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Techn. Hochsch., Diss.--Aachen, 2000. / Includes bibliographical references (p. [235] - 244) and index.

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Ph.D. (Mathematics) / Algebraic methods have been largely ignored within the eld of hybrid logics. A main theme of this thesis is to illustrate the usefulness of algebraic methods in this eld. It is a well-known fact that certain properties of a logic correspond to properties of particular classes of algebras, and that we therefore can use these classes of algebras to answer questions about the logic. The rst aim of this thesis is to identify a class of algebras corresponding to hybrid logics. In particular, we introduce hybrid algebras as algebraic semantics for the better known hybrid languages in the literature. The second aim of this thesis is to use hybrid algebras to solve logical problems in the eld of hybrid logic. Specically, we will focus on proving general completeness results for some well-known hybrid logics with respect to hybrid algebras. Next, we study Sahlqvist theory for hybrid logics. We introduce syntactically de ned classes of hybrid formulas that have rst-order frame correspondents, which are preserved under taking Dedekind MacNeille completions of atomic hybrid algebras, and which are preserved under canonical extensions of permeated hybrid algebras. Finally, we investigate the nite model property (FMP) for several hybrid logics. In particular, we give analogues of Bull's theorem for the hybrid logics under consideration in this thesis. We also show that if certain syntactically de ned classes of hybrid formulas are added to the normal modal logic S4 as axioms, we obtain hybrid logics with the nite model property.

This thesis presents a critical reading of the theme of phenomenology in the work of the contemporary French philosopher Alain Badiou. My criticism is exercised through a reading of Badiou’s references to this theme. I demonstrate that Badiou’s magnum opus, Being and Event, and its sequel, Logiques des Mondes, are the two pillars between which the philosopher exercises his constructive attack against the phenomenological tradition. I argue that Badiou’s developmental logic is driven by a subterranean and disavowed dialogue with phenomenology, a tradition he deliberately marginalises. / The thesis begins with a literature review of academic responses currently in circulation. Six respondents and their critiques of Badiou’s enterprise are examined for key points, significance to this research, gaps and omissions, and consequences thereof. Each respondent’s primary focus (for example, existential criticism or the phenomenon) is detailed for its specific connection to Badiou’s disregard for phenomenology. The thesis then examines ten of Badiou’s works and meticulously lists specific references (or lack thereof) to phenomenology. I demonstrate that Badiou’s philosophical arguments all carry the ghost of phenomenology that the philosopher has, largely, left unexamined. / The thesis ends with a detailed exegesis of Badiou’s most recent text, Logiques des Mondes. With the release of this text, Badiou returns to the question of phenomenology to present an explicit position regarding questions of experience, existence, phenomenality and appearing. Badiou’s references to phenomenology throughout his texts prior to the release of this sequel are clearly marginal, but his attack on the phenomenological tradition is renewed here via a new theory of appearing. Highly dependent on arguments established in Being and Event, Badiou’s theory of appearing provides him with a superior mathematico-logical model (category theory and set theory) to explain the philosophical notions of ontology (what-is) and being-there (there-is) which create the material world.

This thesis presents a critical reading of the theme of phenomenology in the work of the contemporary French philosopher Alain Badiou. My criticism is exercised through a reading of Badiou’s references to this theme. I demonstrate that Badiou’s magnum opus, Being and Event, and its sequel, Logiques des Mondes, are the two pillars between which the philosopher exercises his constructive attack against the phenomenological tradition. I argue that Badiou’s developmental logic is driven by a subterranean and disavowed dialogue with phenomenology, a tradition he deliberately marginalises. / The thesis begins with a literature review of academic responses currently in circulation. Six respondents and their critiques of Badiou’s enterprise are examined for key points, significance to this research, gaps and omissions, and consequences thereof. Each respondent’s primary focus (for example, existential criticism or the phenomenon) is detailed for its specific connection to Badiou’s disregard for phenomenology. The thesis then examines ten of Badiou’s works and meticulously lists specific references (or lack thereof) to phenomenology. I demonstrate that Badiou’s philosophical arguments all carry the ghost of phenomenology that the philosopher has, largely, left unexamined. / The thesis ends with a detailed exegesis of Badiou’s most recent text, Logiques des Mondes. With the release of this text, Badiou returns to the question of phenomenology to present an explicit position regarding questions of experience, existence, phenomenality and appearing. Badiou’s references to phenomenology throughout his texts prior to the release of this sequel are clearly marginal, but his attack on the phenomenological tradition is renewed here via a new theory of appearing. Highly dependent on arguments established in Being and Event, Badiou’s theory of appearing provides him with a superior mathematico-logical model (category theory and set theory) to explain the philosophical notions of ontology (what-is) and being-there (there-is) which create the material world.

