This thesis is about the problem of compositionality in distributional semantics. Distributional semantics presupposes that the meanings of words are a function of their occurrences in textual contexts. It models words as distributions over these contexts and represents them as vectors in high dimensional spaces. The problem of compositionality for such models concerns itself with how to produce distributional representations for larger units of text (such as a verb and its arguments) by composing the distributional representations of smaller units of text (such as individual words). This thesis focuses on a particular approach to this compositionality problem, namely using the categorical framework developed by Coecke, Sadrzadeh, and Clark, which combines syntactic analysis formalisms with distributional semantic representations of meaning to produce syntactically motivated composition operations. This thesis shows how this approach can be theoretically extended and practically implemented to produce concrete compositional distributional models of natural language semantics. It furthermore demonstrates that such models can perform on par with, or better than, other competing approaches in the field of natural language processing. There are three principal contributions to computational linguistics in this thesis. The first is to extend the DisCoCat framework on the syntactic front and semantic front, incorporating a number of syntactic analysis formalisms and providing learning procedures allowing for the generation of concrete compositional distributional models. The second contribution is to evaluate the models developed from the procedures presented here, showing that they outperform other compositional distributional models present in the literature. The third contribution is to show how using category theory to solve linguistic problems forms a sound basis for research, illustrated by examples of work on this topic, that also suggest directions for future research.

Dans cette thèse, nous présentons les relations entre le principe de réflexion MRP introduit par Moore, les propriétés d'arbres généralisées ITP et ISP introduites par Weiß, ainsi que les propriétés square introduites par Jensen et développées par Schimmerling. Le résultat principal de cette thèse est que MRP+MA entraine ITP(λ, ω2) pour tout cardinal λ ≥ ω2. Ce résultat implique par conséquent que les méthodes actuelles pour prouver la consistance de MRP+MA nécessitent au moins l'existence d'un cardinal supercompact. Il s'avère que MRP seul ne suffit pas à démontrer ce résultat, et nous donnons la démonstration que MRP n'entraine pas la propriété d'arbre plus faible, à savoir TP(ω2, ω2). De plus MRP+MA n'entraine pas le principe d'arbre plus fort ISP(ω2, ω2). Enfin nous étudions les relations entre MRP et des versions faibles de square. Nous montrons que MRP implique la négation de square(λ, ω) et MRP+MA implique la négation de square(λ, ω1) pour tout λ ≥ ω2.

"Thèse présentée à la Faculté des études supérieures en vue de l'obtention du grade de Docteur en droit (LL.D.)" / Cette suite d'essais analyse la conception de la monnaie en droit, cherchant à isoler l'originalité de sa nature abstraite. La tradition juridique caractérise la monnaie à la fois comme un fait et comme un droit parce qu'elle présuppose un sens substantif au nom commun 'monnaie', étant ainsi incapable d'admettre que la monnaie, par sa place unique dans les catégories du droit, est le mécanisme qui suppose l'avenir indéterminé en y enchâssant le présent. La difficulté de la monnaie est que, comme catégorie, elle n'est pas incluse aux catégories usuelles de droit privé. Son caractère abstrait l'empêche d'ailleurs d'être incluse parmi les objets qui ont une extension. La monnaie se définit plutôt par négation relativement aux catégories usuelles. Elle est donc reconnaissable entre toutes. Dans la relation sujet-objet, la monnaie versée n'est évidemment pas un sujet. Dans son sens strict, la monnaie réfère aujourd'hui au papier-monnaie. Il est vrai que ce dernier existe matériellement puisqu'il est tangible. Mais paradoxalement, en tant qu'objet, la monnaie est ni une somme, ni une obligation en nature, ni un bien, ni une représentation de dette, ni une mesure, ni consomptible, ni fongible au sens pertinent de ces mots. Comment saisir la substance d'une notion qui se soustrait aux catégories usuelles de la doctrine? Voilà la difficulté fondamentale de la thèse. Répétons son mode original de définition: la monnaie n'est pas identique à une somme due, mais - en étant payée - elle en éteint une; conversement, la somme due n'est pas identique à la monnaie perçue, mais -lorsque payée en trop - cette dernière est déclarée indue et sujette à répétition (l'indu devient dû). La définition de la monnaie procède par 'corécurrence' : elle définit quelque chose d'indéterminé puisqu'un membre de la définition réfère à l'autre et viceversa. Sa nature s'exprime par sa fonction dans la structure des prestations. Mais la doctrine la traite d'abord comme une somme due, sans distinguer outre mesure ce type de dette des autres prestations. Or, à titre