Standard theories of expected utility require that preferences are complete, and/or Archimedean. We present in this paper a theory of decision under uncertainty for both incomplete and non-Archimedean preferences. Without continuity assumptions, incomplete preferences on a lottery space reduce to an order-extension problem. It is well known that incomplete preferences can be extended to complete preferences in the full generality, but this result does not necessarily hold for incomplete preferences which satisfy the independence axiom, since it may obviously happen that (...) the extension does not satisfy the independence axiom. We show, for incomplete preferences on a mixture space, that an extension which satisfies the independence axiom exists. We find necessary and sufficient conditions for a preorder on a finite lottery space to be representable by a family of lexicographic von Neumann–Morgenstern Expected Utility functions. (shrink)

The connections between nonmonotonic reasoning and belief revision are well-known. A central problem in the area of nonmonotonic reasoning is the problem of default entailment, i.e., when should an item of default information representing “if θ is true then, normally, φ is true” be said to follow from a given set of items of such information. Many answers to this question have been proposed but, surprisingly, virtually none have attempted any explicit connection to belief revision. The aim of this paper (...) is to give an example of how such a connection can be made by showing how the lexicographic closure of a set of defaults may be conceptualised as a process of iterated revision by sets of sentences. Specifically we use the revision method of Nayak. (shrink)

This research tackles computer linguistic terminology used incorrectly or ambiguously by Arab computer users in academic institutions and by English-to-Arabic translators. To serve the purpose of this research, we inserted and/or contextualized a number of computer linguistic terms in texts or contexts. The terms are computer signs and words loaded with technical meanings that are often used in word processing and statistical software packages. Five translators were requested to translate those texts including the chosen semiotic signs and/or codes. Simultaneously, we (...) reviewed computer books taught in two Arab countries (Jordan and the UAE) because these countries have witnessed good educational developments. After filtering out the translators' products from English into Arabic and after investigating the computer terminologies (signs, codes, words, etc., and their semiotic meanings), we found that many computer terms and their levels of meaning are problematic. We classified the types of problematic vocabulary items and then tabulated them under four semiotic levels or categories: ambiguous, inaccurate, unchangeable, and statistical. We also found that problematic words were difficult to translate because of the Arabic culture or the inefficiency of English/arabic bilingual dictionaries. The research concludes with a number of practical and research-directed recommendations. (shrink)

This article mainly discusses the standardization of the translation of personal and place names. In the first section, common problems in the translations of foreign names and Chinese names are summarized. The basic principles of the translation of personal names are discussed and several systems used in the transliteration history of Chinese names are presented in detail. The author also makes a brief review and comments on bilingual dictionaries of personal names published in modern China. In the second section, (...) based on the practices and lessons of translation of place names from and into Chinese, the author refines the basic principles of the standardization of translated place names, summarizes the methods and strategies for place names translation, and sums up the unified translations of certain disputed place names based on the summary of common problems in place names translation in official publications. In the third section, it is believed that the standardization of place names translation depends on the compilation of authoritative dictionaries of place names. In this section, several representative translated dictionaries of place names in late Qing dynasty, the Republic of China, and the People’s Republic of China are reviewed. The author analyses the characteristics of these dictionaries and their contributions to the unification of translated place names and sums up the overall translation history of the standardization of place names in modern China. (shrink)

We consider a spatial bargaining model where players collectively choose a facility location on a two-dimensional rectilinear distance space through bargaining using the unanimity rule. We show that as players become infinitely patient, their stationary subgame perfect equilibrium utilities converge to the utilities that satisfy the lexicographic maximin utility criterion introduced by Sen (Collective choice and social welfare, 1970).

Arrow's account (1951/1963) of the problem of social choice is based upon the assumption that the preferences of each individual in the relevant group are expressible by a single ordering. This paper lifts that assumption and develops a multidimensional generalization of Arrow's framework. I show that, like Arrow's original framework, the multidimensional generalization is affected by an impossibility theorem, highlighting not only the threat of dictatorship of a single individual, but also the threat of dominance of a single dimension. In (...) particular, even if preferences are single-peaked across individuals within each dimension – a situation called intradimensional single-peakedness – any aggregation procedure satisfying Arrow-type conditions will make one dimension dominant. I introduce lexicographic hierarchies of dimensions as a class of possible aggregation procedures under intradimensional single-peakedness. The interpretation of the results is discussed. (shrink)

Experts in the field of organ transplantation had to rank order a set of 32 patients according to their priority in receiving a donated kidney. The patients were described by the five characteristics that are incorporated in the kidney allocation algorithm applied by Eurotransplant. The priority rankings as defined by the experts were analyzed and patterns of dedsion making identified in the rankings investigated in this study. All patterns could be explained by some type of lexicographical ranking. The larger group (...) of experts preordered tissue compatibility or, more technically speaking, the criterion of HLA match, while the complementary group applied the criterion of the length of waiting time first. Analyzing the finer decision structures of expert rankings and com paring the method of pattern exploration with a conjoint measurement analysis led to two follow-up questions: First, how can the value judgments of the experts be described adequately? Second, which type of aggregated ordering derived from the individual rankings represents them ‘best’? (shrink)

