Conditional Obligations Research Articles

Contrary-to-Duty Reasoning: A Categorical Approach

This paper provides an analysis of contrary-to-duty reasoning from the proof-theoretical perspective of category theory. While Chisholm’s paradox hints at the need of dyadic deontic logic by showing that monadic deontic logics are not able to adequately model conditional obligations and contrary-to-duties, other arguments can be objected to dyadic approaches in favor of non-monotonic foundations. We show that all these objections can be answered at one fell swoop by modeling conditional obligations within a deductive system defined as an instance of a symmetric monoidal closed category. Using category theory as a foundational framework for logic, we show that it is possible to model conditional normative reasoning and conflicting obligations within a monadic approach without adding further operators or considering deontic conditionals as primitive.

Epistemicism, paradox, and conditional obligation

Stewart Shapiro has objected to the epistemicist theory of vagueness on grounds that it gives counterintuitive predictions about cases involving conditional obligation. This paper details a response on the epistemicist’s behalf. I first argue that Shapiro’s own presentation of the objection is unsuccessful as an argument against epistemicism. I then reconstruct and offer two alternative arguments inspired by Shapiro’s considerations, and argue that these fail too, given the information-sensitive nature of conditional obligations.

The impact of egocentric vs. allocentric agency attributions on the neural bases of reasoning about social rules

We used the “standard” and “switched” social contract versions of the Wason Selection-task to investigate the neural bases of human reasoning about social rules. Both these versions typically elicit the deontically correct answer, i.e. the proper identification of the violations of a conditional obligation. Only in the standard version of the task, however, this response corresponds to the logically correct one. We took advantage of this differential adherence to logical vs. deontical accuracy to test the different predictions of logic rule-based vs. visuospatial accounts of inferential abilities in 14 participants who solved the standard and switched versions of the Selection-task during functional-Magnetic-Resonance-Imaging. Both versions activated the well known left fronto-parietal network of deductive reasoning. The standard version additionally recruited the medial parietal and right inferior parietal cortex, previously associated with mental imagery and with the adoption of egocentric vs. allocentric spatial reference frames. These results suggest that visuospatial processes encoding one׳s own subjective experience in social interactions may support and shape the interpretation of deductive arguments and/or the resulting inferences, thus contributing to elicit content effects in human reasoning.

Commitment: some formal interpretations

Abstract We often use sentences that seem conditional in nature when we reason about normative issues, e.g. ‘If you have promised to do something, you should keep your promise’ and ‘If you have done something bad, you should apologize’. We seem to think that promise-making in some sense commits us to promise-keeping and that acting bad in some sense creates an obligation to apologize. It is, however, not obvious how we should symbolize such sentences in a formal language. The purpose of this essay is to investigate some different possible formalizations of different conditional obligation sentences. I consider seven different interpretations of the concept of commitment or conditional obligation and I say something about the logical properties of these different interpretations.

Programming norm change

To adequately deal with unpredictable and dynamic environments, normative frameworks typically deployed in mechanisms for modifying the norms at runtime are crucial. We present the syntax and operational semantics of programming constructs to facilitate runtime norm modification, allowing a programmer to specify when and how the norms may be changed by external agents or by the normative mechanism. The norms take on the form of conditional obligations and prohibitions, instantiating obligations and prohibitions. We present rule-based constructs for runtime modification of the norms and their instances, and a mechanism for automatically updating the instances when their underlying norms change. Moreover, we investigate a mechanism for avoiding norm conflicts.

A Remark on Iffy Oughts

Every adequate semantics for conditionals and deontic ought must offer a solution to the miners paradox about conditional obligations. Kolodny and MacFarlane have recently argued that such a semantics must reject the validity of modus ponens. I demonstrate that rejecting the validity of modus ponens is inessential for an adequate solution to the paradox. 1 The Miners Paradox Every adequate semantics for conditionals and deontic ought must offer a solution to the miners paradox about conditional obligations. Kolodny and MacFarlane (2010) have recently argued that such a semantics must reject the validity of modus ponens. My goal in this paper is to demonstrate that rejecting modus ponens is inessential for solving the puzzle. I begin with a brief outline of Kolodny’s and MacFarlane’s analysis of the paradox and their reasons for rejecting modus ponens. Then I develop and defend a semantics for deontic conditionals that avoids the miners paradox while preserving the validity of modus ponens. The key observation of this paper is that Kolodny’s and MacFarlane’s case against modus ponens trades heavily on assumptions about logical consequence that their very own semantics shows are dubious. The validity of modus ponens may very well have its limits, but we have no compelling reason to think that it is invalid for deontic conditionals and certainly would need more than the miners paradox to show that it is. Here is the miners paradox. Ten miners are trapped either in shaft A or in shaft B, but we do not know which one. Water threatens to flood the shafts. We only have enough sandbags to block one shaft but not both. If one shaft is blocked, all of the water will go into the other shaft, killing every miner inside. If we block neither shaft, both will be partially flooded, killing one miner. Published in the Journal of Philosophy 109(7): 449–461, 2012 1I observe elsewhere that modus ponens is in fact a problematic rule of inference for socalled “Thomason conditionals” such as “If Mary is deceiving me, I’ll never believe it” (see Willer (2010) for discussion). My goal here is then not to offer an unqualified defense of modus ponens but rather to contribute to the (no less interesting) project of determining the exact scope of its validity.