d'exécution d'une obligation, une somme d'argent non seulement éteint d'autant les montants, dus à une époque ou l'autre, mais, puisque ces derniers sont appariés aux obligations en nature en tant que prix dû en contrepartie des prestations caractérisées à être effectuées, la perception des sommes d'argent conduit encore à la mobilité des biens parmi les personnes. D'où le paradoxe: une somme d'argent est destinée à circuler précisément pour être la fin des sommes dues. La doctrine enseigne la thèse unitaire du paiement des obligations (en son acception large du droit civil) : sont mis dans un même sac les faits exécutés pour satisfaire à des obligations en nature et les paiements de sommes d'argent dues. Or, elles sont en premier dues, puis payées. Ils sont dits former un ensemble. Ce sac est le temps lui-même. Il s'agit d'une interprétation de l'univers des prestations, précisément une interprétation de la notion d'univers où l'actualité homogène d'un ensemble exclut de faire une place à l'éventualité de valeurs futures par contraste aux valeurs passées. Pour réduire la notion d'univers à celle d'ensemble actuel, l'astuce est de fermer la dualité 'ensemble/membre' en substituant au membre l'ensemble: l'un des objets inclus à l'ensemble doit être à la fois un élément existant de l'ensemble et la collection de tous ses éléments, constituant ainsi la jonction substantive sous-jacente à cette dualité. IV Cet objet fondateur est d'habitude nommé le zéro de l'ensemble. Traitant ainsi l'ensemble des exécutions des obligations, il doit y avoir un élément qui ait à la fois la nature d'une promesse et celle d'un fait. Cet élément est la monnaie. Ainsi, la monnaie a une nature double, à la fois concept et référent du concept. La somme due est exécutée en monnaie et, conversement, la monnaie est la somme transférée à titre de paiement: substituant une définition dans l'autre, l'exécution de la somme due est la somme transférée, une formule conduisant à la régression infinie. Qui donc est le débiteur de cette somme transférée depuis aussi longtemps que la monnaie a circulé et circulera? La difficulté conceptuelle de la monnaie est de comprendre cette métamorphose, où l'exécution d'un fait en satisfaction d'une obligation se révèle elle même être une promesse. Pourquoi alors distinguer une obligation et son exécution? La monnaie cumule la nature catégorique d'une chose matérielle délivrée - autrefois l'or, aujourd'hui le papier-monnaie - et la nature d'une somme due; cette façon de penser mène à réifier les dettes, à leur conférer une existence matérielle. Mais devoir l'argent est fondamentalement la durée du terme d'une relation entre deux personnes. Et payer la monnaie est l'extinction de ce terme. Alors paradoxalement, l'exprimant dans une dualité catégorique, la monnaie a une durée et en même temps n'en a pas. Cette postulation d'une union des termes opposés d'une dualité n'est pas sans précédent. Pour aider le lecteur à s'en rendre compte, je documente que le thème de la migration de la valeur pécuniaire des choses par la médiation de la monnaie dans le paiement des sommes dues rappelle celui de la métempsycose (migration de l'âme) utilisée pour conceptualiser le fondement de la Couronne médiévale, le don de Dieu qui sacrait la continuité des règnes successifs d'une lignée héréditaire de régents. À cette époque, on conceptualisait la continuité historique d'un peuple par les deux corps du roi; sa nature cumulait à la fois celle d'un individu et celle de l'ensemble des individus soumis à son règne. Unique entre tous, on considérait que l'un des individus était un ensemble d'un. Cette attitude platonique était crue nécessaire en droit public pour résoudre la difficulté conceptuelle de la continuité historique d'une communauté en dépit de la nature temporelle de ses membres; elle recevait son écho en droit privé. La thèse unitaire du paiement d'obligations - où, tout comme en économique, la capacité de permutation de biens est elle-même considérée être un bien ordinaire - semble reposer sur cette même conception d'une nécessaire nature double. Dans l'univers des prestations, selon la doctrine, un ensemble infini de valeurs successives formées sur une période de temps indéfinie est considéré être fondé sur un objet transcendant qui cumule les faces opposées d'une dualité: à la fois somme (d'argent) et chose, à la fois droit et fait accompli en exécution d'une obligation, à la fois fait et valeur future. Ce paradigme traditionnel est indifférent à la dualité des prestations: non pécuniaire et pécuniaire. TI y arrive en substantivant la non-existence d'une somme. L'explication proposée ici en est une de structure. L'univers des prestations serait plutôt une dichotomie de deux dualités distinctes: 10 une dualité catégorique, celle de l'exécution de prestations particulières - où avoir fait quelque chose et ne pas l'avoir fait sont des action et abstention caractérisées, et 20 une dualité modale (circulaire), devoir un montant libellé en iv-a devise ou (exclusivement) ne pas le devoir, l'avoir payé ou non. L'obligation de livrer une prestation caractérisée à quelqu'un est appariée