Textual entailment is a relationship that obtains between fragments of text when one fragment in some sense implies the other fragment. The automation of textual entailment recognition supports a wide variety of text-based tasks, including information retrieval, information extraction, question answering, text summarization, and machine translation. Much ingenuity has been devoted to developing algorithms for identifying textual entailments, but relatively little to saying what textual entailment actually is. This article is a review of the logical and philosophical issues involved in (...) providing an adequate definition of textual entailment. We show that many natural definitions of textual entailment are refuted by counterexamples, including the most widely cited definition of Dagan et al. We then articulate and defend the following revised definition: T textually entails H = df typically, a human reading T would be justified in inferring the proposition expressed by H from the proposition expressed by T. We also show that textual entailment is context-sensitive, nontransitive, and nonmonotonic. (shrink)

This essay critically examines three theories of moral rights, theBenefit, the Interest, and the Choice theories. The Interest andChoice theories attempt to explain how rights can be more robustthan seems possible on the Benefit theory. In particular, moralrights are supposed to be resistant to trade-offs to supportprincipled anti-paternalism, to constitute a distinct dimensionof morality, and to provide right holders with a range ofdiscretionary choice. I argue that these and other featuresare better yet provided by a fourth theory of moral rights, (...) theJurisdiction theory. (shrink)

1. Introduction This essay deals with the hard topic of the permissible killing of the innocent. The relevance of this topic to the morality of war is obvious. For even the most defensive and just wars, i.e., the most defensive and just responses to existing or imminent large-scale aggression, will inflict harm upon – in particular, cause the deaths of – innocent bystanders. 1 The most obvious and relevant example is that of innocent Soviet noncombatants who would be killed by (...) even the most precise defensive strike against Soviet strategic weapons or troop formations that is now possible. Should there be no vindication or, at least, no excuse for some killings of such innocent bystanders, morality would dictate that even defensive counterforce measures against largescale attacks should be renounced. (shrink)

The two main theses of are: (i) that persons possess an original, non-acquired right not to be precluded from making extra-personal material their own (or from exercising discretionary control over what they have made their own); and (ii) that this right can and does take the form of a right that others abide by the rules of a (justifiable) practice of property which facilitates persons making extra-personal material their own (and exercising discretionary control over what they have made their own). (...) I articulate some of the good reasons we have to affirm persons' possession of an original, non-acquired right of self-ownership and argue that the same good reasons support the ascription to persons of a natural right of property. I contrast an conception of the actions through which (initial) rights over extra-personal objects arise with a conception of (initial) entitlement-generating actions. I argue that the fact that the natural right to property can and does take the form of persons' rights that others abide by the rules of a (justifiable) practice of property explains how there are many instances of (initial) entitlement generation which are not plausibly explained by those wed to the inherent feature conception of entitlement-generating actions and why there is a strong conventional dimension in the procedures through which persons acquire (initial) property rights. (shrink)

This two-part article offers a defense of a libertarian doctrine that centers on two propositions. The first is the self-ownership thesis according to which each individual possesses original moral rights over her own body, faculties, talents, and energies. The second is the anti-egalitarian conclusion that, through the exercise of these rights of self-ownership, individuals may readily become entitled to substantially unequal extra-personal holdings. The self-ownership thesis remains in the background during Part I of this essay, while the anti-egalitarian conclusion is (...) supported in two ways. First, I offer a reconstruction of Robert Nozick's well-known `How Liberty Upsets Patterns' argument against all end-state and pattern theories of distributive justice; and I defend this reconstructed stance against what might seem to be telling criticisms. Second, I defend the two key principles of Nozickian historical entitlement theory against criticisms offered by G.A. Cohen. Part II will center on Cohen's contention that the crucial basis for the anti-egalitarian conclusion is the self-ownership thesis. There I argue that Cohen is correct to hold that he must reject the self-ownership thesis if he is to avoid the anti-egalitarian conclusion; but he is wrong to think that he has an adequate basis for rejecting this thesis. Thus, both elements in the libertarianism under consideration are vindicated. And, the self-ownership thesis plays a surprisingly direct role in vindicating the anti-egalitarian conclusion. (shrink)

