Dissertations / Theses on the topic 'Logical category'

Cette thèse porte sur le rôle du contenu conceptuel dans l'inférence et le raisonnement. Les deux premiers chapitres offrent une analyse critique de la "thèse formaliste", i.e., l'idée selon laquelle l'inférence rationnelle est un mécanisme qui applique des règles syntaxiques à des pensées avec structure linguistique. Le Chapitre 3 porte sur la relation entre l'inférence et la représentation. Il est avancé que l'inférence doit être étudiée depuis une perspective pluraliste en raison de sa dépendance à l'égard de différents formats de représentation des informations qui caractérisent la cognition humaine. Les quatre chapitres suivants sont ceux de la mise en œuvre de la théorie des espaces conceptuels à trois types d'inférence basés sur des concepts. Tout d'abord, une explication formelle de la notion d'inférence matérielle chez Wilfrid Sellars est avancée. Ensuite, le modèle est étendu pour saisir l’inférence non monotone en étudiant le rôle des "attentes" (expectations) dans le raisonnement. Enfin, un nouveau modèle mathématique d'induction avec des concepts (category-based induction) est présenté. Il est indiqué que la fécondité explicative de cette approche novatrice montre l'échec de la thèse formaliste et appelle le développement d’un modèle unifié d'inférence rationnelle centré sur la sémantique. Le dernier chapitre de la thèse porte sur la manière dont l'inférence et les concepts interagissent dans le raisonnement scientifique, qui fait constamment appel à des structures symboliques hybrides pour représenter les informations conceptuelles<br>This thesis focuses on the role of conceptual content in inference and reasoning. The first two chapters offer a critical analysis of the " formalist thesis ", i.e., the idea that rational inference is a mechanism that applies syntactic rules to propositionally-structured thoughts. Chapter 3 deals with the relationship between inference and representation. It is argued that inference must be studied from a pluralistic perspective because of its dependence on different formats representation in which conceptual information can be encoded. The next four chapters apply Peter Gärdenfors’ theory of conceptual spaces to three types of concept-based inference. First, an explication of Wilfrid Sellars' notion of material inference is advanced. Second, the model is extended to capture non-monotonic inference by studying the role of "expectations" in reasoning. Finally, a new mathematical model of category-based induction is presented. It is argued that the explanatory fruitfulness of the conceptual spaces-approach shows the failure of the formalistic thesis and calls for a unified model of rational inference centered on semantics. The last chapter of the thesis focuses on how inference and concepts interact in scientific reasoning, which constantly uses hybrid symbolic structures to represent conceptual information

Il rapporto del giovane Heidegger con Duns Scoto viene analizzato con particolare riferimento alla tesi del 1916 "La dottrina delle categorie e del significato in Duns Scoto". Il pensatore scolastico viene indicato come fonte di primaria importanza per lo sviluppo dell'ontologia heideggeriana matura attraverso alcuni elementi chiave: l'univocità del concetto di essere, la razionalità di principio dell'individuo, la ricerca di un linguaggio descrittivo adatto alla filosofia. Carl Braig risulta uno degli autori il cui contributo determinò maggiormente in Heidegger l'interesse per i problemi dell'ontologia scotista.<br>The young Heidegger’s relationship to Duns Scotus is analysed with particular reference to the thesis on “Duns Scotus’s Doctrine of Categories and Meaning” (1916). The scholastic thinker is shown to be a source of primary importance for Heidegger’s mature ontology by the means of some key features: the univocity of the concept of Being, the basic intelligibility of the individual, the search for a descriptive language suitable for philosophy. Carl Braig turns out to be one of the authors who contributed the most to determine Heidegger’s interest in the problems of scotist ontology.

Il rapporto del giovane Heidegger con Duns Scoto viene analizzato con particolare riferimento alla tesi del 1916 "La dottrina delle categorie e del significato in Duns Scoto". Il pensatore scolastico viene indicato come fonte di primaria importanza per lo sviluppo dell'ontologia heideggeriana matura attraverso alcuni elementi chiave: l'univocità del concetto di essere, la razionalità di principio dell'individuo, la ricerca di un linguaggio descrittivo adatto alla filosofia. Carl Braig risulta uno degli autori il cui contributo determinò maggiormente in Heidegger l'interesse per i problemi dell'ontologia scotista.<br>The young Heidegger’s relationship to Duns Scotus is analysed with particular reference to the thesis on “Duns Scotus’s Doctrine of Categories and Meaning” (1916). The scholastic thinker is shown to be a source of primary importance for Heidegger’s mature ontology by the means of some key features: the univocity of the concept of Being, the basic intelligibility of the individual, the search for a descriptive language suitable for philosophy. Carl Braig turns out to be one of the authors who contributed the most to determine Heidegger’s interest in the problems of scotist ontology.

We investigate categorical models of the unit-free multiplicative and multiplicative-additive fragments of linear logic by representing derivations as particular structures known as dinatural transformations. Suitable categories are considered to satisfy a property known as full completeness if all such entities are the interpretation of a correct derivation. It is demonstrated that certain Hyland-Schalk double glueings [HS03] are capable of transforming large numbers of degenerate models into more accurate ones. Compact closed categories with finite biproducts possess enough structure that their morphisms can be described as forms of linear arrays. We introduce the notion of an extended tensor (or ‘extensor’) over arbitrary semirings, and show that they uniquely describe arrows between objects generated freely from the tensor unit in such categories. It is made evident that the concept may be extended yet further to provide meaningful decompositions of more general arrows. We demonstrate how the calculus of extensors makes it possible to examine the combinatorics of certain double glueing constructions. From this we show that the Hyland-Tan version [Tan97], when applied to compact closed categories satisfying a far weaker version of full completeness, produces genuine fully complete models of unit-free multiplicative linear logic. Research towards the development of a full completeness result for the multiplicative-additive fragment is detailed. The proofs work for categories of finite arrays over certain semirings under both the Hyland-Tan and Schalk [Sch04] constructions. We offer a possible route to finishing this proof. An interpretation of these results with respect to linear logic proof theory is provided, and possible further research paths and generalisations are discussed.