à la somme d'argent due par ce dernier en contrepartie de cela; on alterne d'une obligation non pécuniaire à la promesse de payer un montant d'argent sans que quiconque puisse cumuler le beurre et l'argent du beurre à un instant donné. Mais encore, une somme due en suit une autre au travers de la monnaie, cette dernière étant toujours le revers de la somme due. Il n'est pas nécessaire de dire que la monnaie existe, ni de dire qu'elle n'existe pas; il suffit de dire qu'elle éteint la somme due. Non seulement la somme due - versée (renversée) en monnaie - est éteinte, mais encore par le nominalisme elle peut toujours acquitter de nouveau une somme d'autant; il suffit qu'un créancier accepte qu'on la lui doive plutôt que de s'en remettre au troc de choses existantes. Cette nouvelle perspective du paiement des obligations distingue deux types de raisonnements. La vérification catégorique rétrospective d'une exécution en nature survenue se démarque de la modalité où la conséquence juridique de l'extinction d'une somme due se retourne en la possibilité a priori de réitérer cette conséquence encore contre une somme pouvant pourtant n'être pas encore déterminée. La possibilité d'une continuité historique n'a pas la nature finie d'un fait. L'objet qu'est la monnaie déborde de la notion ordinaire d'objet puisqu'il est circulaire: la 'monnaie' est "éteindre une somme (due) puis (est encore) monnaie". Dans la lignée héréditaire des sommes, constituées pour être éteintes, éteintes pour être constituées, la monnaie est ni le prédécesseur, ni un successeur particulier; elle est la fonction qui ouvre continuellement l'éventualité d'autres successeurs. La monnaie est une abstraction et sa nature unique est confirmée au Canada depuis 1967. Une fois la convertibilité du papier-monnaie abandonnée, la monnaie n'est plus une promesse de payer: la banque centrale n'est plus tenue de délivrer l'or à la demande du porteur, ni d'échanger le billet de banque en billets du Dominion. Le papiermonnaie est, depuis, trivialement remplacé seulement par du papier-monnaie. Enfin, l'abstraction monétaire donne à la banque centrale une personnalité morale inédite. Si la Couronne est créancière des uns et débitrice aux autres, alors en contraste la banque centrale qui n'est pas une banque - est ni créancière, ni débitrice du papier-monnaie. La problématique de l'inclusion de la monnaie dans les catégories traditionnelles du droit a une solution inédite. La monnaie s'offre en complément des concepts du discours juridique. L'encaissement d'une somme due emporte comme conséquence la fin de son terme, mais encore il en appelle à nouveau une autre, éventuellement. Ainsi, la monnaie est le bain de renouvellement des sommes. Sa qualification ni ... ni... louvoie entre les deux termes en les niant alternativement. / This series of essays analyses the concept of money in the law, seeking to isolate its unique and highly abstract nature. Traditionallaw teaching characterizes money both as a fact and as a right premised as it is on the idea that common nouns like 'money' must have substantive meaning; it is thereby unable to accept that money, by virtue of its unique place amongst the categories of private law, is the mechanism supposing the indeterminate future by embedding the present into it. The difficulty with money is that, as a category, it is not included amongst the usual categories ofprivate law. Its abstract character prevents it from being included amongst objects that have extension. Rather money is defined by negation with respect to the usuallegal categories. It is thereby uniquely recognizable. In the subject-object relationship, paid money is obviously not a subject. In its strict meaning, money refers today to paper-money. It is true that the latter does exist physically because it is tangible. But paradoxicalIy, as an object, money is neither a sum owed, nor an obligation in kind, nor a good, nor representing a debt, nor a measurement, nor consumable, nor fungible in the relevant sense ofthose terms. How does one capture the substance of a notion that defies the usual categories of legal discourse? That is the fundamental difficulty of the thesis. The entirely unique way of defining money bears repeating: Cash money is not identical to a sum owed but extinguishes one as it is being paid; conversely, a sum owed is not identical with money received, since when money is paid without obligation, the sum can be recovered as undue (the undue becomes due). The definition ofmoney proceeds by 'corecurrence': it defines something indeterminate, in that one definition refers to the other and vice versa. Its nature stems from its function in the structure of prestations. But the legal scholarship treats it principally as a sum owed, without further distinguishing this type of debt from other prestations. Now, as the performance of an obligation, a sum ofmoney not only as much pays off any amount, due at one time or another, but, because those are paired to obligations in kind as the price owed in consideration ofparticular performances to be accomplished; the cashing of sums of money still conducts the movement of goods among persons. Whence a paradox: A sum of money is destined to circulate precise1y to extinguish sums (due). Legal scholarship generally teaches the thesis of unity of performance of obligations (payment in its broad civillaw meaning): AlI acts accomplished in the performance of obligations in kind and all payments of sums of money are put in the same bag. Now, they are first owed, then received. These operations are said to form a single set. This bag is time itself. 