An adaptive logic framework for conditional obligations and deontic dilemmas

Lou Goble proposed powerful conditional deontic logics (CDPM) that are able to deal with deontic conflicts by means of restricting the inheritance principle. One of the central problems for dyadic deontic logics is to properly treat the restricted applicability of the principle “strengthening the antecedent”. In most cases it is desirable to derive from an obligation A under condition B, that A is also obliged under condition B and C. However, there are important counterexamples. Goble proposed a weakened rational monotonicity principle to tackle this problem. This solution is suboptimal as it is for some examples counter-intuitive or even leads to explosion. The paper identifies also other problems of Goble’s systems. For instance, to make optimal use of the restricted inheritance principle, in many cases the user has to manually add certain statements to the premises. An adaptive logic framework based on CDPM is proposed which is able to tackle these problems. It allows for certain rules to be applied as much as possible. In this way counter-intuitive consequences as well as explosion can be prohibited and no user interference is required. Furthermore, for non-conflicting premise sets the adaptive logics are equivalent to Goble’s dyadic version of standard deontic logic.

Knowledge State Algorithms

We introduce the novel concept of knowledge states. The knowledge state approach can be used to construct competitive randomized online algorithms and study the trade-off between competitiveness and memory. Many well-known algorithms can be viewed as knowledge state algorithms. A knowledge state consists of a distribution of states for the algorithm, together with a work function which approximates the conditional obligations of the adversary. When a knowledge state algorithm receives a request, it then calculates one or more “subsequent” knowledge states, together with a probability of transition to each. The algorithm uses randomization to select one of those subsequents to be the new knowledge state. We apply this method to randomized k-paging. The optimal minimum competitiveness of any randomized online algorithm for the k-paging problem is the kth harmonic number, $H_{k}=\sum^{k}_{i=1}\frac{1}{i}$. Existing algorithms which achieve that optimal competitiveness must keep bookmarks, i.e., memory of the names of pages not in the cache. An H k -competitive randomized algorithm for that problem which uses O(k) bookmarks is presented, settling an open question by Borodin and El-Yaniv. In the special cases where k=2 and k=3, solutions are given using only one and two bookmarks, respectively.

What is Really Wrong with Torture?

How can deontologists reconcile the stringency of the moral prohibition on torture with the recognition that it may sometimes be the only means to prevent catastrophe? This article proposes a conception of deontology that allows for the resolution of this dilemma. Casting deontology in terms of the distinction between categorical and conditional obligations, we articulate a theoretical distinction between principles and exceptions. Torture can never be permitted or authorized by a rule or principle. Whenever it is justifiably performed it is performed under urgent and exceptional circumstances. On this basis the practical necessity of torture may be acknowledged, while the categorical nature of the prohibition on torture is maintained. This explains how torture might be categorically prohibited by international law, yet at the same time be subject to a defence of necessity or duress under international criminal law.

Taking Ross's Paradox Seriously A note on the original problems of deontic logic

: It is argued that Ross's Paradox in deontic logic is a problem which should be taken seriously, and which can be given a solution which also solves some other wellknown paradoxes and the traditional problems with conditional obligation.

Institutions with a hierarchy of authorities in distributed dynamic environments

A single global authority is not sufficient to regulate heterogenous agents in multiagent systems based on distributed architectures, due to idiosyncratic local situations and to the need to regulate new issues as soon as they arise. On the one hand institutions should be structured as normative systems with a hierarchy of authorities able to cope with the dynamics of local situations, but on the other hand higher authorities should be able to delimit the autonomy of lower authorities to issue valid norms. In this paper, we study the interplay of obligations and strong permissions in the context of hierarchies of authorities using input/output logic, because its explicit norm base facilitates reasoning about norm base maintenance, and it covers a variety of conditional obligations and permissions. We combine the logic with constraints, priorities and hierarchies of authorities. In this setting, we observe that Makinson and van der Torre’s notion of prohibition immunity for permissions is no longer sufficient, and we introduce a new notion of permission as exception and a new distinction between static and dynamic norms. We show how strong permissions can dynamically change an institution by adding exceptions to obligations, provide an explicit representation of what is permitted to the subjects of the normative system and allow higher level authorities to limit the power of lower level authorities to change the normative system.

Combinations of tense and deontic modality: On the [formula omitted] approach to temporal logic with historical necessity and conditional obligation

We consider three infinite hierarchies of what I call “two-dimensional temporal logics with explicit realization operators”, viz. (i) one without historical or deontic modalities, (ii) one with historical but without deontic modalities, and (iii) one with historical and with dyadic deontic modalities for conditional obligation and permission. Sound and complete axiomatizations are obtained for all three hierarchies relative to a simplified version of the finite co-ordinate-system semantics given for so-called T × W logic of historical necessity in [L. Åqvist, The logic of historical necessity as founded on two-dimensional modal tense logic, J. Philos. Logic 28 (1999) 329–369].

