[pt] Para um pensamento úmido - a filosofia a partir de Jacques Derrida é um estudo que visa a apresentar alguns aspectos estruturais à constituição do pensamento ocidental que parecem ter sido recalcados pela filosofia ao longo de sua história. Para tanto, a fim de apresentar esta estrutura - ao mesmo tempo constitutiva e recalcada - do pensamento, recorreu-se à metáfora baconiana do úmido ou, mais precisamente, da umidade do úmido. Em seu Novum Organum, dedicado à formulação de um método científico que evite o erro e conduza o homem no caminho do conhecimento verdadeiro, Francis Bacon rechaça com veemência a esfera da comunicação como lugar, por excelência, do erro, fruto da ambigüidade ocasionada pelo uso indevido das palavras. O termo úmido é, então, tomado como exemplo para ilustrar os equívocos produzidos pela linguagem por não ser de precisa definição, não sendo seco nem molhado. A tese em questão parte do princípio de que o intuito de Bacon pode ser entendido como uma atitude típica da filosofia, qual seja, a sua necessidade de clareza, distinção, imunidade, contenção, determinação, consistência, unidade, isolamento etc., e vê nesta característica uma semelhança com a crítica que muito comumente se associa ao pensamento de Jacques Derrida e ao seu esforço para não oferecer nenhuma definição precisa, nenhuma conceitualização possível, apresentando, sob o nome desconstrução, um pensamento contaminado e disseminado através de seus quase conceitos: os indecidíveis. Com isso, uma análise paciente da indecidibilidade nas primeiras obras de Derrida constitui a primeira parte da tese, seguida de uma tentativa de se compreender a umidade do úmido a partir de algumas características assumidas pelo pensamento desconstrutor: a contaminação pela alteridade, a metaforicidade, a ficcionalidade, a tradutibilidade e o elemento autobiográfico do texto. / [en] Towards a moisty thought - the philosophy in the perspective of Jacques Derrida is a research that intends to present some traits which, although are central to the constitution of the Western Thought, has been excluded by Philosophy along its History. In order to present those structures of thought - constituted to and at the same time excluded by Philosophy itself -, we started with Bacon´s metaphor concerning the term moist, or, more precisely, the moistness of the moist. In his Novum Organum, dedicated to the formulation of a scientific method that avoids error and leads men through the path of the true way of knowledge, Francis Bacon firmly discards the realm of communication which, according to him, constitutes the place of error for excellence. In other words, Bacon understands communication as resulting from the ambiguity occasioned by the wrong use of words. The term moist is then taken as an example to illustrate the equivoques produced by language, because according to Bacon it doesn´t allow a precise definition, being neither dry nor wet. We take Bacon´s attitude as being representative of a typical philosophical attitude with its necessity of clearness, distinction, immunity, contention, determination, consistency, unity, isolation etc. Also, we see the very structure of this attitude as operative in the critics usually addressed to Jacques Derrida and its efforts to offer no precise definition and conceptualization. Contrarily to the classical philosophical thelos, Derrida presents, under the name Deconstruction, a thought which is contaminated and disseminated by its quasi-concepts: namely, the undecidables. A patient analysis of undecidability in Derrida´s first woks constitutes the first part of the thesis, followed by an attempt to formulate an idea of moistness, starting from some characteristics assumed by the deconstructive thought: contamination by Otherness, metaphoricity, ficcionality, traductibility and autobiographical elements of the text.

Le sujet visé par cette dissertation est la logique ordinale de Turing. Nous nous référons au texte original de Turing «Systems of logic based on ordinals» (Turing [1939]), la thèse que Turing rédigea à Princeton sous la direction du professeur Alonzo Church. Le principe d’une logique ordinale consiste à surmonter localement l’incomplétude gödelienne pour l’arithmétique par le biais de progressions d’axiomes récursivement consistantes. Étant donné son importance considérable pour la théorie de la calculabilité et les fondements des mathématiques, cette recherche méconnue de Turing mérite une attention particulière. Nous retraçons ici le projet d’une logique ordinale, de ses origines dans le théorème d’incomplétude de Gödel jusqu'à ses avancées dans les développements de la théorie de la calculabilité. Nous concluons par une discussion philosophique sur les fondements des mathématiques en fonction d’un point de vue finitiste. / The main subject of this dissertation is Turing’s ordinal logic, i.e. Turing’s attempt to locally overcome Gödel’s incompleteness by means of transfinite recursive progressions. We shall refer to the original 1939 text «Systems of logic based on ordinals» which is, in fact, Turing’s Ph.D thesis at Princeton University under the direction of Professor Alonzo Church. Considering its importance for the theory of computability and the foundations of mathematics, Turing’s paper certainly didn’t get enough attention in the literature. Therefore, we want to retrace Turing’s project of an ordinal logic from its very foundation in Gödel’s incompleteness theorem to its further development in calculability theory. A discussion on the foundations of mathematics from a computational point of view will conclude this memoir.