This two-part article offers a defense of a libertarian doctrine that centers on two propositions. The first is the self-ownership thesis according to which each individual possesses original moral rights over her own body, faculties, talents, and energies. The second is the anti-egalitarian conclusion that, through the exercise of these rights of self-ownership, individuals may readily become entitled to substantially unequal extra-personal holdings. The self-ownership thesis remains in the background during Part I of this essay, while the anti-egalitarian conclusion is (...) supported in two ways. First, I offer a reconstruction of Robert Nozick's well-known `How Liberty Upsets Patterns' argument against all end-state and pattern theories of distributive justice; and I defend this reconstructed stance against what might (otherwise) seem to be telling criticisms. Second, I defend the two key principles of Nozickian historical entitlement theory (the principle of just transfer and the principle of just initial acquisition) against criticisms offered by G.A. Cohen. Part II will center on Cohen's contention that the crucial basis for the anti-egalitarian conclusion is the self-ownership thesis. There I argue that Cohen is correct to hold that he must reject the self-ownership thesis if he is to avoid the anti-egalitarian conclusion; but he is wrong to think that he has an adequate basis for rejecting this thesis. Thus, both elements in the libertarianism under consideration are vindicated. And, the self-ownership thesis plays a surprisingly direct role in vindicating the anti-egalitarian conclusion. Key Words: egalitarianism • historical entitlement • moral rights • self-ownership. (shrink)

Part I of this essay supports the anti-egalitarian conclusion that individuals may readily become entitled to substantially unequal extra-personal holdings by criticizing end-state and pattern theories of distributive justice and defending the historical entitlement doctrine of justice in holdings. Part II of this essay focuses on a second route to the anti-egalitarian conclusion. This route combines the self-ownership thesis with a contention that is especially advanced by G.A. Cohen. This is the contention that the anti-egalitarian conclusion can be inferred from (...) the self-ownership thesis without the aid of additional controversial premises. Cohen advances this contention, not because he wants to support the anti-egalitarian conclusion, but rather because he wants to emphasize the need for one to reject the self-ownership thesis if one is to reject the anti-egalitarian conclusion. In Part II of this essay, I support this second route to the anti-egalitarian conclusion by reinforcing Cohen's special contention while rejecting his challenges to the self-ownership thesis. Cohen's special contention is reinforced by way of an explanation of why the redistributive state must trench upon some people's self-ownership rights. One important challenge to the self-ownership thesis is answered through the articulation of a new and improved Lockean proviso. Another challenge offered by Cohen is answered by arguing that the philosophical costs of denying the self-ownership thesis are as great as the self-ownership libertarian maintains. Thus, I defend both of the key elements of self-ownership libertarianism, the self-ownership thesis and the anti-egalitarian conclusion. Key Words: autonomy • distributive justice • egalitarianism • exploitation • Lockean proviso • self-ownership • slavery. (shrink)

Part I of this essay supports the anti-egalitarian conclusion that individuals may readily become entitled to substantially unequal extra-personal holdings by criticizing end-state and pattern theories of distributive justice and defending the historical entitlement doctrine of justice in holdings. Part II of this essay focuses on a second route to the anti-egalitarian conclusion. This route combines the self-ownership thesis with a contention that is especially advanced by G.A. Cohen. This is the contention that the anti-egalitarian conclusion can be inferred from (...) the self-ownership thesis without the aid of additional controversial premises. Cohen advances this contention, not because he wants to support the anti-egalitarian conclusion, but rather because he wants to emphasize the need for one to reject the self-ownership thesis if one is to reject the anti-egalitarian conclusion. In Part II of this essay, I support this second route to the anti-egalitarian conclusion by reinforcing Cohen's special contention while rejecting his challenges to the self-ownership thesis. Cohen's special contention is reinforced by way of an explanation of why the redistributive state must trench upon some people's self-ownership rights. One important challenge to the self-ownership thesis is answered through the articulation of a new and improved Lockean proviso. Another challenge offered by Cohen is answered by arguing that the philosophical costs of denying the self-ownership thesis are as great as the self-ownership libertarian maintains. Thus, I defend both of the key elements of self-ownership libertarianism, the self-ownership thesis and the anti-egalitarian conclusion. (shrink)