Arab lexicographers rarely attempted to search for a foreign origin of Arabic words, trying instead to derive them—not very persuasively—from autochthonous Arabic roots. Known exceptions mostly involve Persian, a foreign language par excellence for most Arab philologists. This article explores this phenomenon in a different linguistic domain, viz., loanwords from Classical Ethiopic (Geʿez), the language of the ancient kingdom of Axum (the Horn of Africa). Our harvest, obtained from a systematic perusal of the lexica Lisān al-ʿarab and Tāj al-ʿarūs, is (...) not very rich, but not totally insignificant either; a considerable number of conspicuous examples, often unrecognized in previous scholarship, have been detected, both within the quranic corpus and outside it. Taken together, this evidence provides a unique glimpse into language contacts between Arabia and Ethiopia. It also invites us to reconsider, in a more positive vein, the problem of the etymological awareness of traditional Arab philology. (shrink)

A new investigation is launched into the problem of decision-making in the face of ‘complete ignorance’, and linked to the problem of social choice. In the first section the author introduces a set of properties which might characterize a criterion for decision-making under complete ignorance. Two of these properties are novel: ‘independence of non-discriminating states’, and ‘weak pessimism’. The second section provides a new characterization of the so-called principle of insufficient reason. In the third part, lexicographic maximin and maximax (...) criteria are characterized. Finally, the author's results are linked to the problem of social choice. (shrink)

This paper is concerned with ordinal comparisons of welfare inequality and its use in social welfare judgements, especially in the context of Rawls' ‘difference principle’. In Section 1 the concept of ordinal inequality comparisons is developed and a theorem on ordinal comparisons of welfare inequality for distributional problems is noted. Section 2 is devoted to Harsanyi's (1955) argument that a concern for reducing welfare inequalities among persons must not enter social welfare judgements. In Section 3 an axiomatic derivation of (...) Rawls' lexicographic maximim rule is presented; this relates closely to results established by Hammond (1975), d'Aspremont and Gevers (1975) and Strasnick (1975). In the last section the axioms used are examined and some alternative axioms are analysed with the aim of a discriminating evaluation of the Rawlsian approach to judgements on social welfare. (shrink)

This chapter analyzes lexicographic maximization (leximax) as a fairness criterion that maxinmizes the smallest utility, then the second smallest, and so forth. Leximax fairness generalizes the Rawlsian maximin criterion and avoids some of its shortcomings, such as the fact that a maximin solution can leave available resources used. The chapter describes the socially optimal solution subject to a budget constraint both with and without utility bounds; in the latter case, it is the same as the maximin solution. Since leximax (...) fairness is not represented by a social welfare function in the usual sense, the chapter generalizes the concept of monotone separability to show that the leximax problem is regionally decomposable. (shrink)

Polysemy is a term used in semantic and lexical analysis to describe a word with multiple meanings. Although such words present few difficulties in everyday communication, they do pose near-intractable problems for linguists and lexicographers. The contributors in this volume consider the implications of these problems for linguistic theory and how they may be addressed in computational linguistics.