<p>In recent years, there has been much advancement in the area of verification of infinite-state systems. A system can have an infinite state-space due to unbounded data structures such as counters, clocks, stacks, queues, etc. It may also be infinite-state due to parameterization, i.e., the possibility of having an arbitrary number of components in the system. For parameterized systems, we are interested in checking correctness of all the instances in one verification step. </p><p>In this thesis, we consider systems which contain both sources of infiniteness, namely: (a) real-valued clocks and (b) parameterization. More precisely, we consider two models: (a) the timed Petri net (TPN) model, which is an extension of the classical Petri net model; and (b) the timed network (TN) model in which an arbitrary number of timed automata run in parallel. </p><p>We consider verification of safety properties for timed Petri nets using forward analysis. Since forward analysis is necessarily incomplete, we provide a semi-algorithm augmented with an acceleration technique in order to make it terminate more often on practical examples. Then we consider a number of problems which are generalisations of the corresponding ones for timed automata and Petri nets. For instance, we consider zenoness where we check the existence of an infinite computation with a finite duration. We also consider two variants of boundedness problem: syntactic boundedness in which both live and dead tokens are considered and semantic boundedness where only live tokens are considered. We show that the former problem is decidable while the latter is not. Finally, we show undecidability of LTL model checking both for dense and discrete timed Petri nets. </p><p>Next we consider timed networks. We show undecidability of safety properties in case each component is equipped with two or more clocks. This result contrasts previous decidability result for the case where each component has a single clock. Also ,we show that the problem is decidable when clocks range over the discrete time domain. This decidability result holds when the processes have any finite number of clocks. Furthermore, we outline the border between decidability and undecidability of safety for TNs by considering several syntactic and semantic variants.</p>

In recent years, there has been much advancement in the area of verification of infinite-state systems. A system can have an infinite state-space due to unbounded data structures such as counters, clocks, stacks, queues, etc. It may also be infinite-state due to parameterization, i.e., the possibility of having an arbitrary number of components in the system. For parameterized systems, we are interested in checking correctness of all the instances in one verification step. In this thesis, we consider systems which contain both sources of infiniteness, namely: (a) real-valued clocks and (b) parameterization. More precisely, we consider two models: (a) the timed Petri net (TPN) model, which is an extension of the classical Petri net model; and (b) the timed network (TN) model in which an arbitrary number of timed automata run in parallel. We consider verification of safety properties for timed Petri nets using forward analysis. Since forward analysis is necessarily incomplete, we provide a semi-algorithm augmented with an acceleration technique in order to make it terminate more often on practical examples. Then we consider a number of problems which are generalisations of the corresponding ones for timed automata and Petri nets. For instance, we consider zenoness where we check the existence of an infinite computation with a finite duration. We also consider two variants of boundedness problem: syntactic boundedness in which both live and dead tokens are considered and semantic boundedness where only live tokens are considered. We show that the former problem is decidable while the latter is not. Finally, we show undecidability of LTL model checking both for dense and discrete timed Petri nets. Next we consider timed networks. We show undecidability of safety properties in case each component is equipped with two or more clocks. This result contrasts previous decidability result for the case where each component has a single clock. Also ,we show that the problem is decidable when clocks range over the discrete time domain. This decidability result holds when the processes have any finite number of clocks. Furthermore, we outline the border between decidability and undecidability of safety for TNs by considering several syntactic and semantic variants.

