An extension of the deontic calculus DSC1

The chief aim of the paper is to extend the calculusDSC ₁ (see [4]) in such a way as to satisfy all the requirements listed in [4] as well as a further stipulation — called ‘the principle of uninvolvement’ — to the effect that neither deontic compatibility nor deontic incompatibility of codes (see [2]) should be presupposed in deontic logic.     

A deontic logic of action

The formal language studied in this paper contains two categories of expressions, terms and formulas. Terms express events, formulas propositions. There are infinitely many atomic terms and complex terms are made up by Boolean operations. Where and are terms the atomic formulas have the form = ( is the same as ), Forb ( is forbidden) and Perm ( is permitted). The formulae are truth functional combinations of these. An algebraic and a model theoretic account of validity are given and an axiomatic system is provided for which they are characteristic.The closure principle, that what is not forbidden is permitted is shown to hold at the level of outcomes but not at the level of events. In the two final sections some other operators are considered and a semantics in terms of action games.     

Conditions for the acceptance of deontic conditionals.

Recent psychological research has investigated how people assess the probability of an indicative conditional. Most people give the conditional probability of q given p as the probability of if p then q. Asking about the probability of an indicative conditional, one is in effect asking about its acceptability. But on what basis are deontic conditionals judged to be acceptable or unacceptable? Using a decision theoretic analysis, we argue that a deontic conditional, of the form if p then must q or if p then may q, will be judged acceptable to the extent that the p & q possibility is preferred to the p & not-q possibility. Two experiments are reported in which this prediction was upheld. There was also evidence that the pragmatic suitability of permission rules is partly determined by evaluations of the not-p & q possibility. Implications of these results for theories of deontic reasoning are discussed.     

Two approaches to the formalisation of defeasible deontic reasoning

This paper compares two ways of formalising defeasible deontic reasoning, both based on the view that the issues of conflicting obligations and moral dilemmas should be dealt with from the perspective of nonmonotonic reasoning. The first way is developing a special nonmonotonic logic for deontic statements. This method turns out to have some limitations, for which reason another approach is recommended, viz. combining an already existing nonmonotonic logic with a deontic logic. As an example of this method the language of Reiter's default logic is extended to include modal expressions, after which the argumentation framework in default logic of [20, 22] is used to give a plausible logical analysis of moral dilemmas and prima facie obligations.An earlier version of this article was written while the author was working at the Department of Computing, Imperial College London, supported by ESRC/MRC/SERC Joint Council Initiative Project G9212036. Work on the present version was supported by a research fellowship of the Royal Netherlands Academy of Arts and Sciences, and by Esprit WG 8319 Modelage. I thank one of the referees for his interesting comments. Also, many thanks are due to Marek Sergot for valuable discussions on the topic of this paper.     

Expressivity results for deontic logics of collective agency

We use a deontic logic of collective agency to study reducibility questions about collective agency and collective obligations. The logic that is at the basis of our study is a multi-modal logic in the tradition of stit (‘sees to it that’) logics of agency. Our full formal language has constants for collective and individual deontic admissibility, modalities for collective and individual agency, and modalities for collective and individual obligations. We classify its twenty-seven sublanguages in terms of their expressive power. This classification enables us to investigate reducibility relations between collective deontic admissibility, collective agency, and collective obligations, on the one hand, and individual deontic admissibility, individual agency, and individual obligations, on the other.

     

Development of the deontic advantage in reasoning: Reply to Cummins

In response to Cummins’s report that comments on our article (Dack & Astington, Journal of Experimental Child Psychology, 2011, Vol. 110, pp. 94–114), this article clarifies our perspective on what constitutes the deontic advantage, and notes similarities and differences between Cummins’s perspective and our own. Like Cummins, we believe that young children are capable of deontic reasoning and that methodological factors alone cannot explain this ability. However, we maintain that it is important to be precise about methodology in order to facilitate investigation of how the deontic advantage changes over developmental time, and this question is our main interest, although as yet incompletely answered. Contrary to Cummins, we do not think that existing data can speak to the issue of the potential innateness of deontic reasoning. We also disagree with Cummins’s perspective on norm versus normative proposition and with some of her comparisons between deontic and epistemic phenomena.     