1t is an interpretation of the universe of prestations, more precise1y an interpretation of the notion of universe where the homogeneous actuality of a set excludes to give place to the possibility of future values by contrast to past values. To close the notion of a universe to that of an actual vi set, the trick is to close the duality 'set/member' by replacing the member by the set: one of the objects included in the set must be at once an existing element of the set and be the collection of aIl its elements, constituting thereby the substantive junction underlying this duality. This foundational object is usually called the zero of the set. In the set of performances of obligations (prestations) with which we are dealing here, there must similarly be an element in the nature of both a promise and a fact. That element is money. So money has a dual nature, both concept and referent of the concept. The sum owed is performed in money and, conversely, money is the sum transferred as payment: substituting one definition in the other, the performance of the sum owed is the sum transferred, a formula leading to infinite regression. Who then is the debtor of this sum transferred for as long as money did and will circulate? The conceptual difficulty with money is to understand this metamorphosis, where the performance of a fact in satisfaction of an obligation reveals itselfto be a promise. Why then bother to distinguish a promise from the performance of it? Money cumulates the categorical nature of a physical thing being delivered - in olden days gold, today paper-money - and the nature of a sum owed; this way of thinking would tend to reify debts, to confer them physical existence. Yet to owe money is fundamentally the duration of the term of a relationship between two persons. And to pay money is to put an end to this term. So paradoxically, to express it in a categorical duality, money has duration and at the same time it has none. Such a union of the polar opposites of a duality is not unprecedented. To help the reader realise this, l document how the theme of migration ofpecuniary value ofthings by means ofmoney being given in payment of amounts owed is reminiscent of metempsychosis (migration of the soul) used to conceptualise the foundation of the medieval Crown, the gift ofGod that consecrated the continuity of successive reigns of an hereditary line of regents. At that time, the historical continuity of the people was conceptualised by the King's two bodies: both that of an individual and that of the set of individuals subject to his reign. Unique amongst aIl, one foundational individual was considered to constitute a set of one. This platonic attitude was believed necessary in public law to resolve the conceptual difficulty of the historical continuity of a community despite the temporal nature of its individuals; it was put to similar use in private law with respect to money. The thesis of unity of performance of obligations - where, like in economics, the capacity to exchange goods is considered an ordinary good itself - appears to rely on the same conception of a necessary dual nature. In the universe of prestations, according to traditionallegal scholarship, an infinite set of successive values taking shape over an indefinite period of time is viewed as founded on a transcendental object which cumulates the opposite faces ofa duality: both sum (of money) and thing, both right and act accomplished in the performance of an obligation, both fact and future value. This traditional paradigm disregard the duality of prestations: pecuniary and non-pecuniary. It does so by giving a substantive value to the non vi-a existence of a sumo The explanation proposed here is one of structure. The universe of prestations is rather a dichotomy of two distinct dualities: 10 a categorieal duality, that of the performance of specifie prestations - where to have done something and not to have done it are characterised action and abstention, and 20 a modal (circular) duality: to owe an amount in currency or (exclusively) not to owe it, to have paid it or not. The obligation to deliver a particular performance to someone is paired to the sum of money owed by him in consideration of it; we altemate from nonpecuniary obligation to promises to pay an amount of money without one being able to have his cake and eat it too at any time. But still, one amount owed follow another thru money, money always being the tuming over of the sum owed. We are not obliged to state that money exists, or that it does not; it suffiees to say that it extinguishes the sum owed. Not only is the sum owed extinguished upon money