Le sujet visé par cette dissertation est la logique ordinale de Turing. Nous nous référons au texte original de Turing «Systems of logic based on ordinals» (Turing [1939]), la thèse que Turing rédigea à Princeton sous la direction du professeur Alonzo Church. Le principe d’une logique ordinale consiste à surmonter localement l’incomplétude gödelienne pour l’arithmétique par le biais de progressions d’axiomes récursivement consistantes. Étant donné son importance considérable pour la théorie de la calculabilité et les fondements des mathématiques, cette recherche méconnue de Turing mérite une attention particulière. Nous retraçons ici le projet d’une logique ordinale, de ses origines dans le théorème d’incomplétude de Gödel jusqu'à ses avancées dans les développements de la théorie de la calculabilité. Nous concluons par une discussion philosophique sur les fondements des mathématiques en fonction d’un point de vue finitiste. / The main subject of this dissertation is Turing’s ordinal logic, i.e. Turing’s attempt to locally overcome Gödel’s incompleteness by means of transfinite recursive progressions. We shall refer to the original 1939 text «Systems of logic based on ordinals» which is, in fact, Turing’s Ph.D thesis at Princeton University under the direction of Professor Alonzo Church. Considering its importance for the theory of computability and the foundations of mathematics, Turing’s paper certainly didn’t get enough attention in the literature. Therefore, we want to retrace Turing’s project of an ordinal logic from its very foundation in Gödel’s incompleteness theorem to its further development in calculability theory. A discussion on the foundations of mathematics from a computational point of view will conclude this memoir.

Description logics (DLs) are used to represent knowledge of an application domain and provide standard reasoning services to infer consequences of this knowledge. However, classical DLs are not suited to represent vagueness in the description of the knowledge. We consider a combination of DLs and Fuzzy Logics to address this task. In particular, we consider the t-norm-based semantics for fuzzy DLs introduced by Hájek in 2005. Since then, many tableau algorithms have been developed for reasoning in fuzzy DLs. Another popular approach is to reduce fuzzy ontologies to classical ones and use existing highly optimized classical reasoners to deal with them. However, a systematic study of the computational complexity of the different reasoning problems is so far missing from the literature on fuzzy DLs. Recently, some of the developed tableau algorithms have been shown to be incorrect in the presence of general concept inclusion axioms (GCIs). In some fuzzy DLs, reasoning with GCIs has even turned out to be undecidable. This work provides a rigorous analysis of the boundary between decidable and undecidable reasoning problems in t-norm-based fuzzy DLs, in particular for GCIs. Existing undecidability proofs are extended to cover large classes of fuzzy DLs, and decidability is shown for most of the remaining logics considered here. Additionally, the computational complexity of reasoning in fuzzy DLs with semantics based on finite lattices is analyzed. For most decidability results, tight complexity bounds can be derived.

This thesis deals with the algorithmic undecidability (unsolvability) of provability in some non-classical logics. In fact, there are two natural variants of this problem. Fix a logic, we can study its set of theorems or its consequence relation, which is a more general problem. It is well-known that both these problems can be undecidable already for propositional logics and we provide further examples of such logics in this thesis. In particular, we study propositional substructural logics which are obtained from the sequent calculus LJ for intuitionistic logic by dropping structural rules. Our main results are the following. First, (finite) consequence relations in some basic non-associative substructural logics are shown to be undecidable. Second, we prove that a basic associative substructural logic with the contraction rule, which is notorious for being hard to handle, has an undecidable set of theorems. Since the studied logics have natural algebraic semantics, we also obtain corresponding algebraic results which are interesting in their own right.

Abstract Due to increasing amount of concurrency, systems have become difficult to design and analyse. In this effort, formal verification, which means proving the correctness of a system, has turned out to be useful. Unfortunately, the application domain of the formal verification methods is often indefinite, tools are typically unavailable, and most of the techniques do not suit especially well for the verification of software systems. These are the questions addressed in the thesis. A typical approach to modelling systems and specifications is to consider them parameterised by the restrictions of the execution environment, which results in an (infinite) family of finite-state verification tasks. The thesis introduces a novel approach to the verification of such infinite specification-system families represented as labelled transition systems (LTSs). The key idea is to exploit the algebraic properties of the correctness relation. They allow the correctness of large system instances to be derived from that of smaller ones and, in the best case, an infinite family of finite-state verification tasks to be reduced to a finite one, which can then be solved using existing tools. The main contribution of the thesis is an algorithm that automates the reduction method. A specification and a system are given as parameterised LTSs and the allowed parameter values are encoded using first order logic. Parameters are sets and relations over these sets, which are typically used to denote, respectively, identities of replicated components and relationships between them. Because the number of parameters is not limited and they can be nested as well, one can express multiply parameterised systems with a parameterised substructure, which is an essential property from the viewpoint of modelling software systems. The algorithm terminates on all inputs, so its application domain is explicit in this sense. Other proposed parameterised verification methods do not have both these features. Moreover, some of the earlier results on the verification of parameterised systems are obtained as a special case of the results presented here. Finally, several natural and significant extensions to the formalism are considered, and it is shown that the problem becomes undecidable in each of the cases. Therefore, the algorithm cannot be significantly extended in any direction without simultaneously restricting some other aspect.