This thesis explores how symbolic ideas embedded in an accounting instrument come to be enacted in practice: detailing the processes through which they are realised by actors. It draws on theories of governmentality and the institutional logics perspective to develop a holistic theorisation of how programmes, ideas or ‘logics’ come to be enacted in practice as individuals interact with a performance appraisal process. It seeks to develop a theorised narrative that unpicks the various realities which actors construct in a particular assemblage. The story is informed by an abductive case study of one branch of John Lewis Department Stores. It develops a model which details the factors which influence the effective performativity of the accounting instrument. As such it explores how governance occurs as non-local ideas are prescribed to, and then enacted in, a local domain. The model describes how actors interact with a ‘mediating instrument’ and thereby constitute multiple realities based on three moderating factors: underlying ties to existing logics, self-interest and others’ influence. In outlining these moderating factors the thesis also highlights that multiple logics are more likely to be enacted when they are added or merged to existing sense making, in comparison to when they are framed or reframed according to those existing framings. As such it contributes to governmentality by detailing the process of governing and unpacking the factors which influence whether a mediating instrument is effectively performative. Additionally it contributes to institutional theory by providing a more nuanced understanding of how the symbolic elements of logics come to be enacted in practice through interactions with such material artefacts and how actors come to recognise the legitimacy of alternatives.

CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior / NÃs investigamos a teoria dos modelos de LÃgicas Preferenciais, LÃgica HÃbrida e fragmentos da LÃgica de Segunda-Ordem com relaÃÃo a modelos finitos. A semÃnticas dessas lÃgicas diferem da abordagem clÃssica pelo uso de relaÃÃes entre modelos ou por restringir a cardinalidade dos modelos a cardinais finitos. Este trabalho tem trÃs partes. Na primeira parte deste trabalho nÃs estudamos a teoria dos modelos de lÃgicas preferenciais. LÃgicas preferenciais surgem no contexto do raciocÃnio nÃo-monotÃnico em InteligÃncia Artificial. A principal caracterÃstica dessas lÃgicas à a existÃncia de uma relaÃÃo entre modelos. Isso permite a definiÃÃo de uma relaÃÃo de consequÃncia nÃo monotÃnica considerando-se os modelos minimais de um conjunto de sentenÃas. Usando a abordagem da Teoria dos Modelos Abstrata, nÃs generalizamos alguns resultados de expressividade para classes de lÃgicas preferenciais. NÃs mostramos que sempre que uma classe de modelos minimais de um conjunto finito de sentenÃas à axiomatizÃvel, entÃo tal classe à finitamente axiomatizÃvel. NÃs mostramos que se tal classe define implicitamente um sÃmbolo do vocabulÃrio, existe uma axiomatizaÃÃo finita de uma forma particular, a saber, o conjunto finito de sentenÃas inicial mais uma definiÃÃo explÃcita para o sÃmbolo definido. Na segunda parte desse trabalho, nÃs investigamos a teoria dos modelos finitos da LÃgica HÃbrida. LÃgicas HÃbridas sÃo extensÃes da lÃgica modal atravÃs de termos hÃbridos que se referem a estados individuais em um modelo de Kripke. NÃs estudamos a complexidade computacional dos problemas de model- e frame- checking para a LÃgica HÃbrida. NÃs mostramos que para cada problema de grafos na Hierarquia Polinomial e cada nÃmero n, existe uma fÃrmula que exprime esse problema para grafos de cardinalidade n. NÃs mostramos que o tamanho das fÃrmulas à limitado por um polinÃmio em n. NÃs mostramos que podemos abrir mÃo das modalidades globais se nos limitarmos a grafos conexos com loops. NÃs definimos fragmentos da LÃgica HÃbrida que correspondem a cada nÃvel da Hierarquia Polinomial. Isso nos leva a uma prova alternativa da NP-dificuldade do problema de model-checking para um fragmento especÃfico de da LÃgica HÃbrida. Na Ãltima parte desse trabalho, nÃs exploramos a complexidade descritiva da lÃgica obtida ao restringirmos a quantificaÃÃo de segunda-ordem a relaÃÃes de grau limitado. Baseados em trabalhos anteriores de Schwentick et al. e de Grandjean e Olive, nÃs introduzimos a LÃgica de Segunda-Ordem de Grau Limitado e mostramos que ela captura a classe ALIN de classes de estruturas unÃrias aceitas por uma mÃquina de acesso randÃmico em tempo linear e um nÃmero fixo de alternÃncias dependente apenas do problema. NÃs estendemos essa lÃgica com o operador de fecho transitivo sobre relaÃÃes de ordem superior sobre relaÃÃes de grau limitado. NÃs mostramos que a LÃgica de Segunda- Ordem de Grau Limitado com Fecho Transitivo captura quantidade linear de registradores em uma mÃquina de acesso randÃmico nÃo-determinÃstica onde os valores armazenados em cada registrador durante a