being tumed (paid) in, but by virtue of nominalism it still can extinguish anew a further sum of same amount; it is sufficient that a creditor accept to be owed a sum ofmoney rather than to revert to the barter ofphysical things. This new reading of the payment of obligations draw apart two types of reasoning. The categorieal proof of a past specifie performance is different from the modality where the legal consequence of the extinction of a sum due is tumed over into the a priori possibility to still reiterate that same consequence against a sum that now may not yet be determined. The possibility of an historieal continuity does not have the finite nature of a fact. Money as an object transcends the concept of an ordinary object because it is circular: 'money' is "the end of a sum (owed) and (is still) money". In the hereditary line of sums, created to be extinguished or extinguished to be created, money is neither the predecessor nor a particular successor; it is the function of continuously opening up the possibility of further successors. Money is an abstraction and its unique character is confirmed in Canada since 1967. Once the convertibility of paper-money is dropped, money is no longer a promissory note: no longer does the central bank undertakes to exchange a bank note for gold or Dominion bonds. Paper-money is now trivially replaced only by paper-money. Finally, the abstract character ofmoney gives the central bank an most unusual status as a legal person. If the Crown is creditor of sorne persons and debtor to others, then by contrast the central bank - who is not a bank - is neither creditor, nor debtor ofpaper-money. The problem of fitting money within the traditional categories of the law does have an unexpected ending. Money presents itself as the complement of the concepts oflegal discourse. The cashing in of a sum triggers the end of its term, but still it calls one anew, eventually. So money is the bath of renewal of sums. In being characterised as neither... nor... it hops between the two terms by altematively negating them.

The clinical utility of the Intermediate Category Test, a measure of executive functioning in children 9 to 14 years of age, is currently limited by the availability of only a Total Error score for normative interpretation. The Process Scoring System (PSS) was developed to provide a standardized method of assessing specific processing patterns and problem-solving errors. The purpose of this study was to determine the ability of the PSS scores to discriminate between children with and without suspected executive deficits, thereby providing evidence of criterion-related validity.

The thesis focuses on a chapter from Kant's Critique of Pure Reason, "The Schematism of the Pure Concepts of the Understanding". Kant assumes two independent sources of knowledge, understanding and intuition. These sources need to be overcome, because of their heterogeneity. Schematism is closely related to "The Deduction of the Pure Concepts of the Understanding". That is why the analysis of schemata is preceded by the analysis of this chapter. It shows a more detailed description of a role of intuition with respect to understanding. Firstly, the validity of the categories regarding whatever form of intuition is proved. Secondly, the proof of the validity of the categories regarding specific forms of time and space follows. The chapter on schematism deals with the specific methods by means of which the categories relate to intuition. Kant introduces transcendental schemata bridging the heterogeneity of understanding and intuition. The relation between category and schema is understood as one of analogy. The categories are rules of discursive type of unity of any kind of intuition, whereas schemata are determined as rules of perceptive unity of intuition. Intuition is brought under unity of apperception by means of schemata of imagination. Inseparable part of the thesis is the schematism of...

By extending Husserl’s own historico-critical study to include the conceptual mathematics of more contemporary times – specifically category theory and its emphatic development since the second half of the 20th century – this paper claims that the delineation between mathematics and philosophy must be completely revisited. It will be contended that Husserl’s phenomenological work was very much influenced by the discoveries and limitations of the formal mathematics being developed at Göttingen during his tenure there and that, subsequently, the rôle he envisaged for his material a priori science is heavily dependent upon his conception of the definite manifold. Motivating these contentions is the idea of a mathematics which would go beyond the constraints of formal ontology and subsequently achieve coherence with the full sense of transcendental phenomenology. While this final point will be by no means proven within the confines of this paper it is hoped that the very fact of opening up for the possibility of such an idea will act as a supporting argument to the overriding thesis that the relationship between mathematics and phenomenology must be problematised.