My research takes as its guiding thread the statement from Hegel's lectures on the philosophy of spirit of 1805-06, that «cognition is recognition[Erkennen ist Anerkennen]». In this perspective I delineate, first, the consequences of this position for Hegel's epistemology, in particular with reference to the question of skepticism. Then, I show in what sense the recognitive conception of knowledge makes it possible for Hegel to comprehend unitarily, on one hand, cognition as exercise of natural capacities and cognition as exercise of (...) normative capacities socially articulated, and,on the other hand, theoretical self-consciousness and practical self-consciousness. The gnoseological importance of this solution can be comprehended only if we reconstruct the evolution of Hegel's thought in that span of time in which he most directly tackles the issue of skepsis: that is, from 1797 - the beginning of his Frankfurt period - when he began to occupy himself with gnoseological questions, until the end of his stay in Jena,which begins in 1801 and concludes in 1807 with the writing of the Phenomenology. The analysis of the development of the Hegelian theory of knowledge - worked out in the first part of my study - is dealt with in the context of a reconstruction of the historico-argumentative constellation within which it matured. The constellation of importance for our analysis is represented by the skeptical crisis - triggered by authors such as Schulze, Maimonand Platner - that invested the post-Kantian galaxy, within which the idealist solutions to the problem of cognition matured. Through the analysis of journals and authors with whom Hegel came directly or indirectly into contact - from Platner to Reinhold, Jacobi, Fichte and Schelling, to Hölderlin and Sinclair, concluding with Zeender, Krug, Bouterwek and Werneburg, and among the journals Fülleborn's Beiträge and Niethammer's Journal in particular - it is possible to map the various solutions proposed for the skeptical problem andsee how it is in relation to this problem that the conceptions of self-consciousness evolve and the very concept of "interpersonality" - "intersubjectivity" - emerges for the first time. At the same time, pursuing my objective of broadening the investigation of the phenomenon of recognition, which in my view is not reducible to the field of practical philosophy, I proposea fresh reconstruction of the lexical and conceptual evolution of the various terms -Erkennen, Wiedererkennen, Recognition, Anerkennen - through which the various modalities of the phenomenon of recognition were indicated in the philosophical tradition to which Hegel refers: recognition of objects as perceptive reidentification; reminiscence on the level of theory of memory; recognition of subjects as self-recognition (apperception) and attribution to others of intentionality; logical recognition as recognition of the validity of a proposition; moral recognition, where "recognizing" generally means approving, accepting(more specifically, someone may be "recognized" as an autonomous subject and as a unique,genuine individuality). I focus in particular on the theory of memory as «recognitio» in Wolff and in his school, on the conception of «reconnaissance» in Bonnet, on Kantian«Recognition» and on the theory of «Anerkennen» in Ernst Platner. This investigation serves, on the one hand, to show how the phenomenon of recognition is central for a comprehension of the structure both of the lower and of the higher cognitive faculties. This ought to allow us to understand in what sense Hegel, taking intersubjective recognition as hisleading phenomenon, attempts to reunite the various meanings of recognition within a theory of knowledge on the basis of which «cognition is recognition». On the other hand, my conceptual and lexicographic investigation also serves to bring to light - in a new way with respect to the studies on Anerkennung - a hitherto unknown problematic constellation and the input of certain authors, such as Werneburg and Platner, whose conceptions may haveinfluenced Hegel's approach.The second part and the third of my study - a reconstruction of the pre- phenomenological Jena writings dealing with «Anerkennung» - dwells on the theme of the notion of natural recognition, whose centrality for the Hegelian conception of recognition has not yet been adequately grasped. This reconstruction of the theory of natural recognition gives due weight to the influence of Schelling on Hegel's understanding of «Anerkennung» -while the critical literature has generally concentrated on Fichte. Analyzing the conception of the animal organism developed in particular in the lectures on the philosophy of nature of 1803-04 brings to light how Hegel already individuates the recognitive phenomenon at the level of sexual reproduction: it is from here that he posits the natural prerequisites for the development of consciousness of self. The category of natural recognition will present itself anew in Hegel's analysis of the social ontology of the human world in the philosophy of spirit, where it concerns sexual love, reproduction and child raising: natural recognition is, then, that on the basis of which Hegel develops his theory that cognition is recognition.Recognition, as a «middle» of spirit, is a cognitive phenomenon that is primitive with respectto linguistically structured human intersubjectivity; it is, properly, that cognitive structure which is necessarily presupposed by a self-conscious subjectivity that expresses itself linguistically: linguistic intersubjectivity expresses various modes of recognition, but notevery form of recognition is linguistic. The evolutional theory of cognition as recognition is in fact designed to show how increasingly complex recognitive relations emerge from a basic level of natural interactions to take on a linguistically mediated and universal structure. Withthe notion of spiritual recognition Hegel indicates just that ensemble of normative relations that constitute the infrastructure of action and thus mediate the formation of socially articulated self-conscious knowing of self. In the lectures on the philosophy of spirit of 1803-04 and of 1805-06 Hegel thus reconstructs the recognitive structure of the social institutions of right, of labor, and of exchange, showing that, within a politically structured community,dyadic (I-you) interactions are mediated by the universal viewpoint of the "we" incarnated in institutions that can be recognized by citizens as their own and by which citizens can be recognized. (shrink)

We gather the following miscellaneous results in proof theory from the attic.1. 1. A provably well-founded elementary ordering admits an elementary order preserving map.2. 2. A simple proof of an elementary bound for cut elimination in propositional calculus and its applications to separation problem in relativized bounded arithmetic below S21.3. 3. Equivalents for Bar Induction, e.g., reflection schema for ω logic.4. 4. Direct computations in an equational calculus PRE and a decidability problem for provable inequations in PRE.5. 5. Intuitionistic fixed (...) point theories which are conservative extensions of HA.6. 6. Proof theoretic strengths of classical fixed points theories.7. 7. An equivalence between transfinite induction rule and iterated reflection schema over IΣn.8. 8. Derivation lengths of finite rewrite rules reducing under lexicographic path orders and multiply recursive functions.Each section can be read separately in principle. (shrink)