Dans le dernier siècle, nombreux sciences ont enrichi leur syntaxe pour pouvoir modeler des interactions. Entre eux on peut compter l'informatique, la physique quantique, et aussi la biologie et l’économie : toutes ces sciences sont des exemples de domaines qui ont besoin d'une syntaxe et d'une sémantique soit pour la concurrence que pour la séquentialité.Les diagrammes des cordes sont bien adapté à cet effet. Dans leur syntaxe on peut retrouver deux compositions : une composition parallèle et une composition séquentielle, qui peuvent interagir à travers une loi d'interchange. Si on considère cette loi comme une égalité, les diagrammes de cordes sont une syntaxe pour les catégories monoidales strictes, avec une représentation graphique plus intuitive que les formules algébriques traditionnelles.Dans cette thèse, on étude cette syntaxe de dimension 2 et sa sémantique. On considéré la réécriture des diagrammes et on donne des applications de cet méthode :- une preuve détaillée du théorème de cohérence de MacLanes pour les catégories monoidales symétriques basée sur un système de réécriture convergent donnée en arXiv:1606.01722;;- une interprétation des dérivations de preuves avec les diagrammes de preuve pour le fragment MELL de la logique linéaire, qui capture l’équivalence de preuves. On peut vérifier la séquentialité en temps linéaire, c'est à dire vérifier si un diagramme corresponds à une preuve. Cette interprétation est une extension de celle pour le fragment MLL donnée en arXiv:1606.09016 en donnant aussi un résultat de élimination du coupure<br>In the last century, several sciences enriched their syntax in order to model interactions.Not only computer science and quantum physics, but also biology and economicsare examples of fields requiring syntax and semantics for concurrency as wellas for sequentiality.String diagrams are suitable for that purpose. In that syntax, we have two compositions:the parallel one and the sequential one, which may interact by the interchangerule. If we consider this rule as an equality, string diagrams are a syntax for strictmonoidal categories, with a more intuitive graphical representation than traditionalalgebraic formulas.In this thesis, we study this 2-dimensional syntax and its semantics. We considerdiagram rewriting and we give two applications of those methods:• a detailed proof of Mac Lane’s coherence theorem for symmetric monoidal categoriesbased on convergent diagram rewriting, which is given in arXiv:1606.01722;• an interpretation of proof derivations by string diagrams for the MELL fragmentof linear logic, which captures proof equivalence. We get a linear sequentializabilitytest to verify if a diagram corresponds to a proof . This interpretationextends the one for the MLL fragment given in arXiv:1606.09016,providing also a cut-elimination result

Herein we develop category-theoretic tools for understanding network-style diagrammatic languages. The archetypal network-style diagrammatic language is that of electric circuits; other examples include signal flow graphs, Markov processes, automata, Petri nets, chemical reaction networks, and so on. The key feature is that the language is comprised of a number of components with multiple (input/output) terminals, each possibly labelled with some type, that may then be connected together along these terminals to form a larger network. The components form hyperedges between labelled vertices, and so a diagram in this language forms a hypergraph. We formalise the compositional structure by introducing the notion of a hypergraph category. Network-style diagrammatic languages and their semantics thus form hypergraph categories, and semantic interpretation gives a hypergraph functor. The first part of this thesis develops the theory of hypergraph categories. In particular, we introduce the tools of decorated cospans and corelations. Decorated cospans allow straightforward construction of hypergraph categories from diagrammatic languages: the inputs, outputs, and their composition are modelled by the cospans, while the 'decorations' specify the components themselves. Not all hypergraph categories can be constructed, however, through decorated cospans. Decorated corelations are a more powerful version that permits construction of all hypergraph categories and hypergraph functors. These are often useful for constructing the semantic categories of diagrammatic languages and functors from diagrams to the semantics. To illustrate these principles, the second part of this thesis details applications to linear time-invariant dynamical systems and passive linear networks.

Intensionality is a phenomenon that occurs in logic and computation. In the most general sense, a function is intensional if it operates at a level finer than (extensional) equality. This is a familiar setting for computer scientists, who often study different programs or processes that are interchangeable, i.e. extensionally equal, even though they are not implemented in the same way, so intensionally distinct. Concomitant with intensionality is the phenomenon of intensional recursion, which refers to the ability of a program to have access to its own code. In computability theory, intensional recursion is enabled by Kleene's Second Recursion Theorem. This thesis is concerned with the crafting of a logical toolkit through which these phenomena can be studied. Our main contribution is a framework in which mathematical and computational constructions can be considered either extensionally, i.e. as abstract values, or intensionally, i.e. as fine-grained descriptions of their construction. Once this is achieved, it may be used to analyse intensional recursion. To begin, we turn to type theory. We construct a modal &lambda;-calculus, called Intensional PCF, which supports non-functional operations at modal types. Moreover, by adding Löb's rule from provability logic to the calculus, we obtain a type-theoretic interpretation of intensional recursion. The combination of these two features is shown to be consistent through a confluence argument. Following that, we begin searching for a semantics for Intensional PCF. We argue that 1-category theory is not sufficient, and propose the use of P-categories instead. On top of this setting we introduce exposures, which are P-categorical structures that function as abstractions of well-behaved intensional devices. We produce three examples of these structures, based on Gödel numberings on Peano arithmetic, realizability theory, and homological algebra. The language of exposures leads us to a P-categorical analysis of intensional recursion, through the notion of intensional fixed points. This, in turn, leads to abstract analogues of classic intensional results in logic and computability, such as Gödel's Incompleteness Theorem, Tarski's Undefinability Theorem, and Rice's Theorem. We are thus led to the conclusion that exposures are a useful framework, which we propose as a solid basis for a theory of intensionality. In the final chapters of the thesis we employ exposures to endow Intensional PCF with an appropriate semantics. It transpires that, when interpreted in the P-category of assemblies on the PCA K1, the Löb rule can be interpreted as the type of Kleene's Second Recursion Theorem.

Traditional recursion theory is the study of computable functions on the natural numbers. This thesis considers recursion theory in first-order arithmetical theories and categories, thus expanding the work of Ritchie and Young, Lambek, Scott, and Hofstra. We give a complete characterisation of the representability of computable functions in arithmetical theories, paying attention to the differences between intuitionistic and classical theories and between theories with and without induction. When considering recursion theory from a category-theoretic perspective, we examine syntactic categories of arithmetical theories. In this setting, we construct a strong parameterised natural numbers object and give necessary and sufficient conditions to construct a Turing category associated to an intuitionistic arithmetical theory with induction.

Introduced by C.C. Chang in the 1950s, MV algebras are to many-valued (Łukasiewicz) logics what boolean algebras are to two-valued logic. More recently, effect algebras were introduced by physicists to describe quantum logic. In this thesis, we begin by investigating how these two structures, introduced decades apart for wildly different reasons, are intimately related in a mathematically precise way. We survey some connections between MV/effect algebras and more traditional algebraic structures. Then, we look at the categorical structure of effect algebras in depth, and in particular see how the partiality of their operations cause things to be vastly more complicated than their totally defined classical analogues. In the final chapter, we discuss coordinatization of MV algebras and prove some new theorems and construct some new concrete examples, connecting these structures up (requiring a detour through effect algebras!) to boolean inverse semigroups.

