Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This work presents a method for qualitative and quantitative analysis of WorkFlow nets based on the proof trees of linear logic, and an approach for the verification of workflow specifications in UML through the transformation of UML Activity Diagrams into WorkFlow nets. The qualitative analysis is concerned with the proof of soundness correctness criterion defined for WorkFlow nets. The quantitative analysis is based on the computation of symbolic dates for the planning of resources used to handle each task of the workflow process modeled by a t-Time WorkFlow net. For the verification of the specifications of workflow processes mapped into UML Activity Diagrams are presented formal rules to transform this ones into WorkFlow nets. In this context is proposed the analysis and correction of critical points in UML Activity Diagrams through the analysis of proof trees of linear logic. The advantages of such an approach are diverse. The fact of working with linear logic permits one to prove the correctness criterion soundness in a linear time without considering the construction of the reachability graph, considering the proper structure of the WorkFlow net instead of considering the corresponding automata. Moreover, the computation of symbolic dates for the execution of each task mapped into the t-Time WorkFlow net permits to plan the utilization of the resources involved in the activities of the workflow process, through formulas that can be used for any case handled by the correspondent workflow process, without to examine again the process to recalculate, for each new case, the dates of start and conclusion for the activities involved in the process. Regarding the verification of workflow processes mapped into UML Activity Diagrams, the major advantage of this approach is the transformation of a semi-formal model into a formal model, such that some properties, like soundness, can be formally verified. / Este trabalho apresenta um método para a análise qualitativa e quantitativa de Work- Flow nets baseado nas árvores de prova canônica da lógica linear e uma abordagem para a verificação de especificações de processos de workflow em UML através da transformação de Diagramas de Atividades da UML em WorkFlow nets. A análise qualitativa refere-se à prova do critério de corretude soundness definido para WorkFlow nets. Já a análise quantitativa preocupa-se com o planejamento de recursos para cada atividade de um processo de workflow mapeado em uma t-Time WorkFlow net e baseia-se no cálculo de datas simbólicas para o planejamento de recursos utilizados na realização de cada tarefa do processo de workflow. Para a verificação das especificações de processos de workflow mapeados em Diagramas de Atividades da UML são apresentadas regras formais para transformar estes diagramas em WorkFlow nets. Neste contexto também é proposta a análise e correção de pontos críticos em Diagramas de Atividades da UML através da análise de árvores de prova canônica da lógica linear. As vantagens das abordagens apresentadas neste trabalho são diversas. O fato de trabalhar com lógica linear permite provar o critério de corretude soundness em tempo linear e sem que seja necessária a construção de um grafo das marcações acessíveis, considerando diretamente a própria estrutura da WorkFlow net, ao invés de considerar o seu autômato correspondente. Além disso, o cálculo de datas simbólicas correspondentes à execução de cada tarefa mapeada em uma t-Time WorkFlow net permite planejar a utilização dos recursos envolvidos nas atividades do processo de workflow, através de fórmulas que podem ser utilizadas por qualquer caso tratado pelo processo de workflow correspondente, sem que seja necessário percorrer novamente o processo de workflow inteiro para recalcular, para cada novo caso, datas de início e término das atividades envolvidas no processo. Já no que diz respeito à verificação de processos de workflow mapeados em Diagramas de Atividades da UML, a principal vantagem desta abordagem é a transformação de um modelo semi-formal em um modelo formal, para o qual algumas propriedades, como soundness, podem ser formalmente verificadas. / Mestre em Ciência da Computação

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This work formalizes four methods based on Linear Logic for the verification of interorganizational workflow processes modelled by Interorganizational Workflow nets, which are Petri nets that model such processes. The first method is related to the verification of the Soundness criteria for interorganizational workflow processes. The method is based on the construction and analysis of Linear Logic proof trees, which represent the local processes as much as they do the global processes. The second and third methods are related, respectively to Soundness criteria verification, Relaxed Soundness and Weak Soundness for the interorganizational workflow processes. These are obtained through the analysis of reutilized Linear Logic proof trees that have been constructed for the verification of the Soundness criteria. However, the fourth method has the objective of detecting the deadlock free scenarios in interorganizational workflow and is based on the construction and analysis of Linear Logic proof trees, which initially takes into consideration the local processes and communication between such, and thereafter the