Reflexive Object Research Articles

Friendship, Intimacy, and the Contradictions of Therapy Culture

While therapy culture has long been a part of the repertoires through which people think about and practice their romantic relationships, it has been less prominent in how they envision friendship. However, based on our interviews on experiences of friendlessness in an Atlantic Canadian city, we show that therapeutic styles increasingly shape how people orient to friendship, even as friends rarely seek formal therapy to manage their conflicts. This article focuses on how modern therapy culture, with its emphasis on individual wellbeing, self-knowledge, and ‘healthy’ rather than ‘toxic’ relationships, presents people with conflicting cultural imperatives for how to practice their friendships. On the one hand, therapy culture encourages people to seek out friends to whom they can disclose their most intimate feelings and experiences – friends who will offer support, understanding, and validation. On the other hand, therapy culture equally cautions that one must maintain ‘boundaries’ to protect oneself from friends’ personal revelations or ‘traumas.’ We ask what these dual imperatives mean for modern friendship and how people experience the tension between them. We argue that one reason modern friendship can be difficult is that divulging one’s intimate feelings or experiences to a friend can be interpreted as either building intimacy or burdening others with one’s problems, or crucially, both at the same time. Our findings lead us to ask how therapy culture might increasingly turn friendship into a reflexive object or something else to ‘optimize’ rather than providing an escape from relationships that demand ‘work.’

ԱՆԴՐԱԴԱՐՁ ԿԱՌՈՒՅՑՆԵՐԻ ՀԱՄԱՎԵՐԱԲԵՐԱՅԻՆ ԵՎ ԻՄԱՍՏԱՅԻՆ ՎԵՐԼՈՒԾՈՒԹՅՈՒՆԸ ԱՆԳԼԵՐԵՆՈՒՄ (ՀԱՅԵՐԵՆԻ ԶՈՒԳԱԴՐՈՒԹՅԱՄԲ) / COREFERENTIAL AND SEMANTIC ANALYSIS OF REFLEXIVE CONSTRUCTIONS IN ENGLISH (WITH REFERENCE TO ARMENIAN)

The paper is devoted to coreferential divergencies between English reflexive pronouns and their antecedents. The comparative analysis also shows that the Armenian counterparts of the English reflexive pronouns are independent linguistic units, used separately from their antecedents. The scale of reflexivity is defined by the extent of affectedness the object undergoes as a result of the action performed by the subject. The scope of affectedness of the object ranges from radical physical changes to zero affect, in which case the subject and the reflexive object display a complete confluence.

Loss of intersective gradience as the lifeboat of a dying construction. An analysis of the diachronic change of causativebring

AbstractThis paper focusses on diachronic processes which lead to the disambiguation between different constructions involving the same verb. It follows the development ofbringas a periphrastic causative over the course of the Early Modern and Late Modern English periods and compares it to the development of otherbringconstructions. In a corpus-based analysis, it utilizes measures of cue strength as well as collostructional analysis to determine whether reflexive objects, negation, modals or the passive are cues strongly associated with the dying periphrastic causative XbringcauseYto-inf. Results indicate that the construction indeed increasingly attracts reflexive objects in combination with a modal or negation. This finding is interpreted as an indication that non-prototypical verbal properties developing into strong cues for a construction may serve to make a rare construction more salient and thus easier to recognize and process. Furthermore, the construction’s restriction to reflexive patients vastly reduces variability in the object slot.

Case, deficient pronouns and the arbitrary pronoun men in Frisian

ABSTRACT The Frisian arbitrary pronoun men is analysed here as a deficient pronoun, since it does not allow expansion of its projection by means of premodification, coordination or relativisation. Furthermore, men occurs adjacent to the tensed verb in main clauses and to the complementiser in embedded clauses. To explain these data, we suggest that men is case licensed in Phonetic Form under adjacency by means of a head–head relation, being deficient as a maximal projection. The relation between case and deficiency is further reflected in the defective (or suppletive) morphological case paradigm of men. Evidence is presented that the paradigm of men in written Frisian originated in the 16th and 17th centuries by suppletion of forms of the indefinite pronoun ien/jin ‘one’. Out of these arose the reflexive object form of the arbitrary pronoun men: jin, and as its reflexive jin thus truly became part of men’s paradigm.