Les questions <EM>"Qu'est-ce qu'une preuve?"</EM> et <EM>"Quand deux preuves sont-elles identiques?"</EM> sont fondamentales pour la théorie de la preuve. Mais pour la logique classique propositionnelle --- la logique la plus répandue --- nous n'avons pas encore de réponse satisfaisante. C'est embarrassant non seulement pour la théorie de la preuve, mais aussi pour l'informatique, où la logique classique joue un rôle majeur dans le raisonnement automatique et dans la programmation logique. De même, l'architecture des processeurs est fondée sur la logique classique. Tous les domaines dans lesquels la recherche de preuve est employée peuvent bénéficier d'une meilleure compréhension de la notion de preuve en logique classique, et le célèbre problème NP-vs-coNP peut être réduit à la question de savoir s'il existe une preuve courte (c'est-à-dire, de taille polynomiale) pour chaque tautologie booléenne. Normalement, les preuves sont étudiées comme des objets syntaxiques au sein de systèmes déductifs (par exemple, les tableaux, le calcul des séquents, la résolution, ...). Ici, nous prenons le point de vue que ces objets syntaxiques (également connus sous le nom d'arbres de preuve) doivent être considérés comme des représentations concrètes des objets abstraits que sont les preuves, et qu'un tel objet abstrait peut être représenté par un arbre en résolution ou dans le calcul des séquents. Le thème principal de ce travail est d'améliorer notre compréhension des objets abstraits que sont les preuves, et cela se fera sous trois angles différents, étudiés dans les trois parties de ce mémoire: l'algèbre abstraite (chapitre 2), la combinatoire (chapitres 3 et 4), et la complexité (chapitre 5).

This thesis studies some constructions for building new models of Martin-Löf type theory out of old. We refer to the main techniques as gluing and idempotent splitting. For each we give general conditions under which type constructors exist in the resulting model. These techniques are used to construct some examples of Dialectica models of type theory. The name is chosen by analogy with de Paiva's Dialectica categories, which semantically embody Gödel's Dialectica functional interpretation and its variants. This continues a programme initiated by von Glehn with the construction of the polynomial model of type theory. We complete the analogy between this model and Gödel's original Dialectica by using our techniques to construct a two-level version of this model, equipping the original objects with an extra layer of predicates. In order to do this we have to carefully build up the theory of finite sum types in a display map category. We construct two other notable models. The first is a model analogous to the Diller-Nahm variant, which requires a detailed study of biproducts in categories of algebras. To make clear the generalization from the categories studied by de Paiva, we illustrate the construction of the Diller-Nahm category in terms of gluing an indexed system of types together with a system of predicates. Following this we develop the general techniques needed for the type-theoretic case. The second notable model is analogous to the Dialectica category associated to the error monad as studied by Biering. This model has only weak dependent products. In order to get a model with full dependent products we use the idempotent splitting construction, which generalizes the Karoubi envelope of a category. Making sense of the Karoubi envelope in the type-theoretic case requires us to face up to issues of coherence in our models. We choose the route of making sure all of the constructions we use preserve strict coherence, rather than applying a general coherence theorem to produce a strict model afterwards. Our chosen method preserves more detailed information in the final model.

We study three category-theoretic types in the context of functional query languages (typed lambda-calculi extended with additional operations for bulk data processing). The types we study are:<br>Engineering and Applied Sciences

This thesis consists of four papers about the intersection between semigroup theory, category theory and representation theory. We say that a representation of a semigroup by a matrix semigroup is effective if it is injective and define the effective dimension of a semigroup S as the minimal n such that S has an effective representation by square matrices of size n. A multisemigroup is a generalization of a semigroup where the multiplication is set-valued, but still associative. A 2-category consists of objects, 1-morphisms and 2-morphisms. A finitary 2-category has finite dimensional vector spaces as objects and linear maps as morphisms. This setting permits the notion of indecomposable 1-morphisms, which turn out to form a multisemigroup. Paper I computes the effective dimension Hecke-Kiselman monoids of type A. Hecke-Kiselman monoids are defined by generators and relations, where the generators are vertices and the relations depend on arrows in a given quiver. Paper II computes the effective dimension of path semigroups and truncated path semigroups. A path semigroup is defined as the set of all paths in a quiver, with concatenation as multiplication. It is said to be truncated if we introduce the relation that all paths of length N are zero. Paper III defines the notion of a multisemigroup with multiplicities and discusses how it better captures the structure of a 2-category, compared to a multisemigroup (without multiplicities). Paper IV gives an example of a family of 2-categories in which the multisemigroup with multiplicities is not a semigroup, but where the multiplicities are either 0 or 1. We describe these multisemigroups combinatorially.

In this licentiate thesis we present a proof of the initiality conjecture for Martin-Löf’s type theory with 0, 1, N, A+B, ∏AB, ∑AB, IdA(u,v), countable hierarchy of universes (Ui)iєN closed under these type constructors and with type of elements (ELi(a))iєN. We employ the categorical semantics of contextual categories. The proof is based on a formalization in the proof assistant Agda done by Guillaume Brunerie and the author. This work was part of a joint project with Peter LeFanu Lumsdaine and Anders Mörtberg, who are developing a separate formalization of this conjecture with respect to categories with attributes and using the proof assistant Coq over the UniMath library instead. Results from this project are planned to be published in the future. We start by carefully setting up the syntax and rules for the dependent type theory in question followed by an introduction to contextual categories. We then define the partial interpretation of raw syntax into a contextual category and we prove that this interpretation is total on well-formed input. By doing so, we define a functor from the term model, which is built out of the syntax, into any contextual category and we show that any two such functors are equal. This establishes that the term model is initial among contextual categories. At the end we discuss details of the formalization and future directions for research. In particular, we discuss a memory issue that arose in type checking the formalization and how it was resolved.<br><p>Licentiate defense over Zoom.</p>

In thinking about quantum causality one would like to approach rigorous QFT from outside the perspective of QFT, which one expects to recover only in a specific physical domain of quantum gravity. This thesis considers issues in causality using Category Theory, and their application to field theoretic observables. It appears that an abstract categorical Machian principle of duality for a ribbon graph calculus has the potential to incorporate the recent calculation of particle rest masses by Brannen, as well as the Bilson-Thompson characterisation of the particles of the Standard Model. This thesis shows how Veneziano n point functions may be recovered in such a framework, using cohomological techniques inspired by twistor theory and recent MHV techniques. This distinct approach fits into a rich framework of higher operads, leaving room for a generalisation to other physical amplitudes. The utility of operads raises the question of a categorical description for the underlying physical logic. We need to consider quantum analogues of a topos. Grothendieck's concept of a topos is a genuine extension of the notion of a space that incorporates a logic internal to itself. Conventional quantum logic has yet to be put into a form of equal utility, although its logic has been formulated in category theoretic terms. Axioms for a quantum topos are given in this thesis, in terms of braided monoidal categories. The associated logic is analysed and, in particular, elements of linear vector space logic are shown to be recovered. The usefulness of doing so for ordinary quantum computation was made apparent recently by Coecke et al. Vector spaces underly every notion of algebra, and a new perspective on it is therefore useful. The concept of state vector is also readdressed in the language of tricategories.

