Reflexive Object Research Articles

MEI AND DOU IN CHINESE: A TALE OF TWO QUANTIFIERS *

This study addresses two outstanding puzzles about the two well-known quantifiers mei and dou in Chinese: (i) the indefinite/definite asymmetry when mei leads the subject NP: dou is not needed when there is an indefinite or a reflexive object within the scope of mei and (ii) the subject/object asymmetry: when mei leads the subject NP, its distribution is restricted, depending on the type of the objects, and, by contrast, when it leads the object NP, its distribution is much freer. We propose a novel account for these puzzles. We argue that (i) the indefinite/definite asymmetry can be explained away if we assume that mei is a distributive quantifier with a portmanteau semantic structure, i.e., that it is a standard universal quantifier plus a matching function; (ii) mei can be domain-shifted into a distributive determiner to satisfy interpretability, and this explains the subject/object asymmetry and (iii) this domain-shifting is regulated by the Principle of Economy (cf. Reinhart (2006)), which is a last resort to satisfy interpretability.

Localizations, colocalizations and non additive ∗-objects

Given two arbitrary categories, a pair of adjoint functors between them induces three pairs of full subcategories, as follows: the subcategories of reflexive objects, that is objects for which the unit (respectively counit) of the adjunction is an isomorphism; the subcategories of local (respectively colocal) objects w.r.t. these adjoint functors; the subcategories of cogenerated (respectively generated) objects w.r.t. this adjoint pair, namely objects for which the unit (counit) of the adjunction is a monomorphism (an epimorphism). We investigate some cases in which the subcategory of reflexive objects coincide with the subcategory of (co)local objects or with the subcategory of (co)generated objects. As an application we define and characterize (weak) ∗-objects in the non additive case, more precisely weak ∗-acts.

The on-line application of binding Principle A in English as a second language

We report the results from two experiments investigating proficient Japanese-speaking learners' processing of reflexive object pronouns in English as a second language (L2). Experiment 1 used a timed grammaticality judgement task to assess learners' sensitivity to binding Principle A under processing pressure, and Experiment 2 investigated the time-course of reflexive anaphor resolution during L2 reading using the eye-movement monitoring technique. Taken together, our results show that despite having demonstrated native-like knowledge of reflexive binding in corresponding untimed tasks, the learners processed English reflexives differently from native speakers in that they took into consideration a matching discourse-prominent but binding-theoretically inappropriate antecedent when first encountering a reflexive. This suggests that unlike what has been reported in corresponding monolingual processing research (Sturt, 2003), initial antecedent search in L2 English is not constrained by binding Principle A.

Verbal alternations in Akan

It has been recognized (Levin 1993) that the variation in the expression of the arguments of a verb (verbal alternation) is based largely on its meaning. This paper explores the relevant alternations that verbs in Akan, a Kwa language of Ghana, participate in. The following alternations are identified as being applicable to verbs in the language: Causative/Inchoative Alternation, Unexpressed Object Alternations (made up of Understood Object, Unspecified Object, and Reflexive Object Alternations), and Ditransitive Alternations (consisting of Optional Theme Ditransitive and Definite Theme Ascension Alternations). There are also alternations that involve Non-Causative Verbs of Emission and Verbs of Spatial Configuration. An important observation arising out of the study is the interaction between certain types of alternations and a particular form of serial verb construction in the language.

Morita Duality for Grothendieck Categories with Applications to Coalgebras

ABSTRACT Finiteness conditions of reflexive objects of a Morita duality of Grothendieck category is studied. It is observed that the relation between coproduct and product is a fundamental fact. We show that for coalgebras with a duality, the class of reflexive objects coincides with the class of quasi-finite comodules.

A Simplified Method of Teaching the Position of Object Pronouns in Spanish

The placement of direct, indirect, and reflexive object pronouns is often presented disjointedly in textbooks. We offer a succinct, easily-learned pair of mnemonic devices that have universal applicability for the position of object pronouns in Spanish sentences. The acronym IGA indicates that these pronouns follow and are appended to infinitives, gerunds, and affirmative commands; otherwise, the pronouns directly precede the verb. In sentences where two positions are allowed, application of the IGA rule will reveal both possibilities. The acronym RID prescribes the sequential order of two object pronouns to be always reflexive, indirect, and direct, whether they precede or follow the verb. Additionally, the use of accent marks when pronouns are appended to verbs and the substitution of se for le or les are simplified in a concise didactic system.