computaÃÃo sÃo limitados por uma funÃÃo linear na cardinalidade da estrutura de entrada. / We investigate the model theory of Preferential Logics, Hybrid Logic and fragments of Second-Order Logic with respect to finite models. The semantics of these logics differ from the semantics of classical logics either by using relations between models or by restricting the cardinality of the models considered. This work has three main parts. In the first part of this work we study the model theory of preferential logics. Preferential logics arise in the context of nonmonotonic reasoning in Artificial Intelligence. The main characteristic of those logics is the existence of a relation between models. It allows the definition of a nonmonotonic consequence relation by considering the minimal models of a set of sentences. Using the approach of Abstract Model Theory we generalize some expressiveness results to classes of preferential logics. We show that whenever a class of minimal models of a finite set of sentences is axiomatizable, without considering the preference relation, then it is finitely axiomatizable. We also show that when such class of minimal models implicitly defines a symbol, then the finite axiomatization can be put in a very specic form, namely, the initial set of sentences plus a explicit definition for the symbol. In the second part of this work, we investigate the finite model theory of Hybrid Logic. Hybrid Logics are extensions of modal logics with hybrid terms which refer to single states in a Kripke model. We study the complexity of the model- and frame-checking problems for Hybrid Logic. We show that for each graph problem in the Polynomial Hierarchy and each natural number n there is a formula which expresses this problem for graphs of cardinality n. We also show that the size of such formulas is bounded by a polynomial in n. We show that one can disregard the global modalities if one consider only connected graphs with loops. We define fragments which correspond to each degree of the Polynomial Hierarchy. This leads to an alternative proof of the NP-hardness of the model-checking problem for an specic fragment of Full Hybrid Logic. In the last part of this work, we explore the descriptive complexity of the logic obtained by restricting second-order quantication to relations of bounded degree. Based on previous work from Schwentick et al. and Grandjean and Olive, we introduce the Bounded-Degree Second-Order Logic and show that it captures the class ALIN of classes of unary structures accepted by a alternating random access machine in linear time and bounded number of alternations. We also extend this logic with the transitive closure operator on high-order relations on bounded-degree relations. We show that the Bounded-Degree Second-Order Logic with Transitive Closure Operator captures linear number of registers in a nondeterministic random access machine provided that registers store values bounded by a linear function in the cardinality of the input structure.

FERREIRA, Francicleber Martins. Expressividade e complexidade em lógicas preferenciais, híbridas e de grau limitado. 2012. 130 f. Tese (Doutorado em ciência da computação)- Universidade Federal do Ceará, Fortaleza-CE, 2012. / Submitted by Elineudson Ribeiro (elineudsonr@gmail.com) on 2016-07-20T11:58:10Z No. of bitstreams: 1 2012_tese_fmferreira.pdf: 772301 bytes, checksum: b1e1a404221e38ffb8e0712513749a4c (MD5) / Approved for entry into archive by Rocilda Sales (rocilda@ufc.br) on 2016-07-25T11:47:07Z (GMT) No. of bitstreams: 1 2012_tese_fmferreira.pdf: 772301 bytes, checksum: b1e1a404221e38ffb8e0712513749a4c (MD5) / Made available in DSpace on 2016-07-25T11:47:07Z (GMT). No. of bitstreams: 1 2012_tese_fmferreira.pdf: 772301 bytes, checksum: b1e1a404221e38ffb8e0712513749a4c (MD5) Previous issue date: 2012 / We investigate the model theory of Preferential Logics, Hybrid Logic and fragments of Second-Order Logic with respect to finite models. The semantics of these logics differ from the semantics of classical logics either by using relations between models or by restricting the cardinality of the models considered. This work has three main parts. In the first part of this work we study the model theory of preferential logics. Preferential logics arise in the context of nonmonotonic reasoning in Artificial Intelligence. The main characteristic of those logics is the existence of a relation between models. It allows the definition of a nonmonotonic consequence relation by considering the minimal models of a set of sentences. Using the approach of Abstract Model Theory we generalize some expressiveness results to classes of preferential logics. We show that whenever a class of minimal models of a finite set of sentences is axiomatizable, without considering the preference relation, then it is finitely axiomatizable. We also show that when such class of minimal models implicitly defines a symbol, then the finite axiomatization