Made available in DSpace on 2015-05-14T12:11:59Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 891353 bytes, checksum: 2d056c7f53fdfb7c20586b64874e848d (MD5) Previous issue date: 2010-12-01<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>The basic concepts of what later became called category theory were introduced in 1945 by Samuel Eilenberg and Saunders Mac Lane. In 1940s, the main applications were originally in the fields of algebraic topology and algebraic abstract. During the 1950s and 1960s, this theory became an important conceptual framework in other many areas of mathematical research, especially in algrebraic homology and algebraic geometry, as shows the works of Daniel M. Kan (1958) and Alexander Grothendieck (1957). Late, questions mathematiclogics about the category theory appears, in particularly, with the publication of the Functorial Semantics of Algebraic Theories (1963) of Francis Willian Lawvere. After, other works are done in the category logic, such as the the current Makkai (1977), Borceux (1994), Goldblatt (2006), and others. As introduction of application of the category theory in logic, this work presents a study on the logic category propositional. The first section of this work, shows to the reader the important concepts to a better understanding of subject: (a) basic components of category theory: categorical constructions, definitions, axiomatic, applications, authors, etc.; (b) certain structures of abstract algebra: monoids, groups, Boolean algebras, etc.; (c) some concepts of mathematical logic: pre-order, partial orderind, equivalence relation, Lindenbaum algebra, etc. The second section, it talk about the properties, structures and relations of category propositional logic. In that section, we interpret the logical connectives of the negation, conjunction, disjunction and implication, as well the Boolean connectives of complement, intersection and union, in the categorical language. Finally, we define a categorical boolean propositional semantics through a Boolean category algebra.<br>Os conceitos básicos do que mais tarde seria chamado de teoria das categorias são introduzidos no artigo General Theory of Natural Equivalences (1945) de Samuel Eilenberg e Saunders Mac Lane. Já em meados da década de 1940, esta teoria é aplicada com sucesso ao campo da topologia. Ao longo das décadas de 1950 e 1960, a teoria das categorias ostenta importantes mudanças ao enfoque tradicional de diversas áreas da matemática, entre as quais, em especial, a álgebra geométrica e a álgebra homológica, como atestam os pioneiros trabalhos de Daniel M. Kan (1958) e Alexander Grothendieck (1957). Mais tarde, questões lógico-matemáticas emergem em meio a essa teoria, em particular, com a publica ção da Functorial Semantics of Algebraic Theories (1963) de Francis Willian Lawvere. Desde então, diversos outros trabalhos vêm sendo realizados em lógica categórica, como os mais recentes Makkai (1977), Borceux (1994), Goldblatt (2006), entre outros. Como inicialização à aplicação da teoria das categorias à lógica, a presente dissertação aduz um estudo introdutório à lógica proposicional categórica. Em linhas gerais, a primeira parte deste trabalho procura familiarizar o leitor com os conceitos básicos à pesquisa do tema: (a) elementos constitutivos da teoria das categorias : axiomática, construções, aplicações, autores, etc.; (b) algumas estruturas da álgebra abstrata: monóides, grupos, álgebra de Boole, etc.; (c) determinados conceitos da lógica matemática: pré-ordem; ordem parcial; equivalência, álgebra de Lindenbaum, etc. A segunda parte, trata da aproximação da teoria das categorias à lógica proposicional, isto é, investiga as propriedades, estruturas e relações próprias à lógica proposicional categórica. Nesta passagem, há uma reinterpreta ção dos conectivos lógicos da negação, conjunção, disjunção e implicação, bem como dos conectivos booleanos de complemento, interseção e união, em termos categóricos. Na seqüência, estas novas concepções permitem enunciar uma álgebra booleana categórica, por meio da qual, ao final, é construída uma semântica proposicional booleana categórica.

This thesis studies the categorical formalisation of quantum computing, through the prism of type theory, in a three-tier process. The first stage of our investigation involves the creation of the dagger lambda calculus, a lambda calculus for dagger compact categories. Our second contribution lifts the expressive power of the dagger lambda calculus, to that of a quantum programming language, by adding classical control in the form of complementary classical structures and dualisers. Finally, our third contribution demonstrates how our lambda calculus can be applied to various well known problems in quantum computation: Quantum Key Distribution, the quantum Fourier transform, and the teleportation protocol.

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.

Orientadores: Marcelo Esteban Coniglio, Carlos Caleiro<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciencias Humanas<br>Made available in DSpace on 2018-08-04T00:28:23Z (GMT). No. of bitstreams: 1 Bueno-Soler_Juliana_M.pdf: 944055 bytes, checksum: 560404307eedeebf3b45f7ca82f30d78 (MD5) Previous issue date: 2004<br>Mestrado<br>Filosofia<br>Mestre em Filosofia

Cette thèse étudie la cohérence c. -à-d. L'égalité de morphismes canoniques dans les catégories monoïdales symétriques fermée (smcc) libres et non libres, via la théorie de la preuve de la logique linéaire multiplicative intuitionniste (imll) avec unité. L'étude de la cohérence dans les modèles non libres est réduite à l'étude d'équivalences de termes de la catégorie libre, plus fortes que l'équivalence induite par la structure de smcc libre. La catégorie libre est reformulée comme le système de séquents d'imll avec unité, de sorte que seules les équivalences de dérivations de ce système sont à considérer. Nous établissons que deux dérivations sans coupure sont équivalentes relativement à la structure de smcc libre si et seulement si elles sont inter-permutables, et que toute équivalence plus forte est axiomatisée par un ensemble de paires critiques de dérivations. Nous en déduisons l'incomplétude de Post du système d'égalités des smcc et des conditions suffisantes de pleine cohérence<br>This PhD thesis studies coherence, that is the equality of canonical morphisms in free and non free symmetric monoidal closed categories (smcc), using proof theory for intuitionistic multiplicative linear logic (imll) with unit. The study of coherence in non free models is reduced to the study of equivalences of terms of the free category, which are stronger than the equivalence induced by the free smcc structure. The free category is reformulated as the sequent calculus for imll with unit, so that only the equivalences of derivations in this system are to be considered. We establish that two cut-free derivations are equivalent w. R. T. The free smcc structure if and only if they are inter-permutable, and that any stronger equivalence is axiomatized by a set of critical pairs of derivations. From this, we deduce that the system of equalities for smcc is not Post-complete and we also deduce certain sufficient conditions for full coherence

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.