This essay contrasts two approaches to permissible self-defensive killing. The first is the forfeiture approach; the second is the elbow room for self-defense approach. The forfeiture approach comes in many versions — not all of which make prominent use of the word “forfeiture.” However, all versions presume that the permissibility of X killing Y (when X must kill Y in order to prevent herself from being unjustly killed) depends entirely on there being some feature of Y in virtue of which (...) Y has become liable to be killed, that is, in virtue of which Y has forfeited or lost or been stripped of his right not to be killed. Different versions of the forfeiture approach advance different claims about what feature of Y will render Y liable to being killed by X. I criticize versions of this approach offered by Thomson, Otsuka, and McMahan and argue that the shared deep error is the presumption that the permissibility of X’s action turns entirely on some feature of Y. In focusing entirely on Y, the forfeiture approach fails to take seriously X’s right of self-defense. In contrast, the elbow room for self-defense approach starts with an explication of a plausible right of self-defense and maintains that a proper explication of Y’s right not to be killed must make moral elbow room from X’s exercise of this right. Within the elbow room approach, Y’s liability to being killed is based upon X’s right of self-defense rather than the permissibility of X’s killing Y being based upon Y’s forfeiture. (shrink)

I offer a defense of the moral side-constraints to which Robert Nozick appeals in Anarchy, State and Utopia but for which he fails to provide a sustained justification. I identify a line of anti-consequentialist argumentation which is present in Nozick and which, in the terminology of Samuel Scheffler, moves first to affirm a personal prerogative which allows the individual not to sacrifice herself for the sake of the best overall outcome and second moves on to affirm restrictions (i.e., moral side-constraints) (...) which prohibit the individual from suppressing others' exercise of their personal prerogatives even if that suppression would serve the overall good. I argue that one ought to follow this line of anti-consequentialist argumentation all the way to the affirmation of restrictions by showing that the rationale for the adoption of the personal prerogative is not satisfied unless the accompanying restrictions are adopted as well. Footnotesa A distant ancestor of this essay was written during the spring of 1997 when I was a Visiting Scholar at the Social Philosophy and Policy Center, Bowling Green State University. The draft of the present essay was composed during the tenure of a summer research grant from the Murphy Institute of Political Economy at Tulane University. I am very grateful to both institutions and to Ellen Frankel Paul and Mary Sirridge for their exceedingly helpful editorial advice. (shrink)

1. Introduction This essay deals with the hard topic of the permissible killing of the innocent. The relevance of this topic to the morality of war is obvious. For even the most defensive and just wars, i.e., the most defensive and just responses to existing or imminent large-scale aggression, will inflict harm upon – in particular, cause the deaths of – innocent bystanders. 1 The most obvious and relevant example is that of innocent Soviet noncombatants who would be killed by (...) even the most precise defensive strike against Soviet strategic weapons or troop formations that is now possible. Should there be no vindication or, at least, no excuse for some killings of such innocent bystanders, morality would dictate that even defensive counterforce measures against largescale attacks should be renounced. (shrink)

Mack critically surveys a range of arguments characteristic of Randian writings in ethics (including Craig Biddle's Loving Life). He focuses on "the Shuffle," a set of argumentative moves in which there is illicit shifting back and forth between causal and conceptual understandings and defenses of claims of the form: Man's survival requires man's behaving in manner X (e.g., being rational, being productive). Mack concludes that much Randian argumentation is deeply flawed and urges admirers to discriminate between Rand's genuine (...) individualist ethical crusade and her line-by-line argumentation, which includes a much too strict identification of man's good with man's survival. (shrink)

This article examines the character of Scanlon’s contractualism as presented in What We Owe to Each Other . I offer a range of reasons for thinking of Scanlon’s contractualism as a species of natural rights theorizing. I argue that to affirm the principle that actions are wrongful if and only if they are disallowed by principles that people could not reasonably reject is equivalent to affirming a natural right (of an admittedly non-standard sort) against being subject to such reasonably disallowed (...) actions. I argue that Scanlon’s invocation of the value of human life can be seen as an attempted grounding for this principle that is akin to standard natural rights attempts to ground fundamental rights. Lastly, I argue that the invocation of the value of human life does not in fact well support the sort of requirement of justifiability to others that characterizes this contractualist variant on natural rights theorizing; if anything, it better supports the sort of ascriptions of rights characteristic of traditional natural rights theorizing. Key Words: contractualism • natural rights • justifiability to others • wrongfulness. (shrink)

