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Propositional dynamic logic (PDL) is one of the most succesful variants of modal logic. To make it even more useful for applications, many extensions of PDL have been considered in the literature. A very natural and useful such extension is with negation of programs. Unfortunately, it is long-known that reasoning with the resulting logic is undecidable. In this paper, we consider the extension of PDL with negation of atomic programs, only. We argue that this logic is still useful, e.g. in the context of description logics, and prove that satisfiability is decidable and EXPTIME-complete using an approach based on Büchi tree automata.

In its many guises and variations, propositional dynamic logic (PDL) plays an important role in various areas of computer science such as databases, artificial intelligence, and computer linguistics. One relevant and powerful variation is ICPDL, the extension of PDL with intersection and converse. Although ICPDL has several interesting applications, its computational properties have never been investigated. In this paper, we prove that ICPDL is decidable by developing a translation to the monadic second order logic of infinite trees. Our result has applications in information logic, description logic, and epistemic logic. In particular, we solve a long-standing open problem in information logic. Another virtue of our approach is that it provides a decidability proof that is more transparent than existing ones for PDL with intersection (but without converse).

Cette recherche a pour objet la compréhension des énoncés de problèmes arithmétiques complexes et leur résolution. Les problèmes complexes choisis combinent des problèmes simples de types Changement et Combinaison. Ce travail s’appuie sur le modèle de la Construction-Intégration de Kintsch. Les résultats montrent qu’il existe une relation entre le niveau d’expertise en compréhension de textes narratifs et la résolution des problèmes arithmétiques complexes. Comprendre un texte narratif ou un énoncé de problème complexe exige de la part des lecteurs la construction d’un réseau propositionnel hiérarchisé et les résultats suggèrent, entre autres, une sensibilité des élèves aux propositions textuelles et aux ellipses contenues dans les textes. La formation des macropropositions est un processus fondamental et les résultats montrent une relation entre le nombre d’objets contenus dans les énoncés de problème et la procédure préférentiellement choisie par les élèves. Ils suggèrent d’une part, la mise en oeuvre du processus de catégorisation au cours du processus de compréhension et d’autre part, l’affaiblissement des liaisons entre les macropropositions élaborées et le schéma de problème Parties-Tout qui leur sont liés. D’un point de vue pédagogique, les résultats montrent que les questions relatives à l’activation d’une part des concepts superordonnés et d’autre part des schémas de problèmes Parties-Tout ne sont pas à privilégier pour aider les élèves. Finalement, les connaissances du lecteur sont essentielles à la compréhension. Cet élément est confirmé ici et la compréhension des problèmes complexes nécessite des connaissances solides relativement aux problèmes arithmétiques simples. / This research deals with text comprehension processes and complex arithmetic word problems resolution by 9-10 years old children in Reunion Island based upon the CI model of Kintsch. The complex word arithmetic problems used in this research are a combination of Change simple problems and Combine simple problems. The results show a relation between subject’s level of expertise in narrative texts comprehension and complex arithmetic word problems resolution. In order to understand a narrative text or to resolve a complex arithmetic word problem, subjects have to elaborate a coherent hierarchical propositional network : bridging inferences and macropropositions are involved to achieve complex arithmetic word problems resolution too. More precisely, the results suggest children are sensitive to the number of propositions and to the ellipsises. Macropropositions formation is an integral process of reading. The results show a relation between number of objects in complex arithmetic problems and procedure naturally used by children to solve them. They suggest on the one hand, categorization processes are an integral part of reading and on the other hand, some links between macropropositions and arithmetic hypothesis become weaker. Consequently, questions about superordinate concepts and arithmetic hypothesis attached to them are not helpul to resolve complex arithmetic word problems. Finally, reader’s knowlegde is a key element of comprehension processes and to achieve complex arithmetic word problems, problem schemata about simple arithmetic word problems are crucial. The results show a relation between subject’s level of expertise in simple arithmetic word problems and complex arithmetic word problems resolution.