De nombreux domaines comme le jeu vidéo, l’architecture, l’ingénierie ou l’archéologie font désormais appel à la modélisation géométrique. Les objets à représenter sont de natures diverses, et leurs opérations de manipulation sont spécifiques. Ainsi, les modeleurs sont nombreux car tous spécialisés à leur domaine d’application. Or ils sont à la fois chers à développer, souvent peu robustes, et difficilement extensibles. Nous avons proposé dans la thèse l’approche alternative suivante :– fournir un langage dédié à la modélisation qui permet de définir les opérations quelque soit le domaine d’application ; dans ce langage, les objets sont représentés avec le modèle topologique des cartes généralisées, dont nous avons étendu la définition aux plongements ; les opérations sont elles définies par des règles de transformation de graphes, issues de la théorie des catégorie ;– garantir les opérations définies dans le langage à l’aide de conditions de cohérence ; une opération dont la définition vérifie ces conditions ne produit pas d’anomalie ;– développer un noyau de modeleur générique qui interprète ce langage ; les opérations définies sont directement appliquées dans le modeleur, sans implantation dans un langage de programmation ; l’outil assure également la vérification automatique des conditions du langage pour prévenir un utilisateur lorsqu’il propose une opération incohérente.Le langage et le modeleur développés se sont révélés performants à la fois en termes de temps de développement et en termes de temps machine. L’implantation d’une nouvelle opération par une règle ne prend que quelques minutes à l’aide des conditions du langage, au contraire de l’approche classi<br>Geometric modeling is now involved in many fields such as: video games, architecture, engineering and archaeology. The represented objects are very different from one field to another, and so are their modeling operations. Furthermore, many specific types of modeling software are designed for high programing costs, but with a relatively low rate of effectiveness.The following is an alternative approach:– we have conceived a dedicated language for geometric modeling that will allow us to define any operation of any field; objects in this language are defined with the topological model of generalized maps, this definition has been extended to the embedding informations; here the operations are defined as graph transformation rules which originate from the category theory;– we have ensured operation definitions with consistency conditions; these operations that satisfy those conditions do not generate anomalies; – we have designed generic modeling software to serve as an interpreter of this language; the operation definitions are directly applied without the need for more programing; the software also automatically checks the language conditions and warns the user if he designs a non-consistent operation.The provided language and software prove to be efficient, and all for a low programing cost. Designing a new operation takes only minutes thanks to the language conditions, as opposed to hours of programming and debugging with the past approach

Il est bien connu que des constructions théoriques très simples telles que les structures Either (équivalent type théorique de l'opérateur logique "ou"), State (représentant des transformateurs d'état composables), Applicative (application des fonctions généralisée) et Monad (composition de programmes séquentielles généralisée), nommés structures en Haskell, couvrent une grande partie de ce qui est habituellement nécessaire pour exprimer avec élégance la plupart des idiomes informatiques utilisés dans les programmes classiques. Cependant, il est usuellement admis qu'il existe plusieurs classes d'idiomes couramment utilisés qui ne s'intègrent pas bien à ces structures, les exemples les plus remarquables étant les transformations entre arbres (types de données, dont l'utilisation doit s'appuyer soit sur les motifs généralisés soit sur une infrastructure de méta programmation lourde) et traitement des exceptions (qui sont d'habitude supposés nécessiter un langage spécial et une prise en charge de l'exécution). Ce travail a pour but de montrer que beaucoup de ces idiomes peuvent, en fait, être exprimés en réutilisant ces structures bien connues avec des modifications mineures (le cas échéant). En d'autres termes, le but de ce travail est d'appliquer les principes du rasoir KISS (Keep It Stupid Simple) et/ou d'Occam aux structures algébriques utilisées pour résoudre des problèmes de programmation courants. Techniquement parlant, ce travail a pour but de montrer que les généralisations naturelles de classes de types Applicative et Monad de Haskell, associées à la possibilité d'en faire des produits cartésiens, en produisent un cadre commun très simple pour exprimer de nombreuses choses pratiques, dont certaines sont des nouvelles méthodes très commodes pour exprimer des idées de programmation communes, tandis que les autres peuvent être vues comme systèmes d'effets. Sur ce dernier point, si l'on veut généraliser des exemples présentés dans une approche de la conception de systèmes d'effets en général, on peut alors considérer la structure globale de cette approche comme un cadre quasi syntaxique qui permet d'ériger une structure générale du cadre "mariage" au dessus de différents systèmes d'effets adhérant aux principes de base. (Bien que ce travail ne soit pas trop approfondi dans la dernière, car il est principalement motivé par des exemples qui peuvent être immédiatement appliqués à la pratique de Haskell.) Il convient toutefois de noter qu'en fait, ces observations techniques n'ont rien d'étonnant: Applicative et Monad sont respectivement des généralisations de composition fonctionnelle et linéaire des programmes; ainsi, naturellement, les produits cartésiens de ces deux structures doivent couvrir en grande partie ce que les programmes font habituellement<br>It is well-known that very simple theoretic constructs such as Either (type-theoretic equivalent of the logical "or" operator), State (composable state transformers), Applicative (generalized function application), and Monad (generalized sequential program composition) structures (as they are named in Haskell) cover a huge chunk of what is usually needed to elegantly express most computational idioms used in conventional programs. However, it is conventionally argued that there are several classes of commonly used idioms that do not fit well within those structures, the most notable examples being transformations between trees (data types, which are usually argued to require ether generalized pattern matching or heavy metaprogramming infrastructure) and exception handling (which are usually argued to require special language and run-time support). This work aims to show that many of those idioms can, in fact, be expressed by reusing those well-known structures with minor (if any) modifications. In other words, the purpose of this work is to apply the KISS (Keep It Stupid Simple) and/or Occam's razor principles to algebraic structures used to solve common programming problems. Technically speaking, this work aims to show that natural generalizations of Applicative and Monad type classes of Haskell combined with the ability to make Cartesian products of them produce a very simple common framework for expressing many practically useful things, some of the instances of which are very convenient novel ways to express common programming ideas, while others are usually classified as effect systems. On that latter point, if one is to generalize the presented instances into an approach to design of effect systems in general, then the overall structure of such an approach can be thought of as being an almost syntactic framework which allows different effect systems adhering to the general structure of the "marriage" framework to be expressed on top of. (Though, this work does not go into too much into the latter, since this work is mainly motivated by examples that can be immediately applied to Haskell practice.) Note, however, that, after the fact, these technical observation are completely unsurprising: Applicative and Monad are generalizations of functional and linear program compositions respectively, so, naturally, Cartesian products of these two structures ought to cover a lot of what programs usually do