Dans cette thèse, on étudie les propriétés combinatoires, algébriques et analytiques de certains groupes quantiques compacts libres. on prouve au chapitre 2 que les duaux des groupes quantiques de réflexions complexes possèdent, dans la plus part des cas, la propriété d'approximation de Haagerup. au chapitre 3, on décrit les règles de fusion du produit en, couronne libre d'un groupe discret par le groupe quantique des permutations. Pour cela on détermine les espaces d'entrelaceurs entre certaines coreprésentation "basiques" de ces produits en couronnes libres en termes de partitions non croisées décorées par les éléments du groupe. On peut alors identifier les coreprésentations irréductibles et décrire les règles de fusion. On propose ensuite plusieurs applications de ce résultat. On démontre premièrement que les C*-algèbres réduites de ces produits en couronnes libres sont sans la plupart des cas simples et à trace unique. Puis on prouve que les algèbres se von Neumann associées sont des facteurs de type II et que ces facteurs sont pleins. On étend finalement le résultat du chapitre 2, aux produits en couronnes libres des groupes finis par le groupe quantique de permutations. / In this thesis, we study the combinatorial and operator algebraic properties of certain free compact quantum groups. We prove in chapter 2 that the duals of the quantum reflexion groups have, in most cases, the Haagerup property. In chapter 3, we describe the fusion rules of the free wreath product of a discrete group by the quantum permutation group. To do this, we describe the interrwinner spaces berween certain “basic” corepresentations of these free wreath products in terms of non-crossing partitions decorated by the elements of the group . This provides a whole new class of compact quantum groups whose fusions rules are explicitly computed. We give several applications of this result.We prove that, in most cases, the reduced C*-algebras associates with these free wreath products are simple with unique trace. We also prove that the associated II 1 factors are full. To conclude, we extend the result of chapter 2 to the free wreath products of finite groups by the quantum permutation group.

O objetivo desta dissertação de Mestrado é propor a análise do impacto das mudanças tecnológicas na relação entre o capital e o trabalho, especificamente na composição orgânica de ambos, a partir da situação do trabalhador bancário evidenciando a precarização de salários e consequente compressão psicossocial dos trabalhadores desta indústria de serviços, buscando um olhar desta História econômica contemporânea que enxergue as questões políticas e sociais do cotidiano no trabalho qualificado na sociedade informatizada. Para esse intento, veremos a formação do sistema bancário brasileiro, acompanharemos a trajetória do maior banco público brasileiro, o Banco do Brasil, conceituaremos o trabalho imaterial problematizando a apropriação do conhecimento da categoria bancária pelos sistemas informáticos que atendem aos bancos. / The objective of this Master\'s thesis is to propose the analysis of the impact of technological changes on the relation between capital and labor, specifically on the organic composition of both, based on the situation of the banking worker - evidencing the precariousness of wages and consequent psychosocial compression of the workers in this service industry, seeking a look at this contemporary economic history that sees the political and social issues of daily life in the skilled work in the computerized society. For this purpose, we will see the formation of the Brazilian banking system, we will follow the trajectory of the greater Brazilian public bank, Banco do Brasil, we will conceptualize immaterial work and will problematize the appropriation of knowledge of the banking category by the computer systems that serve the banks.