Intractability and optimality are two sides of one coin: Optimal models are often intractable, that is, they tend to be excessively complex, or NP-hard. We explain the meaning of NP-hardness in detail and discuss how modem computer science circumvents intractability by introducing heuristics and shortcuts to optimality, often replacing optimality by means of sufficient sub-optimality. Since the principles of decision theory dictate balancing the cost of computation against gain in accuracy, statistical inference is currently being reshaped by a vigorous new (...) trend: the science of simplicity. Simple models, as we show for specific cases, are not just tractable, they also tend to be robust. Robustness is the ability of a model to extract relevant information from data, disregarding noise.Recently, Gigerenzer, Todd and the ABC Research Group (1999) have put forward a collection of fast and frugal heuristics as simple, boundedly rational inference strategies used by the unaided mind in real world inference problems. This collection of heuristics has suggestively been called the adaptive toolbox. In this paper we will focus on a comparison task in order to illustrate the simplicity and robustness of some of the heuristics in the adaptive toolbox in contrast to the intractability and the fragility of optimal solutions. We will concentrate on three important classes of models for comparison-based inference and, in each of these classes, search for that to be used as benchmarks to evaluate the performance of fast and frugal heuristics: lexicographic trees, linear modes and Bayesian networks. Lexicographic trees are interesting because they are particularly simple models that have been used by humans throughout the centuries. Linear models have been traditionally used by cognitive psychologists as models for human inference, while Bayesian networks have only recently been introduced in statistics and computer science. Yet it is the Bayesian networks that are the best possible benchmarks for evaluating the fast and frugal heuristics, as we will show in this paper. (shrink)

The purpose of this article is to study the role of Gödel’s functional interpretation in the extraction of programs from proofs in well quasi-order theory. The main focus is on the interpretation of Nash–Williams’ famous minimal bad sequence construction, and the exploration of a number of much broader problems which are related to this, particularly the question of the constructive meaning of Zorn’s lemma and the notion of recursion over the non-wellfounded lexicographic ordering on infinite sequences.

The main powerful method for establishing termination of term rewriting systems was discovered by Nachum Dershowitz through the introduction of certain natural well founded orderings (lexicographic path orderings). This leads to natural decision problems which may be of the highest computational complexity of any decidable problems appearing in a natural established computer science context.

In this chapter, we address the challenges and the problems that we have faced while we were trying to develop a dictionary for the Kharia Sabar speech community, which is an indigenous endangered tribal community living in the district of Purulia in the state of West Bengal, India. The challenges that we have faced may be classified into two broad types, namely, extralinguistic challenges and linguistic challenges (Ivanishcheva in Journal of Linguistics 67:73–86, 2016). The extralinguistic challenges are primarily related (...) to awareness about the importance of such a knowledge text among the members of the community; careful investigation of the attitude of the community members relating to the procurement of data and information from their life, living, culture, history, heritage, and ecology (Littell et al. in Proceedings of the 2nd workshop on the use of computational methods in the study of endangered languages. Association for Computational Linguistics, Honolulu, Hawaii, USA, pp. 141–150, 2017); logistic issues in data collection from the Urheimat (i.e., the primaeval habitation) of the community through on-the-spot interviews; demographic and ethical issues in selection of appropriate respondents; availability of funds for conducting elaborate linguistic surveys; a collection of lexical data covering all major aspects of the community life; availability of trained human resource for lexical processing, analysis and dictionary compilation; and availability of agencies who are willing to publish dictionary as a commercial product. The linguistic challenges, on the other hand, are largely associated with collection of lexical data from community members; sufficiency, diversity and variety of lexical data types (Lam et al. in Proceedings of the 2014 workshop on the use of computational methods in the study of endangered languages. Association for Computational Linguistics, Baltimore, Maryland, USA, pp. 54–62, 2014); paucity of lexicographic details for entry words; citation of example sentences for determining usage-based sense variations of polysemous entries; inadequacy of linguistic description of lexical items for addressing referential and pedagogical requirements (Rehg in The Oxford handbook of endangered languages. Oxford University Press, 2018); utilization of pictures, images and diagrams for a visual representation of complex concepts and ideas of the community and similar other issues. Many of these challenges are linked with several theoretical and ethical issues―all of which combine together to make the process of dictionary-making for the Kharia Sabar community an upheaval task fretted with many caveats and shortcomings particularly in those contexts when their folk texts, verbal narratives, written materials and historical records are not available for reference and utilization (Mosel in Language documentation and description, SOAS, 2004). Keeping the challenges in view, in this paper, we discuss the strategies that we have adopted to overcome the hurdles we have faced during the stages of compilation of the dictionary, which is being built to primarily help in the process of preserving and promoting the endangered indigenous language against a backdrop of camouflaged aggression of more powerful neighbouring languages. The dictionary that we are developing will be used by the Kharia Sabar speakers for general reference and pedagogic purposes, while outside people will use it for academic, commercial and localization purposes. (shrink)

Recent work has considered the problem of extending to the case of iterated belief change the so-called `Harper Identity' (HI), which defines single-shot contraction in terms of single-shot revision. The present paper considers the prospects of providing a similar extension of the Levi Identity (LI), in which the direction of definition runs the other way. We restrict our attention here to the three classic iterated revision operators--natural, restrained and lexicographic, for which we provide here the first collective characterisation in (...) the literature, under the appellation of `elementary' operators. We consider two prima facie plausible ways of extending (LI). The first proposal involves the use of the rational closure operator to offer a `reductive' account of iterated revision in terms of iterated contraction. The second, which doesn't commit to reductionism, was put forward some years ago by Nayak et al. We establish that, for elementary revision operators and under mild assumptions regarding contraction, Nayak's proposal is equivalent to a new set of postulates formalising the claim that contraction by ¬A should be considered to be a kind of `mild' revision by A. We then show that these, in turn, under slightly weaker assumptions, jointly amount to the conjunction of a pair of constraints on the extension of (HI) that were recently proposed in the literature. Finally, we consider the consequences of endorsing both suggestions and show that this would yield an identification of rational revision with natural revision. We close the paper by discussing the general prospects for defining iterated revision in terms of iterated contraction. (shrink)