candidate scenarios. A case study is carried out in the context of a Web services composition check, since there is a close correlation between the modelling of the interorganizational workflow process and a Web services composition. Therefore, the four methods proposed in the interorganizational workflow process context, are applied to a Web services composition. The evaluation of the obtained results shows that the reutilization of Linear Logic proof trees initially constructed for verifying the Soundness criteria, in fact occurs in the context of verifying the Relaxed Soundness andWeak Soundness criteria. In addition, the evaluation shows how the Linear Logic sequents and their proof trees explicitly show the possibilities for existing collaborations in a Web service composition. An evaluation that takes into account the number of constructed linear logic proof trees shows that this number can be significantly reduced in the deadlock-freeness scenarios detection method. An approach for resource planning based on the symbolic date calculation, which considers data extracted from Linear Logic proof trees is presented and validated through simulations performed on the CPN tools simulator. Two approaches for the monitoring of deadlockfreeness scenarios are introduced and show how data obtained from the Linear Logic proof trees can be used to guide the execution of such scenarios. / Este trabalho formaliza quatro métodos baseados na Lógica Linear para verificação de processos de workflow interorganizacionais modelados por WorkFlow nets interorganizacionais, que são redes de Petri que modelam tais processos. O primeiro método está relacionado com a verificação do critério de correção Soundness para processos de workflow interorganizacionais. O método é baseado na construção e análise de árvores de prova da Lógica Linear que representam tanto os processos locais quanto o processo global. O segundo e terceiro métodos estão relacionados, respectivamente, com a verificação dos critérios de correção Relaxed Soundness e Weak Soundness para processos de workflow interorganizacionais, e são obtidos através da análise de árvores de prova da Lógica Linear reutilizadas, construídas para a prova do critério de correção Soundness. Já o quarto método tem por objetivo a detecção dos cenários livres de deadlock em processos de workflow interorganizacionais e é baseado na construção e análise de árvores de prova da Lógica Linear que consideram, inicialmente, os processos locais e as comunicações entre estes e, posteriormente, os cenários candidatos. Um estudo de caso é realizado no contexto da verificação de composições de serviços Web, uma vez que há uma relação estreita entre a modelagem de um processo de workflow interorganizacional e uma composição de serviços Web. Assim, os quatro métodos propostos no contexto dos processos de workflow interorganizacionais são aplicados a uma composição de serviços Web. A avaliação dos resultados mostra que o reuso de árvores de prova da Lógica Linear construídas inicialmente para a prova do critério de correção Soundness de fato ocorre no contexto da verificação dos critérios de correção Relaxed Soundness e Weak Soundness. Além disso, a avaliação mostra como os sequentes da Lógica Linear e suas árvores de prova explicitam as possibilidades de colaboração existentes em uma composição de serviços Web. Uma avaliação que leva em conta o número de árvores de prova da Lógica Linear construídas mostra que este número pode ser significativamente reduzido no método para detecção de cenários livres de deadlock. Uma abordagem para planejamento de recursos, baseada no cálculo de datas simbólicas, que considera dados extraídos de árvores de prova da Lógica Linear, é apresentada e validada através de simulações realizadas no simulador CPN Tools. Duas abordagens para a monitoração dos cenários livres de deadlock são introduzidas e mostram como dados obtidos nas árvores de prova da Lógica Linear podem ser utilizados para guiar a execução de tais cenários. / Doutor em Ciência da Computação

In this thesis I study several deductive systems for linear logic, its fragments, and some noncommutative extensions. All systems will be designed within the calculus of structures, which is a proof theoretical formalism for specifying logical systems, in the tradition of Hilbert's formalism, natural deduction, and the sequent calculus. Systems in the calculus of structures are based on two simple principles: deep inference and top-down symmetry. Together they have remarkable consequences for the properties of the logical systems. For example, for linear logic it is possible to design a deductive system, in which all rules are local. In particular, the contraction rule is reduced to an atomic version, and there is no global promotion rule. I will also show an extension of multiplicative exponential linear logic by a noncommutative, self-dual connective which is not representable in the sequent calculus. All systems enjoy the cut elimination property. Moreover, this can be proved independently from the sequent calculus via techniques that are based on the new top-down symmetry. Furthermore, for all systems, I will present several decomposition theorems which constitute a new type of normal form for derivations.

Thèse par articles. / 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. / 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.

