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)

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 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)

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)

This paper sets out a new way of combining Kripke-complete modal logics: lexicographic product. It discusses some basic properties of the lexicographic product construction and proves axiomatization/completeness results.

This volume deals with collocations from a lexicographic perspective by addressing, in detail, the boundaries between collocations and other word combinations, the possibility of adapting the definition of collocation to the objectives of specific dictionaries, and approaches towards collocation extraction for lexicographic purposes.

Using a basic theorem from mathematical logic, I show that there are field-extensions ofRon which a class of orderings that do not admit any real-valued utility functions can be represented by uncountably large families of utility functions. These are the lexicographically decomposable orderings studied in Beardon et al. (2002a). A corollary to this result yields an uncountably large family of very simple utility functions for the lexicographic ordering of the real Cartesian plane. I generalise these results to the (...) class='Hi'>lexicographic ordering of \mathbb{R}^n, for every n > 2, and to lexicographic products of lexicographically decomposable chains. I conclude by showing how almost all of these results may be obtained without any appeal to the Axiom of Choice. (shrink)

This article argues that early Arabic philologists developed a robust, if implicit, theory of metaphorical language, one that was not dictated by theological concerns, and one that took shape outside the technical term majāz. The starting point of the article is the oft-cited claim found in Islamic legal theory, according to which authority over matters of majāz rested in the hands of the lexicographers. For Ibn Taymiyya, this was a lie meant to justify the acceptance of metaphor in the Quran. (...) But evidence from lexicographical, lexicological, and grammatical works supports the jurists’ general claim. There was a difference, however, between the lexemes that the jurists identified as majāz and the metaphorical expressions that the lexicographers pointed out, in that the former were not always codified in the dictionaries and thus more aligned with “live” or creative metaphors. Methodologically, the article proposes an updated model for the study of medieval Arabic technical terms, away from the term itself and toward the concept behind it. (shrink)

Resumen: El presente trabajo ofrece un análisis del diccionario Nuevos chilenismos con el objetivo de identificar los principales aspectos culturales presentes en esta obra chilena de principios del siglo XX. Gracias a un enfoque metodológico sustentado en la teoría fundamentada, es posible establecer que dentro de los aspectos culturales con mayor presencia destaca la conformación de la identidad lingüística chilena, lo que se evidencia a través de la valoración social que ofrece el autor de la norma nacional y, además, la (...) oposición que establece entre esta y la norma peninsular.: This work offers an analysis of the New Chileanisms dictionary with the objective of identifying the main cultural aspects present in this Chilean work of the beginning of the XXth century. Thanks to a methodological approach based on grounded theory, it is possible to establish that within the cultural aspects with greater presence highlights the conformation of Chilean linguistic identity, which is evidenced through the social assessment offered by the author of the national standard and, in addition, the opposition established between it and the peninsular norm. (shrink)

This edited collection presents the state of the art in research related to lexical combinations and their restrictions in Spanish from a variety of theoretical approaches, ranging from Explanatory Combinatorial Lexicology to Distributed Morphology and Generative Lexicon Theory. Section 1 offers a presentation of the main theoretical and descriptive approaches to collocation. Section 2 explores collocation from the point of view of its lexicographical representation, while Section 3 offers a pedagogical perspective. Section 4 surveys current research on collocation in Catalan, (...) Galician and Basque. Collocations and other lexical combinations in Spanish will be of interest to students of Hispanic linguistics. ". (shrink)

Dealing with fragmentary texts is an unavoidable task for anyone working on the Greco-Roman world with the awareness that only a tiny portion of the texts produced in antiquity has survived the perilous process of transmission. Since the Renaissance, generations of scholars have painstakingly collected and sifted quotations, paraphrases and allusions in later authors and grammatical sources, laying the foundation for our knowledge of large parts of that lost world. More recently a spectacular increase was made possible by the papyrological (...) discoveries. Even so, after centuries of explorations in this field, the evidence provided by the indirect sources and, in particular, by the still partly unpublished troves of medieval lexicographical excerpts and compilations is far from having been exhaustively exploited. (shrink)