The aim of this dissertation is to develop categorical foundations for studying lambda calculi and their logics formed into logical systems. We show how internal models for polymorphic lambda calculi arise in any 2-category with a notion of discreteness. We generalise to a 2-categorical setting the famous theorem of Peter Freyd saying that there are no sufficiently (co)complete non-degenerate categories. As a simple corollary, we obtain a variant of Freyd theorem for categories internal to any tensored category. We introduce the concept of an associated category, and relying on it, provide a representation theorem relating our internal models with well-studied fibrational models for polymorphism. Finally, we define Yoneda triangles as relativisations of internal adjunctions, and use them to characterise universes that admit a notion of convolution. We show that such universes induce semantics for lambda calculi. We prove that a construction analogical to enriched Day convolution works for categories internal to a locally cartesian closed category with finite colimits.<br>Celem niniejszej rozprawy jest zbudowanie teoriokategoryjnych fundamentów umożliwiających studiowanie rachunków lambda i ich logik opisanych za pomocą systemów logicznych. Pokazujemy w jaki sposób 2-kategorie z notacją dyskretności pozawalają mówić o modelach dla polimorficznych rachunków lambda. Uogólniamy i internalizujemy w 2-kategoriach klasyczne twierdzenia Petera Freyda o nieistnieniu dostatecznie (ko)zupełnych niezdegenerowanych kategorii. Jako prosty wniosek otrzymujemy wariant twierdzenia Freyda dla kategorii wewnętrznych względem dowolnej kategorii z tensorami. Wprowadzamy pojęcie kategorii stowarzyszonej i bazując na nim dowodzimy twierdzenie o reprezentacji wiążące wprowadzone w rozprawie wewnętrzne modele z dobrze znanymi modelami rozwłóknieniowymi dla polimorfizmu. Definiujemy pojęcie trójkąta Yonedy jako relatywizację wewnętrznych sprzężeń i używamy go do charakteryzacji uniwersów posiadających notację splotu. Pokazujemy, że takie uniwersa indukują semantykę dla rachunków lambda. Dowodzimy, że konstrukcja analogiczna do splotu Day'a dla kategorii wzbogacanych strukturą monoidalną zachodzi także dla kategorii wewnętrznych względem dowolnej lokalnie kartezjańsko domkniętej kategorii ze skończonymi kogranicami.

Дисертація присвячена вивченню істотних формальних і змістових проявів поетики оніма в різноманітних комічних контекстах. У роботі на основі дослідження поетики онімів у художній літературі, міському фольклорі, афоризмах та ситуативно-зумовлених висловленнях, що характеризуються безпосереднім зв’язком із комічним як естетичною категорією, виявлено типологічні характеристики та національно зумовлені властивості використаних засобів. У проаналізованих текстах виявлено ознаки змісту, а в смисловій структурі власних імен – семи, які формують семантичну ауру комічного, що постає внаслідок “руйнування” поетонімом породжуваних контекстом сподівань. Результати дослідження узагальнено в спробі таксономії логіко-семантичних моделей комічного та сприйняття гумористичних ефектів, які досягнуто за допомогою власних імен.<br>Диссертация посвящена изучению формальных и содержательных проявлений поэтики онима в разнообразных комических текстах. Сущность комического состоит в его неоднозначности и противоречивости в речевом воплощении. Несмотря на существование определенных традиций, в лингвистическом исследовании комического все еще остаются проблемы, которые либо не имеют однозначного решения, либо освещены недостаточно. Область познания имен, погруженных в комические тексты, представляется весьма перспективной для новых открытий. Универсальные свойства категории комического предопределяют дальнейшее развитие смеховой культуры. Для адекватного понимания глубинной природы комического необходимо последовательно расширять панораму его репрезентации в исследуемом материале: от художественной литературы до городского фольклора, афоризмов и ситуативно-обусловленных высказываний. Данное исследование представляет собой всего лишь первый шаг в указанном направлении. Традиционные классификации приемов и средств создания комического, во-первых, основываются на учете степени участия собственно языковых средств в воплощении комического: создается смешное только с помощью возможностей языка или оно воплощается путем объединения языковых и ситуативных средств, и, во-вторых, рассматривают речевые приемы комического по отношению к тем элементам языка, с помощью которых создается комизм, то есть к определенным пластам языковой системы. В современном языкознании наблюдается тенденция не только не разделять искусственно речевой и ситуативный комизм, но и признавать примат языкового компонента во взаимодействии вербального и иконического рядов. В работах поэтонимологического типа эта традиция сочетается с последовательным учетом того факта, что поэтоним приобретает свойство обусловливать комическое в контексте. Предложенные в диссертации положения представляют один из возможных путей построения таксономии комических эффектов с участием проприальной лексики. В них реализовано стремление к соответствию базовым концепциям истинности познания вообще и научного познания в частности. Они ориентированы на практическую деятельность, связанную с преодолением трудностей квалификации комических эффектов, достигаемых при участии собственных имен. Кроме того, в них в полной мере учтена уже формирующаяся научная традиция. Комическое рождается во взаимодействии поэтонима и контекста особого рода как результат наложения, взаимодействия и сегрегации отдельных сем, накопленных компонентами высказывания. При взаимодействии составных частей контекста также возникает переосмысление и “уплотнение” значений, которые возводятся на качественно другой уровень. При интерпретации комического осуществляется “расчленение” текста, выбор компонентов, взаимодействующих с семантической аурой поэтонимов, сравнение конгенеративного смысла взаимодействия с имеющимся в сознании носителей определенной языковой культуры представлением о “норме” и, в случае уклонения от нормы, поиск смысловой составляющей юмористического, сатирического или комического, в широком смысле слова, эффекта. Для анализа комического, которое проявляется при взаимодействии поэтонима и контекста, на материал исследования экстраполируются методика компонентного анализа лексического значения и теория поэтонимов В. М. Калинкина. В комическом прослеживается столкновение семантических компонентов глубинных понятийных категорий, которые формировались еще в недрах мифопоэтического сознания и могут быть представлены в виде антиномий (возможный – невозможный, свой – чужой, большой – маленький, живой – мертвый, мужской – женский и т. д.). Результаты исследования обобщены в попытке таксономии логико-семантических моделей комического и восприятия юмористических эффектов, достигнутых с помощью имен собственных. Оппозиции, обогащающие оним дополнительными созначениями, можно рассматривать и как проявление поэтонимогенеза, и в общем контексте культуры.<br>The dissertation is devoted to the study of significant formal and semantic manifestations of onym’s poetics in various comic contexts. In the dissertation, based on a study of the onym’s poetics in literature, urban folklore, aphorisms and situation-conditioned statements which are characterized by direct communication with comic as aesthetic category, the typological characteristics and properties used due to national funds are identified. In the studied contexts signs of content are found. The semes that form the semantic aura of comic that apear as a result of “destruction” by poetonyms generated contextual expectations in semantic structure of proper names are inspected. The survey results are summarized in an attempt of taxonomy of logical and semantic models and perception of the comic humorous effects which are achieved with the help of proper names.