This paper aims to investigate the possible connection between specters and silence in Graham Swift’s Tomorrow (2007) and Mothering Sunday (2016). In both novels, the protagonists predominantly speak in interior monologues, recounting the memories and secrets that haunt them, in what could be construed as an attempt to exorcise the ghosts of their past. The paper’s understanding of specters is based on Jacques Derrida’s Specters of Marx (1993), and the idea that specters - as figures that exist in states of in-between - disrupt not only temporality, but what we know to be true. Much like specters, the protagonists vacillate between states, neither speaking nor remaining silent, as they address absent or imagined listeners. This undecidability leaves one to wonder if their ghosts are - or ever can be - truly exorcised.

納博可夫的《羅麗泰》游走於各文類之間，看似相反的詮釋卻得以並存，進而營造出一種不確定性美學。本論文旨在探討納博可夫的書寫策略以及文本中的各種不確定性。 第一章為概論，援引德希達的理論說明「不確定性」。第二章簡介後設小說的歷史與定義，檢視文本中後設與寫實元素的並存，並藉羅蘭巴特的理論說明可寫性的文本。此外，也以文中例證分析寫實元素以及《羅麗泰》既是童話故事也是諧擬童話故事。第三章進一步說明小說中種種二元對立並存的現象：道德性/不道德性；精神分析式閱讀/嘲諷精神分析；以及故事起源的不確定性。文中的反身性，作者現身以及雙重性俱使道德與不道德間的分野更模糊難辨。羅蘭巴特的文本歡愉恰與納博可夫視藝術為美學至喜的觀點吻合，而《羅麗泰》小說中的美學至喜也形成一種超越世俗定義的超道德。第四章分析《羅麗泰》跨越不同文類的特殊風格，而瀰漫書中的「不確定性美學」使其同時是(一)懺悔錄/諧擬懺悔錄；(二)偵探小說/諧擬偵探小說；(三)喜劇/悲劇；(四)羅曼史/諧擬羅曼史。第五章則是結論：《羅麗泰》小說中的不確定性美學開啟了嶄新的閱讀體驗，讀者得以游走於不同詮釋間，並在閱讀中創造文本的意義。 / Nabokov's Lolita is a text that oscillates around the border between genres. In a close reading of Lolita, readers frequently find a condition of undecidability. This thesis investigates Nabokov’s textual strategy of playing in the boundaries between many genres, and by extension between a series of binary oppositions; and also how the narrative style repeatedly produces moments where the reader could decide to interpret either one way or another way, leading readers continually into a kind of either/or, both/and, neither/nor interpretive dilemma—what I will call an aesthetics of undecidability. Chapter One is an overall introduction to the study, and I refer to Jacques Derrida’s idea of undecidability. In Chapter Two, I explore the binary opposition between metafiction/straightforward storytelling in Lolita. In addition to the history and naming of metafiction, I also analyze Catherine Belsey’s interrogative text and Roland Barthes’ readable (lisible)/writable (scriptible) text. As for the realistic elements of the novel, I dissect textual evidence in Lolita and the undecidability between fairy tale/parody of fairy tale. The coexistence of metafictional and realistic elements is also a part of the undecidability in the text. Chapter Three is about three distinct yet interrelated textual aspects of undecidability: morality versus immorality in Lolita, the undecidability between psychoanalytic reading versus parody of psychoanalysis, and the undecidability of the text’s originality versus its borrowing from a previous short story titled “Lolita” by Heinz von Lichberg. These three critical issues are further complicated by the reflexivity, authorial presence, and the doubleness in Lolita that make it even more difficult to see the text simply as moral or immoral. Taken together, the resulting complexity and sophistication of the aesthetic style enables an active reading experience or what Barthes’ called the “text of bliss”—which coincidently corresponds to Nabokov’s definition of true art as “aesthetic bliss,” and the bliss in Lolita makes it a text that contains a kind of morality. Chapter Four examines additional cases of undecidability between confession/parody of confession, detective story/parody of detective story, comic elements/tragic elements, and romance/parody of romance. Again these are distinct yet interrelated issues of ambiguity, but my purpose is to show that a style of undecidability pervades the novel in many ways. And Chapter Five is the conclusion of this thesis: the aesthetics of undecidability makes Lolita a text that resists a one-sided reading. I hope that my thesis might explain why different readers of Lolita have opposite readings.