Towards a systemic research methodology in agriculture: Rethinking the role of values in science

The recent drastic developmentof agriculture, together with the growingsocietal interest in agricultural practices andtheir consequences, pose a challenge toagricultural science. There is a need forrethinking the general methodology ofagricultural research. This paper takes somesteps towards developing a systemic researchmethodology that can meet this challenge – ageneral self-reflexive methodology that forms abasis for doing holistic or (with a betterterm) wholeness-oriented research and providesappropriate criteria of scientific quality.From a philosophy of research perspective,science is seen as an interactive learningprocess with both a cognitive and a socialcommunicative aspect. This means, first of all,that science plays a role in the world that itstudies. A science that influences its ownsubject area, such as agricultural science, isnamed a systemic science. From thisperspective, there is a need to reconsider therole of values in science. Science is notobjective in the sense of being value-free.Values play, and ought to play, an importantrole in science – not only in form ofconstitutive values such as the norms of goodscience, but also in the form of contextualvalues that enter into the very process ofscience. This goes against the traditionalcriterion of objectivity. Therefore, reflexive objectivity is suggested as a newcriterion for doing good science, along withthe criterion of relevance. Reflexiveobjectivity implies that the communication ofscience must include the cognitivecontext, which comprises the societal,intentional, and observational context. Inaccordance with this, the learning process ofsystemic research is shown as a self-reflexivecycle that incorporates both an involved actorstance and a detached observer stance. Theobserver stance forms the basis for scientificcommunication.To this point, a unitary view of science asa learning process is employed. A secondimportant perspective for a systemic researchmethodology is the relation between the actual,different, and often quite separate kinds ofscience. Cross-disciplinary research ishampered by the idea that reductive science ismore objective, and hence more scientific, thanthe less reductive sciences of complex subjectareas – and by the opposite idea thatreductive science is necessarilyreductionistic. Taking reflexive objectivity asa demarcator of good science, an inclusiveframework of science can be established. Theframework does not take the establisheddivision between natural, social, and humanscience as a primary distinction of science.The major distinction is made between theempirical and normative aspects of science,corresponding to two key cognitive interests.Two general methodological dimensions, thedegree of reduction of the research world andthe degree of involvement in the researchworld, are shown to span this framework. Theframework can form a basis fortransdisciplinary work by way of showing therelation between more and less reductive kindsof science and between more detached and moreinvolved kinds of science and exposing theabilities and limitations attendant on thesemethodological differences.

Innocent game models of untyped [formula omitted]-calculus

We present a new denotational model for the untyped λ-calculus, using the techniques of game semantics. The strategies used are innocent in the sense of Hyland and Ong (Inform. and Comput., to appear) and Nickau (Hereditarily Sequential Functionals: A Game-Theoretic Approach to Sequentiality, Shaker-Verlag, 1996. Dissertation, Universität Gesamthochschule Siegen, Shaker-Verlag, 1996), but the traditional distinction between “question” and “answer” moves is removed. We first construct models D and D REC as global sections of a reflexive object in the categories A and A REC of arenas and innocent and recursive innocent strategies, respectively. We show that these are sensible λη-algebras but are neither extensional nor universal. We then introduce a new representation of innocent strategies in an economical form. We show a strong connexion between the economical form of the denotation of a term in the game models and a variable-free form of the Nakajima tree of the term. Using this we show that the definable elements of D REC are precisely what we call effectively almost-everywhere copycat ( EAC) strategies. The category A EAC with these strategies as morphisms gives rise to a λη-model D EAC which we show has the same expressive power as D ∞ , i.e. the equational theory of D EAC is the maximal consistent sensible theory H ∗ . We show that the model D EAC is sensible, order-extensional and universal (i.e. every strategy is the denotation of some λ-term). To our knowledge this is the first syntax-free model of the untyped λ-calculus with the universality property.

Reflexive objects in topological categories

This paper presents several basic results about the non-existence of reflexive objects in cartesian closed topological categories of Hausdorff spaces. In particular, we prove that there are no non-trivial countably compact reflexive objects in the category of Hausdorff k-spaces and, more generally, that any non-trivial reflexive Tychonoff space in this category contains a closed discrete subspace corresponding to a numeral system in the sense of Wadsworth. In addition, we establish that a reflexive Tychonoff space in a cartesian-closed topological category cannot contain a non-trivial continuous image of the unit interval. Therefore, if there exists a non-trivial reflexive Tychonoff space, it does not have a nice geometric structure.