A Visual Analogue Scale (VAS) e a escala Category-Ratio (CR10) foram aplicadas para mensurar a dor em pacientes com Disfunções Temporomandibulares (DTMs) em dois estudos. No primeiro estudo, em 35 pacientes (Grupo I) foram aplicadas uma versão modificada da escala CR10 em português e a VAS para mensurar a dor espontânea, durante função orofacial e durante palpação antes e após tratamento odontológico. A modificação na CR10 consistiu em um desmembramento das categorias verbais e da escala numérica apresentadas cada uma delas em única coluna em mesma folha. Os coeficientes de correlação de Pearson entre as pontuações da VAS e da CR10 foram 0,85 antes do tratamento odontológico e 0,9 após o tratamento, indicando alta validade de critério. A associação entre os valores numéricos e as categorias verbais da Escala CR10 Modificada mostrou diferenças em relação ao que é proposto na escala original. As categorias: “Moderado", “Forte" e “Muito Forte" foram associadas a valores superiores aos originais. O segundo estudo foi planejado para investigar se essas discrepâncias nas associações das categorias com os seus valores numéricos eram replicáveis e verificar se não dependiam da forma de apresentação da escala CR10 modificada. Para isso, as escalas foram aplicadas para medir dor em duas novas amostras de pacientes com DTMs antes do tratamento odontológico. A CR10 com nova modificação e a VAS foram aplicadas à primeira amostra (Grupo II , n=23 pacientes). A modificação na CR10 consistiu na apresentação primeiro da escala numérica em uma coluna seguida pela apresentação das categorias verbais em três colunas. A CR10 original e a VAS foram aplicadas à segunda amostra (Grupo III, n=17 pacientes). Os coeficientes de correlação de Pearson foram 0,9 para o Grupo II e 0,8 para o Grupo III, indicando também alta validade de critério. Assim como no primeiro estudo, na escala CR10, as categorias verbais: “Moderado", “Forte" e “Muito Forte" foram associadas na escala numérica a valores superiores aos propostos na escala original Em ambos estudos, a escala CR10 foi a mais bem avaliada pelos pacientes, segundo a facilidade de compreensão das instruções e a adequação para o registro da dor. Evidencia-se a necessidade de mais estudos para validar a escala CR10 para a língua portuguesa para determinar com precisão a associação das categorias verbais aos valores numéricos. / Visual Analogue Scale (VAS) and Category-Ratio Scale (CR10) were applied to measure pain in patients with Temporomandibular Disorders (TMDs). In the first study, a modified version of CR10 translated to Portuguese and VAS were applied to measure spontaneous pain, functional pain and pain by touch after and before dentistry treatment in 35 patients (Group I). The CR10 modification consisted of presenting the verbal categories and the numerical scale in separated columns in a sheet. Coefficients of Pearson’s correlation between VAS and CR10 scores were .85 and .90 respectively before and after treatment, indicating a high criterion validation. The association of numerical values and verbal categories of Modified CR10 scale were different from the original CR10. The verbal expressions “moderate", “strong" and “very strong" were attached to higher values. In the second study we investigated if these discrepancies in attaching the verbal categories to the numerical scale were replicable and if they were not an artifact of the way of presenting the modified CR10 scale. To check these topics, the scales were applied to measure pain in two new samples of patients with TMD before dentistry treatment. A new modified version of the CR10 scale and the VAS were applied to the first sample (Group II, n=23 patients). This modification in CR10 scale consisted of presenting first the numerical scale in separate column, and then the verbal categories distributed in three columns. The original CR10 and VAS were applied to the second sample (Group III, n=17 patients). Coefficients of Pearsons correlation between CR10 and VAS were .9 for Group II and .8 for Group III, indicating also high criterion validation. As indicated in the first study, some verbal categories were attached to the numerical scale at higher values than those ones in the original scale. In both studies,, most patients judged the CR10 easier to be understood and more adequate to measure pain than VAS. There is evidence of the necessity of more studies to validate CR10 to Portuguese to determine with precision the association of the verbal categories to the numeric values.

O objetivo geral deste estudo foi escalonar os diferentes tipos de dor, comparativamente entre si, por meio de diferentes métodos psicofísicos e diferentes amostras. Os objetivos específicos foram: comparar o escalonamento dos diferentes tipos de dor entre as diferentes amostras; comparar as escalas derivadas de julgamentos ordinais com as escalas derivadas dos julgamentos de razão; verificar por meio da comparação entre as estimativas de magnitudes e as estimativas de categorias se o contínuo intensidade de dor tem características protéticas ou metatéticas; verificar se a variabilidade das estimativas de magnitudes, de categorias e de comprimento de linhas, é uma função linear das médias geométricas dessas estimativas, ou seja, seguem a Lei de Ekman; validar a escala de razão derivada para o contínuo não métrico de intensidade dos diferentes tipos de dor por meio do método de emparelhamento intermodal; verificar se a variabilidade das estimativas de categorias expandidas aumenta linearmente em