An analytic tableau calculus for a temporalised belief logic

A tableau is a refutation-based decision procedure for a related logic, and is among the most popular proof procedures for modal logics. In this paper, we present a labelled tableau calculus for a temporalised belief logic called TML⁺, which is obtained by adding a linear-time temporal logic onto a belief logic by the temporalisation method of Finger and Gabbay. We first establish the soundness and the completeness of the labelled tableau calculus based on the soundness and completeness results of its constituent logics. We then sketch a resolution-type proof procedure that complements the tableau calculus and also propose a model checking algorithm for TML⁺ based on the recent results for model checking procedures for temporalised logics. TML⁺ is suitable for formalising trust and agent beliefs and reasoning about their evolution for agent-based systems. Based on the logic TML⁺, the proposed labelled tableau calculus could be used for analysis, design and verification of agent-based systems operating in dynamic environments.     

Evidence of deontic reasoning in 3- and 4-year-old children

Deontic reasoning is reasoning about what one may, ought, or ought not do in a given set of circumstances. Virtually all of our social institutions and child-rearing practices presume the capacity to reason about deontic concepts, such as what is permitted, obligated, or prohibited. Despite this, very little is known about the development of deontic reasoning. Two experiments were conducted that contrasted children’s reasoning performance on deontic and indicative reasoning tasks (i.e., the reduced array selection version of the Wason card selection task). Like adults, children as young as 3 years of age were found to adopt a violation-detecting strategy more often when reasoning about the deontic case than when reasoning about the indicative case. These results indicate that violation detection emerges as an effective deontic reasoning very early in human development.     

On the calculus ratiocinator

The project, entertained by Leibniz and others, of creating an ideal language to facilitate ratiocination, is investigated in detail. Six possible relations between the ideal language (IL) and the natural language (NL) it replaces are studied. (1) IL says exactly what NL says, but says it much more clearly. (2) IL says exactly what NL says, but does so more economically. (3) IL says exactly what NL says, but does so more succinctly. (4) IL says part of what NL says, and says it more perspicuously. (5) IL says part of what NL says, and says it more perspicuously; moreover, there is an effective procedure for going from NL to IL. (6) IL says everything that NL says, plus some things that NL cannot say.     

Encoding time and signs exposure time in the representation of diagrammatic deontic meanings

It has been proposed that prohibition and obligation be represented in different ways in reasoning with deontic information (Bucciarelli & Johnson-Laird, 2005). Obligations are salient in permissible situations and prohibitions in impermissible situations. In some specific cases, differential initial representations are also consistently predicted from the comprehension of negations, if prohibition is considered as the negation of an obligation. Three experiments evaluate whether traffic signs of prohibition and obligation speed up the response time to the proposed direction represented and whether this advantage remains when people have more time to think. When making judgements about the manoeuvre performed by a vehicle, participants' response times are consistent with the predicted representation when they have a short time (i.e., 300 ms) to understand the premise. In this case they represent what is permissible by obligatory signs and also what is impermissible by prohibitory signs. However, if they have more time (i.e., 1000 ms) to understand the premise, they still represent what is permissible by obligatory signs but they seem to change their initial representations to what is permissible by prohibitory signs.     

The calculus of dissent: An analysis of terrorists' choice of targets

This article applies formal modeling to study a terrorist group's choice of whether to attack or not, and, in the case of an attack, which of two potential targets to strike. Each potential target individually takes protective measures that influence the terrorists' perceived success and failure, and, hence, the likelihood of attack. For domestic terrorism, a tendency for potential targets to overdeter is indicated. For transnational terrorism, cases of overdeterrence and underdeterrence are identified. We demonstrate that increased information about terrorists' preferences, acquired by the targets, may exacerbate inefficiency when deterrence efforts are not coordinated. In some cases, perfect information may eliminate the existence of a noncooperative solution.Yet the need for improved international cooperation is growing. Terrorism is inherently international in character, so that, paradoxically, the more individual states improve their national measures, the more it becomes attractive for the terrorists to cross frontiers ... (Wilkinson 1986, p. 49)