David Gauthier's Morals by Agreement is an impressive — indeed, daunting — exercise in contractarian moral and political philosophy. The primary purpose of his treatise is to explicate practical rationality as constrained maximization and morality as compliance with these constraints. Gauthier offers an account of which constraints on straightforward utility maximization each rational individual will be prepared to accept and comply with on the condition that other individuals also will accept and comply with them as well as an explanation of (...) why compliance with those constraints counts as morality. However, although Morals by Agreement is in the great tradition of Hobbesian moral and political theorizing, Gauthier's morality by agreement does not begin with the Hobbesian state of nature. Gauthier does not start by envisioning a Hobbesian war of all against all which has been generated by rational individuals, each pursuing his own maximum utility, and then asking what constraints on this no-holds-barred utility maximization would be mutually advantageous and therefore mutually rational. (shrink)

Natural Goodness, PHILIPPA FOOT. Clarendon Press, 2002, 125 pages. Philippa Foot begins her short but intriguingly rewarding book on Natural Goodness by recounting a story about Wittgenstein. Wittgenstein interrupted a speaker who had realized that he was about to say something that, although it seemed compelling, was clearly ridiculous, and was trying (as we all do in such circumstances) to say something sensible instead. “No,” said Wittgenstein. “Say what you want to say. Be crude and then we shall get on.” (...) (p. 1) So it is no surprise that Natural Goodness itself is full of bold sayings which, although elegantly cast, will shock many readers' philosophical sensibilities. In this discussion of Foot's book I will complete compliance with Wittgenstein's advice by way of a crude attempt to interpret Foot's bold sayings. (shrink)

This chapter contains sections titled: Introduction Prerogatives, Rationales, and Restrictions The Individualist Prerogative and Self‐Ownership The Individualist Prerogative and the Right to the Practice of Private Property A Self‐Ownership Proviso Conclusion Notes.

Throughout the biological and biomedical sciences there is a growing need for, prescriptive ‘minimum information’ (MI) checklists specifying the key information to include when reporting experimental results are beginning to find favor with experimentalists, analysts, publishers and funders alike. Such checklists aim to ensure that methods, data, analyses and results are described to a level sufficient to support the unambiguous interpretation, sophisticated search, reanalysis and experimental corroboration and reuse of data sets, facilitating the extraction of maximum value from data sets (...) them. However, such ‘minimum information’ MI checklists are usually developed independently by groups working within representatives of particular biologically- or technologically-delineated domains. Consequently, an overview of the full range of checklists can be difficult to establish without intensive searching, and even tracking thetheir individual evolution of single checklists may be a non-trivial exercise. Checklists are also inevitably partially redundant when measured one against another, and where they overlap is far from straightforward. Furthermore, conflicts in scope and arbitrary decisions on wording and sub-structuring make integration difficult. This presents inhibit their use in combination. Overall, these issues present significant difficulties for the users of checklists, especially those in areas such as systems biology, who routinely combine information from multiple biological domains and technology platforms. To address all of the above, we present MIBBI (Minimum Information for Biological and Biomedical Investigations); a web-based communal resource for such checklists, designed to act as a ‘one-stop shop’ for those exploring the range of extant checklist projects, and to foster collaborative, integrative development and ultimately promote gradual integration of checklists. (shrink)

This book's importance is derived from three sources: careful conceptualization of teacher induction from historical, methodological, and international perspectives; systematic reviews of research literature relevant to various aspects of teacher induction including its social, cultural, and political contexts, program components and forms, and the range of its effects; substantial empirical studies on the important issues of teacher induction with different kinds of methodologies that exemplify future directions and approaches to the research in teacher induction.

This is a review of contemporary philosophical discussions of population policies. The focus is on normative justification, and the main question is whether population policies can be ethically justified. Although few analytical philosophers have directly addressed this question – it has been discussed more in other academic fields – many arguments and considerations can be placed in the analytical philosophical discourse. This article offers a comprehensive review and analysis of ethically relevant aspects of population policies evaluated on the basis of (...) the main ethical theories. This analysis is preceded by a brief historical contextualisation of when and how population policies became ethically contentious and how this relates to philosophical debates in environmental ethics, population ethics and political philosophy. The article also includes a conceptual analysis of population policies in which the empirical intricacies around individual fertility decisions are sorted out and the different ways in which they can be affected are categorised in a taxonomy which highlight the most relevant ethical aspects of population policies. The ethical analysis shows that while population policies can be justified on the basis of most ethical theories, it all depends on what prior assumptions are made about what is at stake. (shrink)