A MALL geometry of interaction based on indexed linear logic

AbstractWe construct a geometry of interaction (GoI: dynamic modelling of Gentzen-style cut elimination) for multiplicative-additive linear logic (MALL) by employing Bucciarelli–Ehrhard indexed linear logic MALL(I) to handle the additives. Our construction is an extension to the additives of the Haghverdi–Scott categorical formulation (a multiplicative GoI situation in a traced monoidal category) for Girard’s original GoI 1. The indices are shown to serve not only in their original denotational level, but also at a finer grained dynamic level so that the peculiarities of additive cut elimination such as superposition, erasure of subproofs, and additive (co-) contraction can be handled with the explicit use of indices. Proofs are interpreted as indexed subsets in the category Rel, but without the explicit relational composition; instead, execution formulas are run pointwise on the interpretation at each index, with respect to symmetries of cuts, in a traced monoidal category with a reflexive object and a zero morphism. The sets of indices diminish overall when an execution formula is run, corresponding to the additive cut-elimination procedure (erasure), and allowing recovery of the relational composition. The main theorem is the invariance of the execution formulas along cut elimination so that the formulas converge to the denotations of (cut-free) proofs.

Calculating the blue economy: producing trust in numbers with business tools and reflexive objectivity

ABSTRACT The ‘blue economy’ has in recent years become a leading concept for envisioning what may come after the fossil-based era. In efforts at calculating the potential economic value of the ocean, policy-oriented documents seek to unite diverse actors around common goals. Through the calculation of numbers, large-scale and long-term policy visions are being crystallized. But how do such numbers come into being in practice? This article interrogates this question with an example from the Norwegian context: the established policy goal of a so-called ‘five-fold increase’ in marine value creation in the year 2050. While powerful numbers are commonly expected to be produced through the procedures of ‘mechanical objectivity’ that involve strict quantification and scientific methods, our analysis shows a rather different route towards a powerful number: By loosely combining tools developed for business management, the number is calculated by, first, openly combining qualitative and narrative operations into the calculation and then, next, decoupling qualitative uncertainties from the quantified potential. The result is a calculative process that takes the form of what we suggest to call ‘reflexive objectivity’ and a policy-oriented number that encourages risk-taking and action over restraint and precaution.

Categorical models of the differential λ-calculus

AbstractThe paper shows how the Scott–Koymans theorem for the untyped λ-calculus can be extended to the differential λ-calculus. The main result is that every model of the untyped differential λ-calculus may be viewed as a differential reflexive object in a Cartesian-closed differential category. This extension of the Scott–Koymans theorem depends critically on unraveling the somewhat subtle issue of which idempotents can be split so that differential structure lifts to the idempotent splitting.The paper uses (total) Turing categories with “canonical codes” as the basic categorical semantics for the λ-calculus. It develops the main result in a modular fashion by showing how to add left-additive structure to a Turing category, and then – on top of that – differential structure. For both levels of structure, it is necessary to identify how “canonical codes” must behave with respect to the added structure and, furthermore, how “universal objects” must behave. The latter is closely tied to the question – which is the crux of the paper – of which idempotents can be split while preserving the differential structure of the setting.This paper is the full version of a conference paper and includes the proofs which were omitted from that version due to page-length restrictions.