Hopf algebras and linear logic

It has recently become evident that categories of representations ofHopf algebrasprovide fundamental examples of monoidal categories. In this expository paper, we examine such categories as models of (multiplicative) linear logic. By varying the Hopf algebra, it is possible to model several variants of linear logic. We present models of the original commutative logic, the noncommutative logic of Lambek and Abrusci, the braided variant due to the author, and the cyclic logic of Yetter. Hopf algebras provide a unifying framework for the analysis of these variants. While these categories are monoidal closed, they lack sufficient structure to model the involutive negation of classical linear logic. We recall work of Lefschetz and Barr in which vector spaces are endowed with an additional topological structure, calledlinear topology. The resulting category has a large class of reflexive objects, which form a *-autonomous category, and so model the involutive negation. We show that the monoidal closed structure of the category of representations of a Hopf algebra can be extended to this topological category in a natural and simple manner. The models we obtain have the advantage of being nondegenerate in the sense that the two multiplicative connectives, tensor and par, are not equated. It has been recently shown by Barr that this category of topological vector spaces can be viewed as a subcategory of a certain Chu category. In an Appendix, Barr uses this equivalence to analyze the structure of its tensor product.

ALL COMPACT HAUSDORFF LAMBDA MODELS ARE DEGENERATE

The first mathematical model of untyped lambda calculus was discovered by DANA SCOTT in the category of algebraic lattices and Scott continuous maps. The question then arises as to which other cartesian closed categories contain a model of the calculus. In this paper we show that any compact Hausdorff model of the calculus must satisfy the property that the semantic map from the calculus to the model is constant. In particular, any compact reflexive object in the category of Hausdorff k-spaces gives rise to a degenerate model of the calculus. We also explore the relationship of the results we derive to the notions of a combinatory model and of an environment model of the calculus.

Categorical models for non-extensional λ-calculi and combinatory logic

The notions of weak Cartesian closed category and very weak CCC are introduced by dropping the extensionality (and the naturality) requirements in the adjunction defining the closed structure of a CCC. A number of specific examples of these categories are given. The weak notions are shown to be equivalent from both the semantic and syntactic standpoint to the typed non-extensional lambda-calculus and to the typed Combinatory Logic, extended with surjective pairs. Type-free models are characterized as reflexive objects in wCCCs. Finally, categorical models for the second-order non-extensional calculus are defined, by introducing a simple generalization of the notion of PL-category.

Leaving the Field

As journeyers into the field, participant observers, and chroniclers, we have been involved in the development of organ transplantation, the artificial kidney, and the artificial heart throughout most of their contemporaneous medical and social history and for many years of our working lives. Since 1951 (RCF) and 1968 (JPS), we have had the privileged opportunity to watch from the inside how dialysis, and kidney, heart, and liver transplantation, which began as remedies for desperate with certain desperate[ly] hopeless conditions,[1] evloved into nonexperimental, though far from ordinary, interventions to treat a wide gamut of end-stage diseases. During those years we have seen the range and combinations of different organs transplanted, the numbers performed, and the array of artificial organs designed increase dramatically, and we have charted first hand the early phases of the drive to replace the human heart with an artificial device. Our intensive, long-term relationship with these therapeutic innovations and their clinical unfolding has had many of the characteristics anthropologist Margaret Mead identified as inherent to field research, no matter where it is located or what its subject matter may be. Field work, as she described it, entails not just the unique but also cumulative experience of immersing oneself in the ongoing life of another people, suspending for the time both one's beliefs and disbeliefs, and of simultaneously attempting to understand mentally and physically this other version of reality.... Immersing oneself in the field is good, but one must be careful not to drown. One must somehow maintain the delicate balance between empathic participation and self-awareness, on which the whole research process depends.... Only very slowly did we [field workers] begin to take into account that we ourselves with each step of the journey, with each new image presented to us...and with each day in the field.[2] Our research did not transport us to geographically and culturally isolated primitive villages, where we lived and worked day after day for months without the respite of returning to our home-world. Yet, in many crucial respects, our field experiences parallel those of Mead. We have journeyed far, horizontally and vertically, in our questining after transplantation, dialysis, and the artificial heart--coast to coast in this country, and to Europe, Hawaii, Majuro, and China; down long corridors into the high-technology surgical and intensive care chambers of the modern hospital; and ever more deeply into the corridors and chambers of ourselves. The people we have studied have been our teachers as well as our subjects, helping us to learn their language and their ways. We have risen at cock crow to accompany transplant teams, donors, and recipients into operating rooms, and we have stayed up all night to listen for some slight change in a patient's or prospective donor's condition and to revel or mourn with medical professionals, patients, and families. We have used ourselves as instruments, striving to attain and reattain the kind of reflexive objectivity that calls for continuous self-scrutiny and self-analysis, along with observing and interpreting the actions and interactions of others. For years, as participating observers and observing participants, we have walked the thin line between detachment and concern and between belief and disbelief. And like Mead, only very slowly did we realize that, as a consequence of our immersion in the field, deep and enduring changes were taking place in us.[3] Foremost among the people whose reality we have been allowed to share are the physicians and nurses, patients and families who have been the chief actors in the experiments perilous through which organ transplants, dialysis, and the efforts to fashion a viable artificial heart have been advanced. It has kept us in close contact with the grave illnesses and frequent deaths they have mutually faced, with the hope and renewal, the breakthroughs, the despair and dissappointments they have experienced, and with the ways of navigating and coping they have forged. …