Philosophy of science and history of science both have a significant relation to science itself; but what is their relation to each other? That question has been a focal point of philosophical and historical work throughout the second half of this century. An analysis and review of the progress made in dealing with this question, and especially that made in philosophy, is the focus of this thesis. Chapter one concerns logical positivist and empiricist approaches to philosophy of science, and the (...) significance of the criticisms levelled at them by analytic epistemologists such as Willard Quine and 'historicist' philosophers, especially Thomas Kuhn. Chapter two details the attempts by Kuhn and Lakatos to integrate these historicist criticisms with historically oriented philosophy of science, in their separate attempts at providing rational explanations of historical developments. Kuhn's latest work seeks to mend fences with philosophy, but his efforts remain too closely tied to the epistemological approaches strongly criticized in his earlier work. Lakatos' treatment of history is much more subtle than most have understood it to be, but the conception of scientific rationality that arises out of it is transformed into an abstract cultural product, more reminiscent of Hegel's geist than of individual human rationality. Chapters three and four discuss the recommendations of Lakatos and Laudan to historians with regard to historiography, and the actual historiographies and philosophy of history of practicing historians and historians of science. The philosophers' contributions indicate little concern for the historians' own methods, materials, and purposes; and the historians' writings present methodologies for history of science that are independent of the normative demarcations of philosophy of science, pace Lakatos and Laudan. Chapter five develops a philosophical position that fosters a more productive engagement between philosophy and history of science, a 'methodological historicism' that embraces the possibility of an important role for social and political factors in a philosophical study of scientific development. The epistemological relativism that might accompany such a historicist position need not be the radical epistemological anarchism of Feyerabend, though it will allow for a significant underdetermination of scientific development by reason nonetheless. (shrink)

There are multiple formal characterizations of the natural numbers available. Despite being inter-derivable, they plausibly codify different possible applications of the naturals – doing basic arithmetic, counting, and ordering – as well as different philosophical conceptions of those numbers: structuralist, cardinal, and ordinal. Nevertheless, some influential philosophers of mathematics have argued for a non-egalitarian attitude according to which one of those characterizations is more “legitmate” in virtue of being “more basic” or “more fundamental”. This paper addresses two related issues. First, (...) we review some of these non-egalitarian arguments, lay out a laundry list of different, legitimate, notions of relative priority, and suggest that these arguments plausibly employ different such notions. Secondly, we argue that given a metaphysical-cum-epistemological gloss suggested by Frege’s foundationalist epistomology, the ordinals are plausibly more basic than the cardinals. This is just one orientation to relative priority one could take, however. Ultimately, we subscribe to an egalitarian attitude towards these formal characterizations: they are, in some sense, equally “legitimate”. (shrink)

Recent attempts to define being moved have difficulties agreeing on its eliciting conditions. The status quaestionis is often summarized as a question of whether the emotion is evoked by exemplifications of a wide range of positive core values or a more restricted set of values associated with attachment. This conclusion is premature. Study participants associate being moved with interactions with their loved ones not merely for what they exemplify but also for their affective bond to them. Being moved is elicited (...) when we apprehend the value of entities to which we are connected through basic as well as extended forms of affiliative attachment. These comprise people, certain objects, and even abstract entities, including the unshakable life-guiding ideas we call “core values.”. (shrink)

In some recent works, Crupi and Iacona have outlined an analysis of ‘if’ based on Chrysippus’ idea that a conditional holds whenever the negation of its consequent is incompatible with its antecedent. This paper presents a sound and complete system of conditional logic that accommodates their analysis. The soundness and completeness proofs that will be provided rely on a general method elaborated by Raidl, which applies to a wide range of systems of conditional logic.