can be put in a very specic form, namely, the initial set of sentences plus a explicit definition for the symbol. In the second part of this work, we investigate the finite model theory of Hybrid Logic. Hybrid Logics are extensions of modal logics with hybrid terms which refer to single states in a Kripke model. We study the complexity of the model- and frame-checking problems for Hybrid Logic. We show that for each graph problem in the Polynomial Hierarchy and each natural number n there is a formula which expresses this problem for graphs of cardinality n. We also show that the size of such formulas is bounded by a polynomial in n. We show that one can disregard the global modalities if one consider only connected graphs with loops. We define fragments which correspond to each degree of the Polynomial Hierarchy. This leads to an alternative proof of the NP-hardness of the model-checking problem for an specic fragment of Full Hybrid Logic. In the last part of this work, we explore the descriptive complexity of the logic obtained by restricting second-order quantication to relations of bounded degree. Based on previous work from Schwentick et al. and Grandjean and Olive, we introduce the Bounded-Degree Second-Order Logic and show that it captures the class ALIN of classes of unary structures accepted by a alternating random access machine in linear time and bounded number of alternations. We also extend this logic with the transitive closure operator on high-order relations on bounded-degree relations. We show that the Bounded-Degree Second-Order Logic with Transitive Closure Operator captures linear number of registers in a nondeterministic random access machine provided that registers store values bounded by a linear function in the cardinality of the input structure. / Nós investigamos a teoria dos modelos de Lógicas Preferenciais, Lógica Híbrida e fragmentos da Lógica de Segunda-Ordem com relação a modelos finitos. A semânticas dessas lógicas diferem da abordagem clássica pelo uso de relações entre modelos ou por restringir a cardinalidade dos modelos a cardinais finitos. Este trabalho tem três partes. Na primeira parte deste trabalho nós estudamos a teoria dos modelos de lógicas preferenciais. Lógicas preferenciais surgem no contexto do raciocínio não-monotônico em Inteligência Artificial. A principal característica dessas lógicas é a existência de uma relação entre modelos. Isso permite a definição de uma relação de consequência não monotônica considerando-se os modelos minimais de um conjunto de sentenças. Usando a abordagem da Teoria dos Modelos Abstrata, nós generalizamos alguns resultados de expressividade para classes de lógicas preferenciais. Nós mostramos que sempre que uma classe de modelos minimais de um conjunto finito de sentenças é axiomatizável, então tal classe é finitamente axiomatizável. Nós mostramos que se tal classe define implicitamente um símbolo do vocabulário, existe uma axiomatização finita de uma forma particular, a saber, o conjunto finito de sentenças inicial mais uma definição explícita para o símbolo definido. Na segunda parte desse trabalho, nós investigamos a teoria dos modelos finitos da Lógica Híbrida. Lógicas Híbridas são extensões da lógica modal através de termos híbridos que se referem a estados individuais em um modelo de Kripke. Nós estudamos a complexidade computacional dos problemas de model- e frame- checking para a Lógica Híbrida. Nós mostramos que para cada problema de grafos na Hierarquia Polinomial e cada número n, existe uma fórmula que exprime esse problema para grafos de cardinalidade n. Nós mostramos que o tamanho das fórmulas é limitado por um polinômio em n. Nós mostramos que podemos abrir mão das modalidades globais se nos limitarmos a grafos conexos com loops. Nós definimos fragmentos da Lógica Híbrida que correspondem a cada nível da Hierarquia Polinomial. Isso nos leva a uma prova alternativa da NP-dificuldade do problema de model-checking para um fragmento específico de da Lógica Híbrida. Na última parte desse trabalho, nós exploramos a complexidade descritiva da lógica obtida ao restringirmos a quantificação de segunda-ordem a relações de grau limitado. Baseados em trabalhos anteriores de Schwentick et al. e de Grandjean e Olive, nós introduzimos a Lógica de Segunda-Ordem de Grau Limitado e mostramos que ela captura a classe ALIN de classes de estruturas unárias aceitas por uma máquina de acesso randômico em tempo linear e um número fixo de alternâncias dependente apenas do problema. Nós estendemos essa lógica com o operador de fecho transitivo sobre relações de ordem superior sobre relações de grau limitado. Nós mostramos que a Lógica de Segunda- Ordem de Grau Limitado com Fecho Transitivo captura quantidade linear de registradores em uma máquina de acesso randômico não-determinística onde os valores armazenados em cada registrador durante a computação são limitados por uma função linear na cardinalidade da estrutura de entrada.