On geometry of interaction for polarized linear logic

We present Geometry of Interaction (GoI) models for Multiplicative Polarized Linear Logic, MLLP, which is the multiplicative fragment of Olivier Laurent's Polarized Linear Logic. This is done by uniformly adding multi-points to various categorical models of GoI. Multi-points are shown to play an essential role in semantically characterizing the dynamics of proof networks in polarized proof theory. For example, they permit us to characterize the key feature of polarization, focusing, as well as being fundamental to our construction of concrete polarized GoI models.Our approach to polarized GoI involves following two independent studies, based on different categorical perspectives of GoI: (i)Inspired by the work of Abramsky, Haghverdi and Scott, a polarized GoI situation is defined in which multi-points are added to a traced monoidal category equipped with a reflexive object U. Using this framework, categorical versions of Girard's execution formula are defined, as well as the GoI interpretation of MLLP proofs. Running the execution formula is shown to characterize the focusing property (and thus polarities) as well as the dynamics of cut elimination.(ii)The Int construction of Joyal–Street–Verity is another fundamental categorical structure for modelling GoI. Here, we investigate it in a multi-pointed setting. Our presentation yields a compact version of Hamano–Scott's polarized categories, and thus denotational models of MLLP. These arise from a contravariant duality between monoidal categories of positive and negative objects, along with an appropriate bimodule structure (representing ‘non-focused proofs’) between them.Finally, as a special case of (ii) above, a compact model of MLLP is also presented based on Rel (the category of sets and relations) equipped with multi-points.

Categorical Models of the Differential λ-Calculus Revisited

The paper shows that the Scott-Koymans theorem for the untyped λ-calculus extends to the differential λ-calculus. The main result is that every model of the untyped differential λ-calculus may be viewed as a differential reflexive object in a Cartesian closed differential category. This extension of the Scott-Koymans theorem depends critically on unravelling the somewhat subtle issue of which idempotents can be split so that differential structure lifts to the idempotent splitting.The paper uses (total) Turing categories with “canonical codes” as the basic categorical semantics for the λ-calculus. It shows how the main result may be developed in a modular fashion by first adding left-additive structure to a Turing category, and then – on top of that – differential structure. For both levels of structure it is necessary to identify how “canonical codes” behave with respect to the added structure and, furthermore, how “universal objects” behave. The latter is closely tied to the question – which is the crux of the paper – of which idempotents can be split in these more structured settings.

Pupillary responses reflect ambiguity resolution in pronoun processing

ABSTRACTThe resolution of ambiguous pronouns is influenced by the preceding linguistic discourse. This raises the question whether the processing of an object pronoun is also influenced by the preceding sentential subject. In an experiment with Dutch adults, we recorded pupil dilation as a measure of the cognitive effort involved in resolving pronominal versus full noun phrase (NP) subjects and pronominal versus reflexive objects. Our results indicate that more effort is needed to resolve a pronominal subject or object compared to a less ambiguous full NP subject or reflexive object. These results support the hypothesis that the ambiguity of a referring expression influences processing. Contrary to our expectations, no evidence was found that the form of the subject influences the processing of a subsequent pronominal object. We conclude that pupillary responses reflect ambiguity resolution in pronoun processing, and that the process to resolve pronouns commences as soon as the pronoun is encountered.

Training student nurses in risk management

At the heart of the complexity of an organised system, the student must learn to manage situations presenting characteristics of known or potential risk. The trainer integrates it into an approach in which reflexive analysis and objectivity are essential in the professional practice.

Commentary: Swapping or Dropping? Electrophysiological Measures of Difficulty during Multiple Object Tracking.

Within cognitive psychology it is widely accepted that the human visual system represents the numerical sameness of objects. In particular, we are able to perceive an object as being the same despite movement and qualitative changes (Pylyshyn, 2007). Empirical research concerning visual sameness has focused on the conditions under which sameness is perceived (Odic et al., 2012) and the nature of mechanisms engaged in representing sameness (Makovski and Jiang, 2009). However, the relation of visual sameness itself has not attracted as much attention and no detailed description of this relation is yet available. One of the most important questions is whether this relation can be understood as classical identity, and thus whether it is an equivalence relation, i.e., reflexive (object is the same as itself), symmetric (if A is the same as B, then B is the same as A), and transitive (if A is the same as B and B is the same as C, then A is the same as C). While the topic of relations' formal properties is not completely alien to psychological research—see classical investigations by Tversky (1977) or more recent by Rips (2011)—there are no investigations that address the equivalence of visual sameness. Despite this research gap, I intend to show that results of some psychological works can be interpreted as having a high relevance for the question of equivalence. I demonstrate this by analyzing a study by Drew et al. (2013) that is not explicitly concerned with the equivalence of visual sameness, but in fact has important implications for this question.