We provide partial answers to the following problem: Is the class of Borel linear orders well-quasi-ordered under embeddability? We show that it is indeed the case for those Borel orders which are embeddable in R ω , with the lexicographic ordering. For Borel orders embeddable in R 2 , our proof works in ZFC, but it uses projective determinacy for Borel orders embeddable in some $\mathbf{R}^n, n , and hyperprojective determinacy for the general case.

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Interpreting a Classic: Demosthenes and His Ancient CommentatorsK. KapparisCraig A. Gibson. Interpreting a Classic: Demosthenes and His Ancient Commentators. Berkeley and Los Angeles: University of California Press, 2002. xii + 261 pp. Cloth, $55.This book aims to provide a comprehensive account of the ancient scholarship on Demosthenes. Gibson points out that Demosthenes was widely read in later antiquity, and this created the need for linguistic and historical commentaries (...) on his speeches. Of these, some have partially survived on papyrus, while excerpts have also been preserved in later lexicographers and the Byzantine scholia found in the margins of Demosthenic manuscripts. The purpose of Gibson's study is to clarify some confusing and difficult issues related to the ancient scholarship on Demosthenes and to provide the text and commentary on the main sources. [End Page 481]Gibson's introduction includes an informative outline of key parameters in the debate, such as the accuracy of excerption from an ancient commentary, the significance of date and place, and the intended readership of these commentaries. The first chapter discusses the form and transmission of ancient commentaries, their relation with lexicographic works, and their impact on the Byzantine scholia. Gibson convincingly argues that the scholia do not reveal direct dependency upon the surviving ancient commentaries but were compiled from lexicographic works such as Harpocration or the Suda, and possibly other works lost for us. The second chapter deals with the sources, critical agenda, and readership of the ancient commentaries. Here, Gibson provides a clear account of the purposes and guiding principles behind the composition of these works. He concludes that ancient commentators were familiar with interpretative problems of the Demosthenic text and tried to explain allusions and references to specific events, people, and places and also provide semantic, etymological and textual explanations of difficult or unusual terms. In this and the third chapter, Gibson discusses in considerable detail the scholarship on Didymus. He rejects the view that Didymus was merely a filter for a "golden era" of Alexandrian scholarship and argues that his prominent position as a commentator is due to the vast quantity of his work and its impact on later scholars. In sum, the first part of the study offers an informative account of ancient Demosthenic scholarship written in a clear and accessible style.The second part of the book contains the texts of ancient commentators of Demosthenes, with English translations, and also linguistic and historical commentary. In the translation, Gibson chooses to leave out many lines from the papyrus texts where only single words or fragments of words are legible; he translates only the most extant sections of the text. This is a valid choice, but readers should be aware of the fact that many important details may be hiding in the leftovers and fragments that have been omitted. Gibson does not provide the readily available text of P.Berol.inv. 9780, the most extensive surviving work of Didymus, while he cites the rest of the texts from reliable modern editions. In the commentary there are interesting discussions on the Spartan mora, the building of the Parthenon, the Helliastic courts, and many other topics noted by the ancient commentators on Demosthenes. An appendix presents and discusses P.Lond.Lit. 179, a prologue and commentary on Dem. 21. The reader will probably find useful the indexes and rich bibliography provided in the last part of this study.Gibson's commentary is certainly thorough but contains a number of errors in detail, and important bibliography is missing on individual topics. For example:Page 113: Gibson adopts the text of Pearson-Stephens. The adjective is, or, as here (later Greek),. Therefore the text should be (see LSJ s.v.).Page 120: Gibson has missed several important contributions to the issue of the theoric fund in recent years (M. H. Hansen, GRBS 17 [1976] 235-46; E. M. [End Page 482] Harris in E. M. Harris and R. Wallace, eds., Transitions to Empire: Essays in Greco-Roman History 360-146 B.C., in Honor of E. Badian [Norman, Okla., 1996]; C. Carey, Apollodoros Against Neaira [Warminster, 1992] 152-57). As a result, his note on P.Berol. 9780, Col. 8.32-44 is... (shrink)

In this paper, we study solution concepts for cooperative games with stochastic payoffs. we define four kinds of solution concepts, namely the most coalitional (marginal) stable solution and the fairest coalitional (marginal) solution, by minimizing the total variance of excesses of coalitions (individual players). All these four concepts are optimal solutions of corresponding optimal problem under the least square criterion. It turns out that the fairest coalitional (marginal) solution belongs to the set of the most coalitional (marginal) stable solutions. Inspired (...) by the definition of nucleolus, we propose various extended nucleolus based on lexicographic criterion. Furthermore, axiomatizations of the proposed solutions are exhibited through the linkage between the stochastic and deterministic models. (shrink)