L’objectif de cette thèse est de fournir un modèle, une méthode et un outil d’aide à la réalisation de scénarios interactifs. Cette solution répond au problème de l’opposition entre la maîtrise du déroulement d’un jeu vidéo et son niveau d’interactivité. En d’autres termes, notre but est d’aider à réaliser des jeux vidéo dont l’évolution satisfait les intentions des auteurs tout en autorisant un déroulement influencé par les choix du joueur (exprimés aux travers de ses actions). Pour cela, notre proposition permet à l’utilisateur de produire un modèle de scénario de jeu de bonne qualité qui est : (a) riche – le scénario fournit suffisamment d’options pertinentes aux personnages joueur/non-joueur de sorte que le joueur puisse déterminer le déroulement du jeu et sente toujours que le discours créé est intéressant, (b) valide – tous les discours possibles dans le scénario sont cohérents et répondent aux effets désirés par les auteurs, (c) opérationnel – la représentation du scénario est exécutable. Ce scénario est ensuite employé comme l’entrée d’un système de pilotage de narration interactive assurant le contrôle de la gestion du déroulement du jeu. Par conséquent, l’évolution des jeux, qui sont dirigés par un tel système de pilotage, garantit que l’exécution du jeu respecte les souhaits des auteurs, et en même temps, autorise la liberté des actions du joueur. Pour répondre au problème exposé ci-dessus, nous appuyons notre solution sur un modèle mathématique calculable (la logique linéaire) qui offre des mécanismes de déductions rigoureux et automatiques.Nous avons fait un tour d'horizon des approches existantes concernant le pilotage de narration interactive et la validation de scénario. Ceci nous permet d'identifier les principes nécessaires à notre solution, tels que les éléments d'architecture d'un système de pilotage ; la construction,la représentation, l'exécution de scénarios narratifs ; les propriétés de narration importantes ; l'évolution de référence des paramètres dramatiques ; la structuration de discours ; la stratégie pour la validation d'un scénario ; les informations qualitatives et statistiques nécessaires… Nos contributions portent (1) sur la définition d'un ensemble de propriétés de narration spécifiant la qualité des scénarios de jeu ; (2) sur la proposition de modèles, algorithmes et outils pour écrire des modèles de scénario respectant ces propriétés. Nous validons nos résultats par la réalisation de deux exemples. Le premier est un extrait d'un jeu éducatif expliquant comment appliquer notre outil en vue de produire un modèle de scénario de jeu valide, qui est exprimé par un séquent de logique linéaire dont la représentation est conforme à un métamodèle du calcul des séquents. Pour le second exemple, nous décrivons le processus de production complet d'un jeu vidéo réel basé sur l'histoire « Le Petit Chaperon rouge », mettant en oeuvre un prototype de système de pilotage que nous avons proposé, ce qui permet de dérouler le jeu selon le scénario valide produit, donc son évolution satisfait les intentions des auteurs, et en même temps, dépend des actions du joueur. / The objective of this PhD thesis is to provide a model, a method and a tool for producing interactive scenarios. Our solution solves the opposition between the controlle devolution of a video game and its interactivity level. In other words, our goal is to assist (authors) in producing video games whose unfolding satisfies authors’ intentions while it is simultaneously influenced by player’s choices (expressed via her/his actions).To this purpose, our proposal is to allow users to produce a good quality game scenario model, which is: (a) rich – the scenario provides enough pertinent options for player/non-player characters so that the player can determine the evolution of the game and always feels that the created discourse is interesting, (b) valid – all the possible discourses in the scenario are consistent and meet authors required effects, (c) operational – the representation of the scenario is executable. This scenario is then used as the input of an interactive storytelling control system to assist it in managing the unfolding of the game. As a consequence, the evolution of the video games, which are directed by such a control system, guarantees authors requirements, while at the same time, it depends on player’s actions. In order to execute the foregoing proposal, we base our solution on a calculable mathematical model (linear logic) which provides rigorous and automatic deduction mechanisms. We have made an overview of existing approaches concerning interactive storytelling controland scenario validation problems. This allows us to identify necessary principles for our solution, such as: architecture elements of a control system; construction, representation, implementation of narrative scenarios; important narrative properties; reference evolution of the drama parameters; discourse structuralization; scenario validation strategy; necessary statistical and qualitative information; etc. Our contributions consist (1) in the definition of a set of narrative properties specifying the quality of game scenarios; (2) in the proposal of models, algorithms and tools in order to produce scenario models respecting these properties. We validate our results by realizing two examples. The first is an extract of an education algame explaining how to apply our tools to produce a valid game scenario model, which is expressed by a linear logic sequent whose representation conforms to a metamodel of the sequent calculus. For the second example, we describe the complete production process of areal video game based on the story "Little Red Cap", implementing a prototype of control system we have proposed, which allows unfolding the game according to the produced valid scenario, so its evolution satisfies authors intentions and simultaneously depends on player's actions.