Il s’agit d’une thèse sur le traité De duobus communissimis principiis scientiarum de Gérard Odon (vers 1320). Dans la première partie, nous faisons l’analyse du texte en nous centrant sur la notion d’« ens tertio adiacens ». Il s’agit de l’étant signifié par la totalité de la proposition et son vérifacteur ; il est univoquement comment à l’ens reale et à l’ens rationis et pour cette raison Odon l’identifie au sujet des principes de non-contradiction et du tiers exclu. L’ens tertio adiacens correspond aussi au premier objet adéquat de l’intellect et au sujet de la logique, entendue comme la science première. Dans la deuxième partie, nous plaçons Odon dans deux débats historiographiques : celui du réalisme propositionnel (à côté de Walter Burley, Grégoire de Rimini et Jean Wyclif) et celui des avancements de la doctrine des surtranscendantaux (à côté de Nicolas Bonet, François de la Marche et d’autres), lequel émerge de la distinction des deux sens de « res » chez Henri de Gand et ensuite chez Duns Scot. / This thesis deals with Geraldus Odonis’ treatise De duobos communissimis principiis scientiarum (ca. 1320). In the first part, we analyze the text by focusing on the concept of "ens tertio adiacens". It is the being signified by the totality of the proposition and its truthmaker; it is univocally common to ens reale and ens rationis, for this reason Odonis identifies it to the subject of the principle of non-contradiction and the principle of excluded middle. The ens tertio adiacens also corresponds to the first adequate object of the intellect and to the subject of logic, which is understood as the first science. In the second part, we place Odonis in two historiographical debates: the propositional realism (alongside Walter Burley, Gregory of Rimini and John Wyclif) and the advancements of the doctrine of supertranscendentals (alongside Nicolas Bonetus, Francis of Marchia and others), which emerges from the distinction between the two senses of "res" in Henry of Ghent and in Duns Scotus .

[pt] Segerberg apresentou uma prova geral da completude para lógicas proposicionais. Para tal, um sistema de dedução foi definido de forma que suas regras sejam regras para um operador booleano arbitrário para uma dada lógica proposicional. Cada regra desse sistema corresponde a uma linha na tabela de verdade desse operador. Na primeira parte desse trabalho, mostramos uma extensão da ideia de Segerberg para lógicas proposicionais finito-valoradas e para lógicas não-determinísticas. Mantemos a ideia de definir um sistema de dedução cujas regras correspondam a linhas de tabelas verdade, mas ao invés de termos um tipo de regra para cada valor de verdade da lógica correspondente, usamos uma representação bivalente que usa a técnica de fórmulas separadoras definidas por Carlos Caleiro e João Marcos. O sistema definido possui tantas regras que pode ser difícil trabalhar com elas. Acreditamos que um sistema de cálculo de sequentes definido de forma análoga poderia ser mais intuitivo. Motivados por essa observação, a segunda parte dessa tese é dedicada à definição de uma tradução entre cálculo de sequentes e dedução natural, onde procuramos definir uma bijeção melhor do que as já existentes. / [en] Segerberg presented a general completeness proof for propositional logics. For this purpose, a Natural Deduction system was defined in a way that its rules were rules for an arbitrary boolean operator in a given propositional logic. Each of those rules corresponds to a row on the operator s truth-table. In the first part of this thesis we extend Segerbergs idea to finite-valued propositional logic and to non-deterministic logic. We maintain the idea of defining a deductive system whose rules correspond to rows of truth-tables, but instead of having n types of rules (one for each truth-value), we use a bivalent representation that makes use of the technique of separating formulas as defined by Carlos Caleiro and João Marcos. The system defined has so many rules it might be laborious to work with it. We believe that a sequent calculus system defined in a similar way would be more intuitive. Motivated by this observation, in the second part of this thesis we work out translations between Sequent Calculus and Natural Deduction, searching for a better bijective relationship than those already existing.

Cette thèse s'inscrit dans le domaine de la représentation des connaissances et du raisonnement en Intelligence Artificielle. Elle traite divers aspects du changement de croyances dans le cadre de fragments de la logique propositionnelle.Dans un premier temps, nous nous intéressons à la complexité du problème de vérification de modèle pour des opérateurs de révision de bases de croyances dans le cadre général de la logique propositionnelle et dans le cadre restreint des formules de Horn et des formules de Krom.Notre contribution principale porte ensuite sur le raffinement des opérateurs de changement de croyances afin que ceux-ci opèrent dans des fragments de la logique propositionnelle. Nous examinons en particulier les opérations de révision, de mise-à-jour et de contraction. Cette approche permet, dans chacun des cas, d'obtenir des opérateurs concrets, dont nous étudions les propriétés logiques en terme de de satisfaction de postulats que doivent satisfaire les opérateurs de changement de croyances rationnels. Divers fragments de la logique propositionnelle sont considérés, notamment les fragment de Horn et de Krom. / This thesis takes place in the field of knowledge representation and reasoning in Artificial Intelligence.It deals with various issues of belief change within fragments of propositional logic.First we focus on the complexity of model-checking for different revision operators within the general framework of propositional logic and within the framework of Horn and Krom fragments.Second, our main contribution is the study of the refinement of belief change operators in such a way that they act within fragments of propositional logic. In particular, we address refinement of revision, update and contraction operators. In each case this approach allows us to define concrete operators, for which we study logical properties in terms of satisfaction of postulates that should hold for any rational belief change operator. Various propositional fragments of propositional logic are considered, such as Horn and Krom fragments.

