op & OqO(p&q)) and disjunctive division (O(p&q) Op Oq).     

从动态命题逻辑PDL到动态道义逻辑DDL

一动态命题逻辑的来源和基本构想动态逻辑DL(DYNAM IC LOGIC)是关于行动和程序推理的形式系统。DL可以描述为三个经典逻辑的合成:一是一阶谓词逻辑;二是模态逻辑;三是正则事件(REGULAR EVENT)的代数。DL区分于经典逻辑的地方是其真值的特性:经典逻辑的真值是静态的,一公式Φ的真值由其结构中自由变元的取值所决定,公式Φ导致的真值和赋值被看做不可改变的。[1]而动态逻辑在这点上正好相反,在DL中,有清晰的被称做程序的语形结构,这些程序的作用就是改变变元的值,由此进而改变公式的值。这些改变在经典谓词逻辑中,是在元逻辑的层…     

Leibniz and the Square: A Deontic Logic for the Vir Bonus

Seventeenth century philosopher Gottfried Leibniz's contributions to metaphysics, mathematics, and logic are well known. Lesser known is his ‘invention’ of deontic logic, and that his invention derives from the alethic logic of the Aristotelian square of opposition. In this paper, I show how Leibniz developed this ‘logic of duties’, which designates actions as ‘possible, necessary, impossible, and omissible’ for a ‘vir bonus’ (good person). I show that for Leibniz, deontic logic can determine whether a given action, e.g. as permitted, is therefore obligatory or prohibited (impossible). Secondly, since the deontic modes are derived from what is possible, necessary, etc., for a good person to do, and that ‘right and obligation’ are the ‘moral qualities’ of a good person, we can see how Leibniz derives deontic logic from these moral qualities. Finally, I show how Leibniz grounds a central deontic concept, namely obligation, in the human capacity for freedom.     

Supererogation in Deontic Logic: Metatheory for DWE and Some Close Neighbours

In "Doing Well Enough: Toward a Logic for Common Sense Morality", Paul McNamara sets out a semantics for a deontic logic which contains the operator It is supererogatory that. As well as having a binary accessibility relation on worlds, that semantics contains a relative ordering relation, . For worlds u, v and w, we say that u w v when v is at least as good as u according to the standards of w. In this paper we axiomatize logics complete over three versions of the semantics. We call the strongest of these logics DWE for Doing Well Enough.     

The Moral Dilemmas Debate, Deontic Logic, and the Impotence of Argument

In this paper I argue for modesty concerning what theoretical reason can accomplish in the moral dilemmas debate. Specifically, I contend that philosophers' conclusions for or against moral dilemmas are driven less by rational argument and more by how the moral world intuitively appears to them.I support this thesis by first considering an argument against moral dilemmas, the argument from deontic logic, and showing that its persuasive force depends on one's having already accepted its conclusion. I then make a different, and general, case that any argument in the moral dilemmas debate concerning the defeasibility of conflicting obligations can be marginalized by making not-unreasonable adjustments in the conditions for wrongdoing.These two strands of argument are related by the notion of inescapable wrongdoing. It is our standing intuitions about inescapable wrongdoing which make the relevant deontic logical principles plausible or implausible to us. And whether wrongdoing can be inescapable is central to deciding what the conditions for wrongdoing are. My conclusion is that the arguments in the moral dilemmas debate merely implement whatever standing intuition we have concerning inescapable wrongdoing, and that apart from any such intuition the arguments are unpersuasive.     

Deontic Interpreted Systems

We investigate an extension of the formalism of interpreted systems by Halpern and colleagues to model the correct behaviour of agents. The semantical model allows for the representation and reasoning about states of correct and incorrect functioning behaviour of the agents, and of the system as a whole. We axiomatise this semantic class by mapping it into a suitable class of Kripke models. The resulting logic, KD45_n ^i-j, is a stronger version of KD, the system often referred to as Standard Deontic Logic. We extend this formal framework to include the standard epistemic notions defined on interpreted systems, and introduce a new doubly-indexed operator representing the knowledge that an agent would have if it operates under the assumption that a group of agents is functioning correctly. We discuss these issues both theoretically and in terms of applications, and present further directions of work.     

论西方可废止性道义逻辑的形式化研究及其存在的问题

道义逻辑和非单调逻辑是在不同的学科内根据不同的原因产生和发展的,分属两种不同的逻辑。但受人工智能理论的启发,西方研究人工智能的专家和逻辑学家逐渐认识到道义理论和非单调推理之间有很大的关系,把两者结合起来研究,不但可以解决道义逻辑中的令人棘手的悖论问题,还可以为道义逻辑提供更为完美的理论框架。于是,在道义逻辑的研究中出现了一种新的方向:与非单调推理相结合,建立具有可废止性的(DEFEASIBLE)道义逻辑系统。目前,国内关于这方面的研究较为陌生,所以我们从语形和语义两个角度对西方可废止性道义逻辑的形式化研究给出系统…     

Action and Knowledge in Alternating-Time Temporal Logic

Alternating-time temporal logic (ATL) is a branching time temporal logic in which statements about what coalitions of agents can achieve by strategic cooperation can be expressed. Alternating-time temporal epistemic logic (ATEL) extends ATL by adding knowledge modalities, with the usual possible worlds interpretation. This paper investigates how properties of agents’ actions can be expressed in ATL in general, and how properties of the interaction between action and knowledge can be expressed in ATEL in particular. One commonly discussed property is that an agent should know about all available actions, i.e., that the same actions should be available in indiscernible states. Van der Hoek and Wooldridge suggest a syntactic expression of this semantic property. This paper shows that this correspondence in fact does not hold. Furthermore, it is shown that the semantic property is not expressible in ATEL at all. In order to be able to express common and interesting properties of action in general and of the interaction between action and knowledge in particular, a generalization of the coalition modalities of ATL is proposed. The resulting logics, ATL-A and ATEL-A, have increased expressiveness without loosing ATL’s and ATEL’s tractability of model checking.     

On the Dynamic Logic of Agency and Action

We present a Hilbert style axiomatization and an equational theory for reasoning about actions and capabilities. We introduce two novel features in the language of propositional dynamic logic, converse as backwards modality and abstract processes specified by preconditions and effects, written as ${\varphi \Rightarrow \psi}$ and first explored in our recent paper (Hartonas, Log J IGPL Oxf Univ Press, 2012), where a Gentzen-style sequent calculus was introduced. The system has two very natural interpretations, one based on the familiar relational semantics and the other based on type semantics, where action terms are interpreted as types of actions (sets of binary relations). We show that the proof systems do not distinguish between the two kinds of semantics, by completeness arguments. Converse as backwards modality together with action types allow us to produce a new purely equational axiomatization of Dynamic Algebras, where iteration is axiomatized independently of box and where the fixpoint and Segerberg induction axioms are derivable. The system also includes capabilities operators and our results provide then a finitary Hilbert-style axiomatization and a decidable system for reasoning about agent capabilities, missing in the KARO framework.     

Generalizing Qualia Inversion

Philosophers who advocate the possibility of spectrum inversionoften conclude that the qualitative content of experiential states pose aserious problem for functionalism. I argue that in order for the inversion hypothesis to supportthis conclusion one needs to show that it generalizes to all species of qualia. By examiningfeatures of touch, taste, and olfactory sensations, I show there is good reason to resistthis generalization, in which case appeals to the possibility of spectral inversion areconsiderably less effective than they may initially appear