Thèse par articles.<br>La présente thèse fait état des avancées en logique déontique et propose des outils formels pertinents à l'analyse de la validité des inférences légales. D'emblée, la logique vise l'abstraction de différentes structures. Lorsqu'appliquée en argumentation, la logique permet de déterminer les conditions de validité des inférences, fournissant ainsi un critère afin de distinguer entre les bons et les mauvais raisonnements. Comme le montre la multitude de paradoxes en logique déontique, la modélisation des inférences normatives fait cependant face à divers problèmes. D'un point de vue historique, ces difficultés ont donné lieu à différents courants au sein de la littérature, dont les plus importants à ce jour sont ceux qui traitent de l'action et ceux qui visent la modélisation des obligations conditionnelles. La présente thèse de doctorat, qui a été rédigée par articles, vise le développement d'outils formels pertinents à l'analyse du discours juridique. En première partie, nous proposons une revue de la littérature complémentaire à ce qui a été entamé dans Peterson (2011). La seconde partie comprend la contribution théorique proposée. Dans un premier temps, il s'agit d'introduire une logique déontique alternative au système standard. Sans prétendre aller au-delà de ses limites, le système standard de logique déontique possède plusieurs lacunes. La première contribution de cette thèse est d'offrir un système comparable répondant au différentes objections pouvant être formulées contre ce dernier. Cela fait l'objet de deux articles, dont le premier introduit le formalisme nécessaire et le second vulgarise les résultats et les adapte aux fins de l'étude des raisonnements normatifs. En second lieu, les différents problèmes auxquels la logique déontique fait face sont abordés selon la perspective de la théorie des catégories. En analysant la syntaxe des différents systèmes à l'aide des catégories monoïdales, il est possible de lier certains de ces problèmes avec des propriétés structurelles spécifiques des logiques utilisées. Ainsi, une lecture catégorique de la logique déontique permet de motiver l'introduction d'une nouvelle approche syntaxique, définie dans le cadre des catégories monoïdales, de façon à pallier les problèmes relatifs à la modélisation des inférences normatives. En plus de proposer une analyse des différentes logiques de l'action selon la théorie des catégories, la présente thèse étudie les problèmes relatifs aux inférences normatives conditionnelles et propose un système déductif typé.<br>The present thesis develops formal tools relevant to the analysis of legal discourse. When applied to legal reasoning, logic can be used to model the structure of legal inferences and, as such, it provides a criterion to discriminate between good and bad reasonings. But using logic to model normative reasoning comes with some problems, as shown by the various paradoxes one finds within the literature. From a historical point of view, these paradoxes lead to the introduction of different approaches, such as the ones that emphasize the notion of action and those that try to model conditional normative reasoning. In the first part of this thesis, we provide a review of the literature, which is complementary to the one we did in Peterson (2011). The second part of the thesis concerns our theoretical contribution. First, we propose a monadic deontic logic as an alternative to the standard system, answering many objections that can be made against it. This system is then adapted to model unconditional normative inferences and test their validity. Second, we propose to look at deontic logic from the proof-theoretical perspective of category theory. We begin by proposing a categorical analysis of action logics and then we show that many problems that arise when trying to model conditional normative reasoning come from the structural properties of the logic we use. As such, we show that modeling normative reasoning within the framework of monoidal categories enables us to answer many objections in favour of dyadic and non-monotonic foundations for deontic logic. Finally, we propose a proper typed deontic system to model legal inferences.

Diese Arbeit beschäftigt sich mit der Speziestheorie aus Mochizukis Beweis(versuch) der abc-Vermutung. Es wird ein Standpunkt eingeführt, der Parallelen zwischen der Kategorientheorie und der Speziestheorie aufzeigt und es werden so die Besonderheiten der Speziestheorie herausgearbeitet. In der Speziestheorie möchte man Konstruktionen ausführen, welche von keinen Auswahlen abhängen. Dieses Problem wird in einem allgemeinen Kontext für universelle Morphismen gelöst. An Beispielen wird die in der Arbeit behandelte Theorie erklärt.

碩士<br>中原大學<br>宗教研究所<br>103<br>Speculative way of recognition could be considered as the ground to understand Hegel’s speculative philosophical system in such a way that Science of Logic has deemed its decisive position and significance among Hegelian studies, especially when the true infinity in the category of Quality is for him the ground-conception of philosophy, so that an investigation on the concept of the qualitative true infinity could ease the comprehension on Hegel’s speculative philosophical system. Meanwhile, logic, according to Hegel, is not merely the determination of nor the form of thought, but it also involved the solution to the metaphysical question, because Science of Logic as the self-exposition of the Absolute, who himself in this spiritual movement gives the determination of his own self, had related both logical and metaphysical problems close to each another. In line with this presupposition, the truthful understanding on Hegel’s concept of qualitative true infinity must not only to be grasped in its immanent movement of concept, that is the immanent movement from the pure being to the infinity, which respectively as the first definition and the new definition of the Absolute, but also to understand further how this movement as the first emergence of the Absolute’s self-exposition is obtained, and the substantial meaning of this movement. Hence, this thesis would address the true infinity in the category of Quality in Science of Logic through textual interpretation within the aforementioned horizon, in order to grasp the substantial significant of his concept of true infinity.

This thesis is about the distributive full Lambek calculus, i.e., intuicionistic logic without the structural rules of exchange, contraction and weakening and particularly about the two semantics of this logic, one of which is algebraic, the other one is a Kripke semantic. The two semantics are treated in separate chapters and some results about them are shown, for example the disjunction property is proven by amalgamation of Kripke models. The core of this thesis is nevertheless the relation of these two semantics, since it is interesting to study what do they have in common and how can they actually differ, both being a semantics of the same logic. We show how to translate frames to algebras and algebras to frames, and, moreover, we extend such translation to morphisms, thus constructing two functors between the two categories. Key words:distributive FL logic, distributive full Lambek calculus, structural rules, distributive residuated lattice, Kripke frames, frame morphisms, category, functor 2

Tesis (Lic. en Ciencias de la Computación)--Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física, 2010.<br>Este trabajo consiste en la implementación de un front-end para un lenguaje de programación Algol-like. El front-end es la primera etapa del proceso de compilación; cuyo objetivo es generar código en un lenguaje intermedio a partir del programa fuente.La generación de código intermedio se realiza a partir de la semántica denotacional del lenguaje, es decir, se elige un modelo que permite pensar las ecuaciones semánticas como traducciones al lenguaje intermedio. El modelo semántico que se elige es una categoría funtorial que permite explicitar en las ecuaciones algunas propiedades deseadas del lenguaje. La implementación se realiza en Agda, un lenguaje funcional con tipos dependientes.