Iterated admissibility embodies a minimal criterion of rationality in interactions. The epistemic characterization of this solution has been actively investigated in recent times: it has been shown that strategies surviving \ rounds of iterated admissibility may be identified as those that are obtained under a condition called rationality and m assumption of rationality in complete lexicographic type structures. On the other hand, it has been shown that its limit condition, with an infinity assumption of rationality ), might not be (...) satisfied by any state in the epistemic structure, if the class of types is complete and the types are continuous. In this paper we analyze the problem in a different framework. We redefine the notion of type as well as the epistemic notion of assumption. These new definitions are sufficient for the characterization of iterated admissibility as the class of strategies that indeed satisfy \. One of the key methodological innovations in our approach involves defining a new notion of generic types and employing these in conjunction with Cohen’s technique of forcing. (shrink)

Higman essentially showed that if A is any language then SUBSEQ(A) is regular, where SUBSEQ(A) is the language of all subsequences of strings in A. Let s1, s2, s3, . . . be the standard lexicographic enumeration of all strings over some finite alphabet. We consider the following inductive inference problem: given A(s1), A(s2), A(s3), . . . . learn, in the limit, a DFA for SUBSEQU). We consider this model of learning and the variants of it that are (...) usually studied in Inductive Inference: anomalies, mind-changes, teams, and combinations thereof. This paper is a significant revision and expansion of an earlier conference version [10]. (shrink)

For each vertex of a simple polygon P an integer valued weight is given. We consider the path p1, p2,..., pk in P which is created according to the following strategy: p1 is a designated start vertex s and pi+1 is obtained by choosing the vertex with smallest weight among all vertices visible from pi and different from p1, p2,..., pi. If there is no such vertex the path is finished. This path is called geometric lexicographic dead end path. (...) We shall prove the problem of determining whether a distinguished vertex t of P is on the geometric lexicographic dead end path or not to be P‐complete. (shrink)

The purpose of the article is to draw comparisons between the major normative rules of distributive justice. This comparison is based on a kind of distribution of goods which is sometimes called the problem of pure distribution, i.e. the distribution of a homogeneous, infinitely distributable good in a situation when claims of different persons on the distributed good were in no way differentiated. This problem is defined against the background of typology of problems of goods distribution. Normative rules of (...) distributive Justice are defined formally as social welfare functionals. Eight rules of justice are distinguished: the rule of the utilitarian, Rawls’s maximin rule, Rawls’s lexicographical maximin rule, the maximax rule of the conservatives, the rule of lexicographical maximax of the conservatives, Nash’s rule, and two rules advanced by egalitarianists which differ by the meaning attributed to equality of distribution. Premises underlying the construction of these rules of justice and which indicate the measurement of preferences and possibilities of interpersonal comparisons are discussed. The same justice rules are also presented graphically. The method of the comparison amounts to examining if a certain set of ethical postulates is fulfilled by the rules under consideration. Several ethical postulates concerning the distribution of goods are formulated. Some of them define conditions any method of evaluating inequality of distribution of goods should fulfil. The remaining postulates involve more general requirements put to methods of making social decisions. Theorems about the fulfilment or nonfulfilment by individual rules of distributive justice of the considered ethical postulates are presented in a recapitulating table. The author demonstrates that almost a1l justice rules fulfil general postulates put to methods of social decision making. Nash’s rule and the two rules of the egalitarians are the exceptions, as they do not fulfil the postulate of separability with respect to unconcerned individuals. Besides, the two rules of the egalitarians do not fulfil the Pareto optimality principle. Significant differences between rules of distributive justice become manifest only when you compare way they fulfil ethical postulates concerning the manner of evaluating the inequality of the distribution. With regard to this set of postulates, they can be arranged along a definite continuum, with Rawls’s lexicographical maximin — the radical egalitarian rule, and the lexicographical maximax of the conservatives – the radical conservative rule as the extreme points of this continuum. (shrink)