Bellʼs 1964 theorem causes a severe problem for the notion that correlations require explanation, encapsulated in Reichenbachʼs principle of common cause. Despite being a hallmark of scientific thought, dropping the principle has been widely regarded as much less bitter medicine than the perceived alternative—dropping relativistic causality. Recently, however, some authors have proposed that modified forms of Reichenbachʼs principle could be maintained even with relativistic causality. Here we break down Reichenbachʼs principle into two independent assumptions—the principle of common cause proper and (...) factorization of probabilities. We show how Bellʼs theorem can be derived from these two assumptions plus relativistic causality and the law of total probability for actual events, and we review proposals to drop each of these assumptions in light of the theorem. In particular, we show that the non-commutative common causes of Hofer-Szabó and Vecsernyés fail to have an analogue of the notion that the common causes can explain the observed correlations. Moreover, we show that their definition can be satisfied trivially by any quantum product state for any quantum correlations. We also discuss how the conditional states approach of Leifer and Spekkens fares in this regard. (shrink)

For each one of the approximately 800,000 people who die from suicide every year, an additional twenty people attempt suicide. Many of these attempts result in hospitalization or in contact with other healthcare services. However, many personal, educational, and institutional barriers make it difficult for healthcare professionals to care for suicidal individuals. We reviewed literature that discusses suicidal patients in healthcare settings in order to highlight common ethical issues and to identify knowledge gaps. A sample was generated via PubMed (...) using keywords “[(ethics OR *ethic*) AND suicid*] AND [English (Language) OR French (Language)]” (final N = 52), ethics content was extracted according to scoping review methodology, and categorized thematically. We identified three main areas posing ethical challenges for health professionals caring for suicidal individuals and their families. These were: (1) making clinical decisions for patients in acute care or when presented with specific circumstances; (2) issues arising from therapeutic relationships in chronic care, and (3) organizational factors. There is considerable uncertainty about how to resolve ethical issues when caring for someone who is suicidal. The stigma associated with suicide and mental illness, problems associated with risk–benefit assessments, and the fear of being held liable for malpractice should a patient die by suicide were overarching themes present across these three categories. Caring for suicidal patients is clinically and ethically challenging. The current literature highlights the complexity and range of decisions that need to be made. More attention should be paid to the difficulties faced by healthcare professionals and the development of solutions. (shrink)

Neuroethics is an interdisciplinary field that arose in response to novel ethical challenges posed by advances in neuroscience. Historically, neuroethics has provided an opportunity to synergize different disciplines, notably proposing a two-way dialogue between an ‘ethics of neuroscience’ and a ‘neuroscience of ethics’. However, questions surface as to whether a ‘neuroscience of ethics’ is a useful and unified branch of research and whether it can actually inform or lead to theoretical insights and transferable practical knowledge to help resolve ethical questions. (...) In this article, we examine why the neuroscience of ethics is a promising area of research and summarize what we have learned so far regarding its most promising goals and contributions. We then review some of the key methodological challenges which may have hindered the use of results generated thus far by the neuroscience of ethics. Strategies are suggested to address these challenges and improve the quality of research and increase neuroscience's usefulness for applied ethics and society at large. Finally, we reflect on potential outcomes of a neuroscience of ethics and discuss the different strategies that could be used to support knowledge transfer to help different stakeholders integrate knowledge from the neuroscience of ethics. (shrink)

This review of 122 research reports (184 independent samples, 14,900 subjects) found average r ϭ .274 for prediction of behavioral, judgment, and physiological measures by Implicit Association Test (IAT) measures. Parallel explicit (i.e., self-report) measures, available in 156 of these samples (13,068 subjects), also predicted effectively (average r ϭ .361), but with much greater variability of effect size. Predictive validity of self-report was impaired for socially sensitive topics, for which impression..

Standard conditionals $\varphi > \psi$, by which I roughly mean variably strict conditionals à la Stalnaker and Lewis, are trivially true for impossible antecedents. This article investigates three modifications in a doxastic setting. For the neutral conditional, all impossible-antecedent conditionals are false, for the doxastic conditional they are only true if the consequent is absolutely necessary, and for the metaphysical conditional only if the consequent is ‘model-implied’ by the antecedent. I motivate these conditionals logically, and also doxastically by properties of (...) conditional belief and belief revision. For this I show that the Lewisian hierarchy of conditional logics can be reproduced within ranking semantics, provided we slightly stretch the notion of a ranking function. Given this, acceptance of a conditional can be interpreted as a conditional belief. The epistemic and the neutral conditional deviate from Lewis’ weakest system $V$, in that ID or even CN are dropped, and new axioms appear. The logic of the metaphysical conditional is completely axiomatised by $V$ to which we add the known Kripke axioms T5 for the outer modality. Related completeness results for variations of the ranking semantics are obtained as corollaries. (shrink)