Interpretação de pronomes e aquisição de dependências referenciais em português L2

This study investigates whether L2 learners of (European) Portuguese display asymmetries in their comprehension of reflexive and non-reflexive pronouns, as has been found in L2 English (e.g., Kim, Montrul & Yoon, 2014). Forty-one intermediate learners of L2 Portuguese, who were L1 speakers of Spanish, English and Chinese, completed a truth-value judgement task (Silva, 2015) testing both reflexive and non-reflexive object clitics. The three groups achieved targetlike results in their interpretation of both types of pronouns. These findings indicate that, unlike strong pronouns, clitic pronouns pose no difficulties for learners, which suggests that, as previously shown for L1 acquisition (e.g., McKee, 1992), the grammatical status of pronouns (strong vs. clitic) is also relevant in L2 acquisition.

Linear lambda terms as invariants of rooted trivalent maps

AbstractThe main aim of the paper is to give a simple and conceptual account for the correspondence (originally described by Bodini, Gardy, and Jacquot) between α-equivalence classes of closed linear lambda terms and isomorphism classes of rooted trivalent maps on compact-oriented surfaces without boundary, as an instance of a more general correspondence between linear lambda terms with a context of free variables and rooted trivalent maps with a boundary of free edges. We begin by recalling a familiar diagrammatic representation for linear lambda terms, while at the same time explaining how such diagrams may be read formally as a notation for endomorphisms of a reflexive object in a symmetric monoidal closed (bi)category. From there, the “easy” direction of the correspondence is a simple forgetful operation which erases annotations on the diagram of a linear lambda term to produce a rooted trivalent map. The other direction views linear lambda terms as complete invariants of their underlying rooted trivalent maps, reconstructing the missing information through a Tutte-style topological recurrence on maps with free edges. As an application in combinatorics, we use this analysis to enumerate bridgeless rooted trivalent maps as linear lambda terms containing no closed proper subterms, and conclude by giving a natural reformulation of the Four Color Theorem as a statement about typing in lambda calculus.

A correspondence between rooted planar maps and normal planar lambda terms

A rooted planar map is a connected graph embedded in the 2-sphere, with one edge marked and assigned an orientation. A term of the pure lambda calculus is said to be linear if every variable is used exactly once, normal if it contains no beta-redexes, and planar if it is linear and the use of variables moreover follows a deterministic stack discipline. We begin by showing that the sequence counting normal planar lambda terms by a natural notion of size coincides with the sequence (originally computed by Tutte) counting rooted planar maps by number of edges. Next, we explain how to apply the machinery of string diagrams to derive a graphical language for normal planar lambda terms, extracted from the semantics of linear lambda calculus in symmetric monoidal closed categories equipped with a linear reflexive object or a linear reflexive pair. Finally, our main result is a size-preserving bijection between rooted planar maps and normal planar lambda terms, which we establish by explaining how Tutte decomposition of rooted planar maps (into vertex maps, maps with an isthmic root, and maps with a non-isthmic root) may be naturally replayed in linear lambda calculus, as certain surgeries on the string diagrams of normal planar lambda terms.

Animation in Transition: A semiotic reading of Ase Mmanwu Masquerade Costume in Performance.

The study takes a critical look at costume in motion. Motion or movement here imposes on costume the image of a living object and as such a composition drawn on a symbiotic relationship between anarticle of material culture and an animator; usually a human factor. This thus infers that, it is in the conjugal relationship of performer and costume that the performancecostume attains full realization and finally, a scaling up in its utility value. The study addresses critically, the Ase Mmanwu costume in performance. As tool to aid artistic exhibition, the Mmanwu costume in performance comes alive as a rich semiotic field explored for signification in the Ase Mmanwu art. The brand, embodied in spatial movements and convolutions, creates and imposes strictly the image of an animated and highly reflexive object which lingers in the consciousness of its beholder(s) long after its perception. With special interest in the masking components of Ase Mmanwu tradition, this discourse is restricted to the animated and antiquated costume of theMmanwumasquerade of Ase people of Nigeria.