Knowledge State Algorithms and the 2-Server Problem

Abstract We introduce the novel concept of knowledge states. A knowledge state simply states conditional obligations of an adversary, by fixing a work function, and gives a distribution for the algorithm. When a knowledge state algorithm receives a request, it then calculates one or more “subsequent” knowledge states, together with a probability of transition to each. The algorithm then uses randomization to select one of those subsequents to be the new knowledge state. Although the formal definition of knowledge state algorithms appears, as yet, in no publication, many well-known algorithms can be viewed as knowledge state algorithms. We have used optimization techniques to construct a non-trivial knowledge state algorithm for the 2-server problem on the line with competitive ratio 71 36 ≈ 1.972 . As much as one avenue of investigation might be to further improve this result for the line, what we really envision is to use this technique to finally settle the question of whether there exists an online algorithm with competitive ratio better than 2 for general spaces – a notorious open problen in online algorithms. For progress in that direction, we consider the class of metric spaces M 2 , 4 , which consists of all metric spaces where every distance is either 1 or 2, and where the perimeter of every triangle is either 3 or 4. Using the knowledge state approach we are able to obtain the result that there exists a C-competitive randomized online algorithm for the 2-server problem in the space M 2 , 4 with C = 173 + 137 112 ≈ 1.649149106 .

Permission from an Input/Output Perspective

Input/output logics are abstract structures designed to represent conditional obligations and goals. In this paper we use them to study conditional permission. This perspective provides a clear separation of the familiar notion of negative permission from the more elusive one of positive permission. Moreover, it reveals that there are at least two kinds of positive permission. Although indistinguishable in the unconditional case, they are quite different in conditional contexts. One of them, which we call static positive permission, guides the citizen and law enforcement authorities in the assessment of specific actions under current norms, and it behaves like a weakened obligation. Another, which we call dynamic positive permission, guides the legislator. It describes the limits on the prohibitions that may be introduced into a code, and under suitable conditions behaves like a strengthened negative permission.

Obligation and the Conditional in Stit Theory

In this paper, we consider two different ways in which modus-ponens type reasoning with conditional obligations may be formalized. We develop necessary and sufficient conditions for the validity of each, and make some philosophical observations about the differences between the minor premises that each formalization requires. All this is done within the context of the Belnap-Perloff stit theory.

McNaughton and Rawling on the Agent-relative/Agent-neutral Distinction

In this paper, I criticize David McNaughton and Piers Rawling's formalization of the agent-relative/agent-neutral distinction. I argue that their formalization is unable to accommodate an important ethical distinction between two types of conditional obligations. I then suggest a way of revising their formalization so as to fix the problem.

Input/Output Logics

In a range of contexts, one comes across processes resembling inference, but where input propositions are not in general included among outputs, and the operation is not in any way reversible. Examples arise in contexts of conditional obligations, goals, ideals, preferences, actions, and beliefs. Our purpose is to develop a theory of such input/output operations. Four are singled out: simple-minded, basic (making intelligent use of disjunctive inputs), simple-minded reusable (in which outputs may be recycled as inputs), and basic reusable. They are defined semantically and characterised by derivation rules, as well as in terms of relabeling procedures and modal operators. Their behaviour is studied on both semantic and syntactic levels.

Conditional obligation and positive permission for agents in time

This paper investigates the semantic treatment of conditional obligation, explicit permission (often called positive permission), and prohibition based on models with agents and branched time. In such models branches (rather than moments) are taken as basic, and the branching provides a way to represent the indeterminism which is normally presupposed by talk of free will, responsibility, action and ability. Careful treatment of the relation between ability and responsibility avoids many common problems with accounts of conditional obligation. Recognition of the generality often involved in conditional obligations makes possible a sensitive way of expressing some kinds of general prohibitions, which in turn makes it possible to account for the special role of explicit permission.

Three characterizability problems in deontic logic

We consider an infinite hierarchy of systems of Alethic Modal Logic with so-called Levels of Perfection, and add to them suitable definitions of such interesting deontic categories as those of supererogation, offence, conditional obligation and conditional permission. We then state three problems concerning the proper characterization of the resulting logic(s) for our defined notions, and discuss two of these problems in some detail.

The Concept of Moral Obligation

The principal aim of this book is to develop and defend an analysis of the concept of moral obligation. The analysis is neutral regarding competing substantive theories of obligation, whether consequentialist or deontological in character. What it seeks to do is generate solutions to a range of philosophical problems concerning obligation and its application. Amongst these problems are deontic paradoxes, the supersession of obligation, conditional obligation, prima facie obligation, actualism and possibilism, dilemmas, supererogation, and cooperation. By virtue of its normative neutrality, the analysis provides a theoretical framework within which competing theories of obligation can be developed and assessed. This study is a major contribution to metaethics that will be of particular interest to all philosophers concerned with normative ethical theory.