Medical practitioners of the sixteenth century had their own body of special terms, just like the doctors of this century. McConchie examines medical terminology used in a selection of thirteen medical works published between 1547 and 1612, and compares it with treatment of these words in the Oxford English Dictionary and other dictionaries of today, showing how well - or ill - the specialist terminology of sixteenth-century medical practitioners has been recorded. He compiles a corpus of new data from a (...) selection of medical texts ranging from scholarly tomes to homely handbooks. The study of this corpus reveals errors, omissions, and biases which raise questions for lexicographical tools in general. Are existing dictionaries adequate in their investigation of Renaissance English? Has current understanding been more biased and more deficient than we thought? If so, how are we to redress the problem? This book uses a specialist semantic domain to raise important issues for lexicographers, and historians of early modern English and medicine. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Zwischen Aufklärungund Vernunftkritık. Studıen zum Kantischen Logıkcorpus by Norbert HinskeRiccardo PozzoNorbert Hinske. Zwischen Aufklärungund Vernunftkritık. Studıen zum Kantischen Logıkcorpus. Bad Cannstatt: Frommann-Holzboog, 1998. Pp. 192. Cloth, DM 156.00.This book is the result of a decade of research that Hinske has undertaken and continues to pursue into Kant’s logical writing in which philological, lexicographic, historical, and genuinely philosophical aspects are connected in an inseparable unity. In fact, it (...) was in order to cope scientifically with the peculiar problems that affect Kant’s logical writings from the point of view of the constitution of the text and of the recognition of the sources due to the mutual explanation and correction of published works, manuscript notes (which appeared in 1914), and lecture transcripts (which appeared first in 1966), that Hinske decided to open the venture of the Kant-Index. Hinske notices that the Kant-Index (seven volumes have appeared so far) had been started with the goal of providing a comprehensive approach to Kant’s logical writing, “whose composite forms [End Page 681] of expression rather hide its wealth of ideas” instead of clarifying it, and at the same time of providing “philological foundations for a responsible new edition of the lecture transcripts, whose scandalous [1966] edition within the fourth section of the Akademie-Ausgabe should have been rewarded with something more than the embarrassed silence of the Kant-Forschung and of both the academies [Berlin and Göttingen] responsible for this disaster” (13f.). The present book accompanies the Kant-Index in the sense that it collects a series of investigations (some of which have already appeared in journals, but have been entirely revised in order to guarantee uniformity to the volume) focusing on the two main issues indicated in its title: Kant’s proximity to the philosophy of German Enlightenment, “that finds expression in Kant’s logical writings in a quite peculiar way,” and the progressive elaboration of the Critique of Pure Reason, “which can be reconstructed at least partially on the basis of the extant lecture transcripts” (14).The development Kant underwent from an enlightened philosopher to the architect of the critique of reason is the subject of the title essay that serves as an introduction to the whole book (17–40). Hinske shows that Kant’s logic lectures are a mirror of the philosophy of the German Enlightenment (20) because Kant was not supposed to teach logic as such, but rather logic as an introduction to philosophy in general. For this reason, one finds in Kant’s logic lectures an original elaboration on the three fundamental issues expressed by the German Enlightenment, namely the programmatic ideas of thinking for oneself, the polemical idea of prejudice, and the basic idea of universal human reason. There was no “overcoming” of the Enlightenment by Kant, just as there was no “double life” of Kant as a teacher in Königsberg and as a scientist within the république des lettres (27); there was rather a genuine connection of teaching and research. In fact, if one considers the relation of the logic lectures to the Critique, it becomes clear that the terminology adopted by G. F. Meier, the author of the Auszug aus der Vernunftlehre, the logic textbook Kant used for over forty years, has a remarkable influence in constituting the terminology of the Critique (28), and that the doctrine of elements and doctrine of method division of the Critique finds its roots in the Enlightenment research on the pair of concepts logica theoretica and logica practica (30). Considering continuities and transformations in Kant’s logical writings (32–40), Hinske shows how Kant step by step puts together a new philosophical language by relying on recent Germanizations of the Enlighteners, especially the ones introduced by Wolff and G. F. Meier (33), as well as on traditional Latin terms (39).The first part of Hinske’s book deals with the heritage of the Enlightenment. It contains papers on Kant’s use of the distinction between learning philosophy and learning to philosophize (42–59), on the prejudice of antiquity (60–73), and on the pair of concepts pluralism-egoism (74... (shrink)

Epistemic decision theory aims to defend a variety of epistemic norms in terms of their facilitation of epistemic ends. One of the most important components of EpDT is known as a scoring rule. This thesis addresses some problems about scoring rules in EpDT. I consider scoring rules both for precise credences and for imprecise credences. For scoring rules in the context of precise credences, I examine the rationale for requiring a scoring rule to be strictly proper, and argue that (...) no satisfactory justification has been given. I then investigate one possible response to my argument and show the problems with this response. The conclusion is that there is a further need for justifying the requirement that a scoring rule should be strictly proper for precise credences. For scoring rules in the context of imprecise credences, an impossibility result has been established in the literature purporting to show that no strictly proper, continuous and real-valued scoring rule exists. However, a precise statement of the impossibility result requires precise definitions both of strict propriety and of continuity in the context of imprecise credences. Moreover, the result implies that we need to drop one of the three properties - strict propriety, continuity or being real-valued - to have a scoring rule for applying EpDT to imprecise credences. So, firstly, I offer definitions of strict propriety and of continuity and clarify the impossibility result. Then, I investigate what will happen if we drop one of the three properties. I argue that we should drop the property of being real-valued and I offer the general forms of two kinds of strictly proper, continuous and lexicographic scoring rules for imprecise credences. (shrink)