Hermitian categories, extension of scalars and systems of sesquilinear forms

We prove that the category of systems of sesquilinear forms over a given hermitian category is equivalent to the category of unimodular 1-hermitian forms over another hermitian category. The sesquilinear forms are not required to be unimodular or defined on a reflexive object (i.e. the standard map from the object to its double dual is not assumed to be bijective), and the forms in the system can be defined with respect to different hermitian structures on the given category. This extends a result obtained by E. Bayer-Fluckiger and D. Moldovan. We use the equivalence to define a Witt ring of sesquilinear forms over a hermitian category, and also to generalize various results (e.g.: Witt's Cancelation Theorem, Springer's Theorem, the weak Hasse principle, finiteness of genus) to systems of sesquilinear forms over hermitian categories.

Facing the grand challenges through heuristics and mindfulness

We address the nature of mindfulness and its salience to education generally and to science education specifically. In a context of the historical embeddedness of mindfulness in Buddhism we discuss research in social neuroscience, presenting evidence for neuronal plasticity of the brain and six emotional styles, which are not biologically predetermined, but are responsive to adaptation through life experiences. We raise ques- tions about the role of science education in mediating the structure and function of the brain. Also, we discuss interventions to increase Mindfulness in Education, including meditation and heuristics, that act as reflexive objects to heighten awareness of charac- teristics of mindfulness and increase the likelihood of changes in the conduct of social life—increasing the mindfulness of those who engage the characteristics included in the heuristic. We present mindfulness and the development of a toolkit for ameliorating emotions when and as necessary as a component of a science curriculum that orientates toward wellness and sustainability. We advocate for changes in the nature of science education to reflect the priorities of the twenty first century that relate to sustainability of the living and nonliving universe and wellness of sentient beings.

Full Abstraction for the Resource Lambda Calculus with Tests, through Taylor Expansion

We study the semantics of a resource-sensitive extension of the lambda calculus in a canonical reflexive object of a category of sets and relations, a relational version of Scott's original model of the pure lambda calculus. This calculus is related to Boudol's resource calculus and is derived from Ehrhard and Regnier's differential extension of Linear Logic and of the lambda calculus. We extend it with new constructions, to be understood as implementing a very simple exception mechanism, and with a "must" parallel composition. These new operations allow to associate a context of this calculus with any point of the model and to prove full abstraction for the finite sub-calculus where ordinary lambda calculus application is not allowed. The result is then extended to the full calculus by means of a Taylor Expansion formula. As an intermediate result we prove that the exception mechanism is not essential in the finite sub-calculus.

What is a categorical model of the differential and the resource λ-calculi?

The differential λ-calculus is a paradigmatic functional programming language endowed with a syntactical differentiation operator that allows the application of a program to an argument in a linear way. One of the main features of this language is that it is resource conscious and gives the programmer suitable primitives to handle explicitly the resources used by a program during its execution. The differential operator also allows us to write the full Taylor expansion of a program. Through this expansion, every program can be decomposed into an infinite sum (representing non-deterministic choice) of ‘simpler’ programs that are strictly linear.The aim of this paper is to develop an abstract ‘model theory’ for the untyped differential λ-calculus. In particular, we investigate what form a general categorical definition of a denotational model for this calculus should take. Starting from the work of Blute, Cockett and Seely on differential categories, we develop the notion of a Cartesian closed differential category and prove that linear reflexive objects living in such categories constitute sound and complete models of the untyped differential λ-calculus. We also give sufficient conditions for Cartesian closed differential categories to model the Taylor expansion. This requires that every model living in such categories equates all programs having the same full Taylor expansion.We then provide a concrete example of a Cartesian closed differential category modelling the Taylor expansion, namely the category MRel of sets and relations from finite multisets to sets. We prove that the extensional model of λ-calculus we have recently built in MRel is linear, and is thus also an extensional model of the untyped differential λ-calculus. In the same category, we build a non-extensional model and prove that it is, nevertheless, extensional on its differential part.Finally, we study the relationship between the differential λ-calculus and the resource calculus, which is a functional programming language combining the ideas behind the differential λ-calculus with those behind Boudol's λ-calculus with multiplicities. We define two translation maps between these two calculi and study the properties of these translations. In particular, this analysis shows that the two calculi share the same notion of a model, and thus that the resource calculus can be interpreted by translation into every linear reflexive object living in a Cartesian closed differential category.