INTRODUZIONE: Il presente progetto di ricerca nasce all’interno di un Dottorato Eureka, sviluppato grazie al contributo della Regione Marche, dell’Università di Macerata e dell’azienda Jobmetoo by Jobdisabili srl, agenzia per il lavoro esclusivamente focalizzata sui lavoratori con disabilità o appartenenti alle categorie protette. Se trovare lavoro è già difficile per molti, per chi ha una disabilità diventa un percorso pieno di ostacoli. Nonostante, infatti, la legge 68/99 abbia una visione tra le più avanzate in Europa, l’Italia è stata ripresa dalla Corte Europea per non rispettare i propri doveri relativamente al collocamento mirato delle persone con disabilità. Tra chi ha una disabilità, la disoccupazione è fra il 50% e il 70% in Europa, con punte dell’80% in Italia. L’attuale strategia europea sulla disabilità 2010-2020 pone come obiettivi fondamentali la lotta alla discriminazione, le pari opportunità e l’inclusione attiva. Per la realizzazione di tali obiettivi assume un’importanza centrale l’orientamento permanente: esso si esercita in forme e modalità diverse a seconda dei bisogni, dei contesti e delle situazioni. La centralità di tutti gli interventi orientativi è il riconoscimento della capacità di autodeterminazione dell’essere umano, che va supportato nel trovare la massima possibilità di manifestarsi e realizzarsi. Ciò vale ancora di più per le persone con disabilità, in quanto risultano fondamentali tutte quelle azioni che consentono loro di raggiungere una consapevolezza delle proprie capacità/abilità accanto al riconoscimento delle caratteristiche della propria disabilità. L’orientamento assume così un valore permanente nella vita di ogni persona, garantendone lo sviluppo e il sostegno nei processi di scelta e di decisione con l’obiettivo di promuovere l’occupazione attiva, la crescita economica e l’inclusione sociale. Oggi giorno il frame work di riferimento concettuale nel campo della disabilità è l’International Classification of Functioning, Disability and Health (ICF), il quale ha portato a un vero e proprio rovesciamento del termine disabilità dal negativo al positivo: non si parla più di impedimenti, disabilità, handicap, ma di funzioni, strutture e attività. In quest’ottica, la disabilità non appare più come mera conseguenza delle condizioni fisiche dell’individuo, ma scaturisce dalla relazione fra l’individuo e le condizioni del mondo esterno. In termini di progetto di vita la sfida della persona con disabilità è quella di poter essere messa nelle condizioni di sperimentarsi come attore della propria esistenza, con il diritto di poter decidere e, quindi, di agire di conseguenza in funzione del proprio benessere e della qualità della propria vita, un una logica di autodeterminazione. OBIETTIVO: Sulla base del background e delle teorie di riferimento analizzate e delle necessità aziendali è stata elaborata la seguente domanda di ricerca: è possibile aumentare la consapevolezza negli/nelle studenti/esse e laureati/e con disabilità che si approcciano al mondo del lavoro, rispetto alle proprie abilità, competenze, risorse, oltre che alle limitazioni imposte dalla propria disabilità? L’obiettivo è quello di sostenere i processi di auto-riflessione sulla propria identità e di valorizzare il ruolo attivo della persona stessa nella sua autodeterminazione, con la finalità ultima di aumentare e migliorare il match tra le persone con disabilità e le imprese. L’auto-riflessione permetterà di facilitare il successivo contatto dialogico con esperti di orientamento e costituirà una competenza che il soggetto porterà comunque come valore aggiunto nel mondo del lavoro. METODI E ATTIVITÀ: Il paradigma teorico-metodologico adottato è un approccio costruttivista: peculiarità di questo metodo è che ciascuna componente della ricerca può essere riconsiderata o modificata nel corso della sua conduzione o come conseguenza di cambiamenti introdotti in qualche altra componente e pertanto il processo è caratterizzato da circolarità; la metodologia e gli strumenti non sono dunque assoggettati alla ricerca ma sono al servizio degli obiettivi di questa. Il primo passo del progetto di ricerca è stato quello di ricostruzione dello stato dell’arte, raccogliendo dati, attraverso la ricerca bibliografica e sitografica su: l’orientamento, la normativa vigente in tema di disabilità, i dati di occupazione/disoccupazione delle persone con disabilità e gli strumenti di accompagnamento al lavoro. A fronte di dati mancanti sul territorio italiano relativi alla carriera e ai fabbisogni lavorativi degli/delle studenti/esse e laureati/e con disabilità, nella prima fase del progetto di ricerca è stata avviata una raccolta dati su scala nazionale, relativa al monitoraggio di carriera degli studenti/laureati con disabilità e all’individuazione dei bisogni connessi al mondo del lavoro. Per la raccolta dati è stato sviluppato un questionario ed è stata richiesta la collaborazione a tutte le Università italiane. Sulla base dei dati ricavati dal questionario, della letteratura e delle indagini esistenti sulle professioni, nella fase successiva della ricerca si è proceduto alla strutturazione di un percorso di auto-orientamento, volto ad aumentare la consapevolezza nelle persone con disabilità delle proprie abilità e risorse, accanto a quella dei propri limiti. In particolare, il punto di partenza per la costruzione del percorso è stata l’Indagine Istat- Isfol sulle professioni (2012) e la teoria delle Intelligenze Multiple di H. Gardner (1983). Si è arrivati così alla strutturazione del percorso di auto-orientamento, composto da una serie di questionari attraverso i quali il candidato è chiamato ad auto-valutare le proprie conoscenze, le competenze, le condizioni di lavoro che gli richiedono più o meno sforzo e le intelligenze che lo caratterizzano, aggiungendo a questi anche una parte più narrativa dove il soggetto è invitato a raccontare i propri punti di forza, debolezza e le proprie aspirazioni in ambito professionale. Per sperimentare il percorso di auto-orientamento creato, nell’ultima fase della ricerca è stato predisposto uno studio pilota per la raccolta di alcuni primi dati qualitativi con target differenti, studenti/esse universitari/e e insegnanti di scuola superiore impegnati nel tema del sostegno e dell’orientamento, e utilizzando diversi strumenti (autopresentazioni, test multidimensionale autostima, focus group). CONCLUSIONI: I dati ottenuti dallo studio pilota, seppur non generalizzabili, in quanto provenienti da un campione esiguo, hanno evidenziato come il percorso di auto-orientamento attivi una riflessione sulla visione di sé nei diversi contesti e un cambiamento, in positivo o in negativo, nell’autostima e nella valutazione di sé in diverse aree, ad esempio nell’area delle relazioni interpersonali, del vissuto corporeo, dell’emotività ecc. Tali dati ci hanno permesso soprattutto di evidenziare punti di forza e debolezza del percorso creato e di apportare modifiche per una maggiore comprensione e adattabilità del prodotto stesso. Il valore del percorso orientativo è connesso al ruolo attivo di auto-valutatore giocato dal candidato con disabilità, affiancando a questa prima fase di autovalutazione un successivo confronto dialogico con un esperto, tale da permettere un ancoraggio alla realtà esterna, al contesto in cui il soggetto si trova a vivere. In questo senso, l’orientamento assume il valore di un processo continuo e articolato, che ha come scopo principale quello di sostenere la consapevolezza di sé e delle proprie potenzialità, agendo all’interno dell’area dello sviluppo prossimale della persona verso la realizzazione della propria identità personale, sociale e professionale.