An approximation theorem for topological lambda models and the topological incompleteness of lambda calculus

It is well known that a reflexive object in the Cartesian closed category of complete partial orders and Scott-continuous functions is a model of λ-calculus (briefly a topological model). A topological model, through the interpretation function, induces a λ-theory, i.e., a congruence relation on λ-terms closed under α- and β-reduction. It is natural to ask if all possible λ-theories are induced by a topological model, i.e., if topological models are complete w.r.t. λ-calculus. The authors prove an Approximation Theorem, which holds in all topological models. Using this theorem, they analyze some topological models and their induced λ-theories, and they exhibit a λ-theory which cannot be induced by a topological model. So they prove that topological models are not complete w.r.t. λ-calculus.

A generalization of the concept of sketch

This paper introduces an extension of the concept of sketch, called a form, which allows the specification of entities other than limits and colimits in a model. A form can require that a diagram become (in a model) an instance of any categorial construction specifiable in an essentially algebraic way. Constructions which can be specified in this way include function space objects in and reflexive objects in a cartesian closed category, power objects in a topos, and list objects in a locos. This generalization is motivated by the desire to specify functional programming languages by sketches.

Retraction map categories and their applications to the construction of lambda calculus models

This paper deals with categorical models of the λ-calculus. We generalize the inverse limit method Scott used for his construction of D ∞ , and introduce order-enriched ccc's, retraction map categories and ɛ-categories. An order-enriched ccc is a cartesian closed category C equipped with a partial order relation ⩽ on the set of the arrows. A retraction map category of C is R =( R , ⩽, i , j ), where ⩽ is a partial order relation on the set | C | of all the objects of C , R is the category of the poset (| C |, ⩽), and i and j are functors from R to C and from R op to C that satisfy the conditions: (1) j a , b ∘ i a , b ⩾ id a and (2) i a , b ∘ j a , b ⩽ id b for every arrow a , b : a → b in R (i.e., a ⩽ b ). The ɛ-category E = E ( C , R ) of C w.r.t. R is the category whose objects are ideals of (| C |, ⩽) and whose arrows are ideals of ( C , ⊑), where ⩽ is the partial order relation in R and ⊑ is the partial order relation defined by f ⊑ g iff dom( f )⩽dom( g ), cod( f )⩽cod( g ) in R and f ⩽ j a , b ∘ g ∘ i ( a , b in C . We show that every ɛ-category E = E ( C , R ) is also an order-enriched ccc. Moreover when E and R satisfy a particular condition, E ( C , R ) has a reflexive object. For example, if there is an ideal U of (| C |, ⩽) satisfying the following conditions, then U is isomorphic to U U in E and a λ-algebra is constructed from E and U : (1) for every pair of a , b ∈ U , U contains b a , and (2) for every c ∈ U , there are a , b ∈ U such that c ∈ b a . We reconstruct P ω and D ∞ using ɛ-categories.

Un Cas Familier De Non-Cliticisation

It is traditionally observed in French grammars that, exceptionally, an indirect object pronoun cannot be cliticized to a verb which has a first person, second person or reflexive direct object clitic. Instead, the indirect object pronominal manifests as a strong pronominal form. It is generally believed today that this failure of cliticization is due to constraints on possible sequences of verbal clitics. The present note shows that this dominant view must be incorrect.

Reflexive Objekte in einer Funktorkategorie mit Dualität

The reflexive objects of a functor category with duality, constructed by the author in [KJL], are characterized. Especially emphasized are the functors on the category L of complete locally convex spaces and continuous linear operators.

TURISME, DIGT OG HISTORIE - TINTERN ABBEY SOM EKSEMPEL PÅ ÆSTETISK OBJEKTIVATION

TOURISM, POETRY, AND HISTORY. TINTERN ABBEY AS AN EXAMPLE OF AESTHETIC OBJECTIVATION | The essay presents a new concept which I call ‘aesthetic objectivation’. It deals with how to understand and grasp specific literary texts, events and conceptualisations due to a specific field of both disrupted and progressive historical features, in which the same object is being perceived, firstly as a sense object, secondly as reflexive object. The concept is shaped by a non-universalistic and non-Hegelian objectivity thinking. The line from Gilpin’s ‘pittoresque’ and sensual description of Tintern Abbey in Observations on the River Wye to the reflexive use of the very same ruin in Wordsworth’s “Tintern Abbey”, Tennyson’s “Tears, Idle Tears”, and Ginsberg’s “Wales Visitation” serves as an exemplifying study case.