função do aumento das estimativas de categorias, tal como ocorre com as estimativas de magnitude; verificar se as ordenações dos diferentes tipos de dor derivadas dos respectivos métodos psicofísicos são similares entre si. Para atingir os objetivos foram realizados 3 experimentos, cada experimento utilizou diferentes métodos psicofísicos: Experimento 1 - Comparação entre os métodos psicofísicos escalares de estimação de magnitude, estimação de categorias e estimação de postos; Experimento 2 - Validação da escala de razão dos diferentes tipos de dor por meio do método de estimação de magnitude e de emparelhamento intermodal com a modalidade de resposta comprimento de linhas; Experimento 3 - Comparação entre os métodos psicofísicos escalares de estimação de magnitude e estimação de categorias expandidas. Participaram do estudo 90 pacientes ambulatoriais de diferentes clínicas, 90 médicos e 90 enfermeiros, sendo 30 de cada grupo que participaram de cada Experimento. Os participantes avaliaram, de acordo com cada método psicofísico, o grau de intensidade de dor, comparativamente entre 20 diferentes tipos de dor. Os resultados foram: 1)A Dor no Câncer, a Dor por Infarto do Miocárdio, a Dor por Cólica Renal, a Dor por Queimadura e a Dor no Parto foram considerados os tipos de dor de maior intensidade, independente do método psicofísico utilizado ou da amostra estudada; 2) Há divergências na percepção das intensidades de alguns tipos de dor, estas divergências foram observadas principalmente entre profissionais e pacientes (médicos-pacientes, enfermeiros-pacientes); 3)As ordenações de posições da intensidade dos diferentes tipos de dor, comparando os diferentes métodos psicofísicos utilizados, resultaram em níveis de concordância significativa; 4)O contínuo não métrico de intensidade dos diferentes tipos de dor, possui características protéticas, ou seja, a percepção da intensidade de um tipo de dor aumenta à medida que se percebe esta com maior intensidade; 5)A variabilidade das respostas dos sujeitos (estimação de magnitudes) foi maior quanto mais intenso foram julgados os diferentes tipos de dor, ou seja, segue a Lei de Ekman; 6)A relação entre as estimativas de magnitudes e as estimativas de emparelhamento de comprimento de linhas é uma função de potência e a escala dos diferentes tipos de dor é válida, estável e consistente. / The general aim of this study was to scale the different types of pain comparatively, by means of various psychophysical methods and different samples. The specific aims were: to compare the scaling of the different types of pain between the different samples; to compare the derived scales of ordinal judgments with the derived scales of ratio judgments; to verify them by comparing between the magnitude estimates and the category estimates whether the continual pain intensity had prothetic or metathetic characteristics; to verify the variability of the magnitude estimates, line-length categories and the linear functions of the geometric means of these estimates, or rather, according to Ekman\'s Law; to validate the ratio scale derived from the non-metric continual of the different types of pain intensities by means of the cross-modal matching; to verify whether the variability of the expanded category estimates increases linearly in function of the increase of the category estimates, as it occurs with the magnitude estimates; to verify whether the rank order of the different types of pain derived from the respective psychophysical methods are similar to each other. In order to achieve these goals three experiments were performed, each utilizing different psychophysical methods: Experiment 1 - Comparison among the psychophysical scaling methods of magnitude estimations, category estimations and rank order estimations; Experiment 2 - The ratio scale validation for the different types of pain utilizing line-lengths response modality; Experiment 3 - A comparison between the psychophysical scaling methods of magnitude estimations and expanded category estimations. The study was comprised of 90 outpatients from various specialty clinics, 90 physicians and 90 nurses, in which there were 30 subjects in each group for each of the experiments. The participants assessed the degree of pain intensity among the 20 different types according to each psychophysical method. The results were: 1) A Cancer Pain, Myocardium Infarct Pain, Renal Colic, Burn Injury Pain, and Childbirth Labor Pain were regarded as the pains of greater intensity, regardless of the psychophysical method utilized or the studied sample; 2) it has divergences in the perception of the intensities of some types of pain, these divergences had been mainly evidenced between professionals and patients (doctors-patients, nurses-patients); 3)A the rank order of pain intensity for the different types of pain, comparing the different psychophysical methods used resulted in levels of significant concordance; 4) A the non-metric continual of the pain intensity for the different types possesses prothetic characteristics, that is, the perception of one type of pain intensity increases as it is perceived with greater intensity; 5) A the variability of the subjects\' responses (magnitude estimations) was greater, the more the different types of pain were judged, or rather, it fallows Ekman\'s Law; 6) A the relation between the magnitude estimates and the cross modal matching estimates of the line-lengths is a power function, and the scale for the different types of pain is valid, stable and consistent.