Here, in the middle of the well-known simile that depicts Aeneas and Turnus as bulls fighting for territory and a herd , Vergil registers the reactions of the onlookers. Commentators and lexicographers disagree about what the heifers are doing, interpreting ‘mussant’ in different ways. Servius glosses the verb as ‘dubitant’. By contrast, Heyne offers the paraphrase ‘anxii expectant’, responding to the theme of fear in the two preceding cola: cf. ‘pavidi’ and ‘metu’. Forbiger's explanatory ‘tacite expectant’ stresses rather the note (...) of silence introduced by ‘stat pecus omne metu mutum’. Lewis and Short and Georges concur with Forbiger when they translate ‘mussant’ ‘expect in silence’ and ‘stumm harren’. Other authorities, however, underscore the verb's onomatopoeic sense. Julius Caesar Scaliger, for example, observes of Vergil's usage: ‘sane verbum factitium, neque absonum a bourn voce’. Accordingly, some older commentators interpret ‘mussant’ as a restrained form of ‘mugiunt’. More recently, the OLD and TLL cite Aen. 12.718 under the definitions ‘mutter in indecision’ and ‘mussantem dubitare’. Although there is general agreement that ‘mussant’ connotes uncertainty, there still remains the problem of whether it indicates silence, faint lowing, or muttering. The purpose of this note is to call attention to an unrecognized etymological wordplay in line 718 which helps explain what the heifers are doing and why there are varying interpretations of ‘mussant’. (shrink)

Scientific explanationScientific explanations cannot take place outside a context and each context has its own hierarchy among competing explanations. The lexicographic ordering among explanations help us rank the relevance of each possible explanation not with respect to a certain set of value judgments but with respect to the available evidence; the more relevant an explanation is, the higher is placed in the ordering. The notion of explanatory indexicals is introduced and is described as a set that involves terms which (...) are unique under each context. The informationInformation these terms carry can be used to help us construct the lexicographic hierarchy. This approach captures many episodes of scientific explanationScientific explanations including explanations induced by false propositions as well as non-causalNon-causal explanations. It furthermore evades problems that probabilistic theories of explanatory virtues face such as the lottery paradoxLottery paradoxes and is not laid open to certain downsides of the well-known “inference to the best explanation” such as the commitment to consider only true propositions as possible explanations. (shrink)

Several philosophers have argued that intention is conceptually governed by a normative standard of correctness. Intention normativism is supposed to be the practical counterpart of belief normativism, which is widely discussed in the literature. In this paper, I discuss the extant formulations of the norm of intention and find all of them wanting. I then suggest and defend a new formulation of the norm of intention. I argue that the suggested formulation is immune to the problems that beset other (...) candidates for the norm of intention. (shrink)

In the final years of his life, the Belgian phenomenologist Marc Richir started to question if philosophical writing would become pointless when artists, great poets for example, have already achieved so well what philosophers have always aspired to achieve. There is no doubt that Richir considers himself in alliance with artists, since he basically believes that “phenomenology is trying to say the same thing as poets or musicians, or even possibly painters, but with philosophical language”. He seems thereby to imply (...) that phenomenology is destined to become self-aware as a sort of art. There is no surprise in this regard if we notice how frequently, throughout his entire career of philosophical production, he employs the Kantian term of the sublime to express what constitutes the phenomenon as nothing but phenomenon. This article goes through his phenomenological interpretation of Kantian aesthetics, his elaboration of the affinity between phenomenology and art, and then his genealogical conception of art, in order to introduce an original thought on what he calls “the moment of the sublime”. (shrink)

This paper explores lexicographically additive representations of multi-attribute preferences on finite sets. Lexicographic additivity combines a lexicographic feature with local value tradeoffs. Tradeoff structures are governed by either transitive or nontransitive additive conjoint measurement. Alternatives are locally traded off when they are close enough within threshold associated with a dominant subset of attributes.

The lexicographic power ΔΓ of chains Δ and Γ is, roughly, the Cartesian power Πγ∈Γ Δ, totally ordered lexicographically from the left. Here the focus is on certain powers in which either Δ = R or Γ = R, with emphasis on when two such powers are isomorphic and on when ΔΓ is 2-homogeneous. The main results are: (1) For a countably infinite ordinal α, Rα* +α ≃ Rα. (2) RR ≄ RQ. (3) For Δ a countable ordinal ≥ (...) 2. ΔR, with its smallest element deleted, is 2-homogeneous. (shrink)

This paper is concerned with implicit computational complexity of the exptime computable functions. Modifying the lexicographic path order, we introduce a path order EPO. It is shown that a termination proof for a term rewriting system via EPO implies an exponential bound on the lengths of derivations. The path order EPO is designed so that every exptime function is representable as a term rewrite system compatible with EPO (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim).

The implementation of the Wujciak algorithm as a new rule for organ allocation by Eurotransplant is of considerable interest for the theorist of choice making. In the process reformers accepted the status quo in principle but expected that their potential opponents would be willing to make minimal or 'tolerable' concessions. Thereby the consensual introduction of new dimensions of value and reforms of allocation practices based thereupon became viable. The paper characterizes a decision procedure based on ‘almost lexicographically pre-ordering established values (...) and practices’ in a stylized manner, presents a formal reconstruction of it and points out some of its potential implications for rule choices in general. (shrink)