A literatura filosófica sobre a Psicologia do Senso Comum se estende desde a década de 1970, e abrange diversas questões sobre nosso entendimento interpessoal cotidiano, nossa capacidade de interação e coordenação de atividades, o arcabouço conceitual intuitivo que relaciona estados mentais e atitudes proposicionais a comportamentos, e os mecanismos cognitivos de leitura mental que nos permitem atribuir estados mentais a outras pessoas. Nesta dissertação eu examino o desenvolvimento histórico desta literatura, identificando dois debates distintos, o primeiro (principalmente entre Paul Churchland e Jerry Fodor dos anos 70 aos anos 90) tendo como foco a relação entre a teoria da Psicologia do Senso Comum e teorias científicas (da neurociência e das ciências cognitivas), e o segundo (o debate contemporâneo) tendo como foco os mecanismos cognitivos de leitura mental e o papel das atribuições de estados mentais e atitudes proposicionais nas teorias da cognição corporificada, situada e estendida. Além do exame histórico do que argumento serem dois debates distintos e da transição conceitual entre ambos, também apresento aqui minha crítica à abordagem eliminativista contemporânea de Matthew Ratcliffe e, como alternativa, articulo os princípios de uma abordagem pluralista que combina leitura mental e interpretação contextual situada como fundamentais para a cognição social / The philosophical literature on Folk Psychology began in the 1970s, and encompasses various questions about our everyday interpersonal understanding, our ability to interact and coordinate activities, the intuitive conceptual framework that relates mental states and propositional attitudes to behaviors, and the cognitive mechanisms of mindreading that allow us to attribute mental states to other people. In this thesis I examine the historical development of this literature, identifying two distinct debates, the first (mainly between Paul Churchland and Jerry Fodor from the 70s to the 90s) focusing on the relationship between the theory of Folk Psychology and scientific theories (in neuroscience and cognitive science), and the second (the contemporary debate) focusing on the cognitive mechanisms of mindreading and the role played by attributions of mental states and propositional attitudes in theories of embodied, situated and extended cognition. In addition to the historical examination of what I argue are two distinct debates as well as of the conceptual transition between them, here I present my criticism of Matthew Ratcliffe\'s contemporary eliminativist approach and, as an alternative to it, I articulate the principles of a pluralistic approach that combines both mindreading and situated contextual interpretation as fundamental for social cognition

本研究採用分層叢集抽樣，從台北市十二行政區中，按比例抽出36所學校。受試者含1-9年級學生合計5475人，有效樣本4917人達89.8%。自編測驗信度、效度考驗：α係數達.80，效標關連效度在.21到.70之間，與智力測驗之相關在各年級均達.01顯著水準，專家效度良好。研究發現包括二部份： 一、邏輯概念之發展：有關台北市立國民中小學學生邏輯概念發展狀況研究結果如次 (1) 形式運思階段之前，兒童可以解答部份的命題邏輯問題。 (2) 具體內容的ＭＰ規則和常見的遞移性關係的遞移推理，分別在國小一年級、及國小四年級已達到發展高原。 (3) 從具體運思到形式運思階段，並沒有發現階段性跳躍的成長現象，邏輯概念發展大致上是向上發展的型態。 (4) 二元運算系統在8,9年級(14、15歲左右)--也就是皮亞傑所指的形式運思階段達到平衡的時期，只能做大約18%?32%的題目，沒有證據顯示大部份的受試者，已經完成了具有「群與格」特徵的命題邏輯結構。本研究的假設一、假設二均未獲得支持。皮亞傑理論對學生的邏輯概念發展有低估和高估的現象。一方面低估了國小中低年級兒童在簡單邏輯規則的發展，另一方面高估了青少年在困難的邏輯規則上所能達到的成就。 二、邏輯概念與數學之相關性：在邏輯與數學的相關性研究方面獲得以下結論： (1) 邏輯成績與數學成績的相關在各年級學生中，均達.0001顯著水準。大部份年級數學成績與智力的相關，大於數學成績與邏輯概念的相關。 (2) 年級對邏輯概念的影響效果顯著，當控制智力高低及數學成就好壞二個因素之後，邏輯概念隨年級而增進。 (3) 數學成就對邏輯概念的影響效果顯著，對各年級學生而言，高數學成就組學生的邏輯概念比其他二組好。但數學成就中等和低等的二組受試者之間，當智力的百分等級在35?56之間時，邏輯概念沒有差異。 (4) 變異數分析顯示，以年級、數學成就與智力的線性模式，可以解釋邏輯概念所有變異量中的63%。共變異數分析顯示，排除智力的影響之後，年級、數學成就仍是可以解釋邏輯概念所有變異量中的63%，與變異數分析結果一致。