Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico. Programa de Pós-Graduação em Ciência da Computação. / Made available in DSpace on 2012-10-21T23:14:47Z (GMT). No. of bitstreams: 1 207778.pdf: 429850 bytes, checksum: 5a8ef0bdb25a1cedbc0312a1d037e76b (MD5) / Este trabalho desenvolve uma forma diferente de se obter árvores de prova por tablôs. Denominamos esse método de direto, por causa da característica em que a possível conclusão é inserida no tablô inicial, sem negá-la. Já o método dos tablôs por refutação se utiliza da negação da possível conclusão. No sistema de tablôs por prova direta para a lógica clássica, cada ramo está relacionado semanticamente à disjunção das fórmulas que o compõem, e o tablô completo corresponde semanticamente à conjunção de todas essas disjunções. Em qualquer um dos métodos baseados em tablôs para a Lógica Clássica, tanto direto quanto indireto, um ramo é considerado fechado se o mesmo contiver duas fórmulas contraditórias. No método direto o fechamento de um ramo corresponde à sua validade semântica, a qual implica, no caso do fechamento de todos os ramos, na validade da possível conclusão. Já no método indireto o fechamento de um ramo corresponde à insatisfatibilidade da negação da possível conclusão, o que por sua vez implica na validade da mesma.

Cette thèse porte sur l’interprétation combinatoire des probabilitésde l’état stationnaire de l’ASEP par les tableaux escaliers, sur les arbresnon-ambigus et sur les polyominos parallélogrammes périodiques.Dans une première partie, nous étudions l’ansatz matriciel de Derrida,Evans, Hakim et Pasquier. Toute solution de ce système d’équation permet decalculer les probabilités stationnaires de l’ASEP. Nos travaux définissent denouvelles récurrences équivalentes à celles de l’ansatz matriciel. En définissantun algorithme d’insertion sur les tableaux escaliers, nous montrons combinatoirementet simplement qu’ils les satisfont. Nous faisons de même pour l’ASEPà deux particules. Enfin, nous énumérons les coins dans les tableaux associésà l’ASEP, nous permettant ainsi de donner le nombre moyen de transitionspossibles depuis un état de l’ASEP.Dans une deuxième partie, nous calculons de jolies formules pour les sériesgénératrices des arbres non-ambigus, desquelles nous déduisons des formulesd’énumérations. Puis, nous interprétons bijectivement certains de ces résultats.Enfin, nous généralisons les arbres non-ambigus à toutes les dimensions finies.Dans la dernière partie, nous construisons une structure arborescente surles polyominos parallélogrammes périodiques, inspirée des travaux de Boussicault,Rinaldi et Socci. Cela nous permet de calculer facilement leur sériegénératrice selon la hauteur et la largeur ainsi que deux nouvelles statistiques :la largeur intrinsèque et la hauteur de recollement intrinsèque. Enfin, nousétudions l’ultime périodicité de leur série génératrice selon l’aire. / This thesis deals with a combinatorial interpretation of the stationnarydistribution of the ASEP given by staircase tableaux and studiestwo combinatorial objects : non-ambiguous trees and periodic parallelogrampolyominoes.In the first part, we study the matrix ansatz introduced by Derrida, Evans,Hakim and Pasquier. Any solution of this equation system can be used tocompute the stationnary probabilities of the ASEP. Our work defines newrecurrences equivalent to the matrix ansatz. By defining an insertion algorithmfor staircase tableaux, we prove combinatorially and easily that they satisfyour new recurrences. We do the same for the ASEP with two types of particles.Finally, we enumerate the corners of the tableaux related to the ASEP, whichgives the average number of transitions from a state of the ASEP.In the second part, we compute nice formulas for the generating functionsof non-ambiguous trees, from which we deduce enumeration formulas. Then, wegive a combinatorial interpretation of some of our results. Lastly, we generalisenon-ambiguous trees to every finite dimension.In the last part, we define a tree structure in periodic parallelogram polyominoes,motivated by the work of Boussicault, Rinaldi and Socci. It allowsus to compute easily the generating function with respect to the height andthe width as well as two new statistics : the intrinsic width and the intrinsicgluing height. Finally, we investigate the ultimate periodicity of the generatingfunction with respect to the area.

The original Macdonald polynomials P_μ form a basis for the vector space of symmetric functions which specializes to several of the common bases such as the monomial, Schur, and elementary bases. There are a number of different types of Macdonald polynomials obtained from the original P_μ through a combination of algebraic and plethystic transformations one of which is the modified Macdonald polynomial H̃_μ. In this dissertation, we study a certain specialization F̃_μ(q,t) which is the coefficient of x₁x₂…x_N in H̃_μ and also the Hilbert series of the Garsia-Haiman module M_μ. Haglund found a combinatorial formula expressing F̃_μ as a sum of n! objects weighted by two statistics. Using this formula we prove a q,t-analogue of the hook-length formula for hook shapes. We establish several new combinatorial operations on the fillings which generate F̃_μ. These operations are used to prove a series of recursions and divisibility properties for F̃_μ. / Ph. D.

Made available in DSpace on 2014-06-11T19:25:19Z (GMT). No. of bitstreams: 0 Previous issue date: 2005-09-27Bitstream added on 2014-06-13T18:26:17Z : No. of bitstreams: 1 silvestrini_lhc_me_mar.pdf: 390849 bytes, checksum: 3e56bcae7fb7fbdc04cda1eb30e5f1ea (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Em 1999, Grácio introduziu a Lógica do Plausível como uma particularização de uma família de sistemas lógicos, caracterizados pela inclusão de um quantificador generalizado na sintaxe da lógica clássica de predicados, a saber, as Lógicas Moduladas, cuja formalização semântica é dada por um subconjunto do conjunto das partes do universo. Nesta particularização de lógica modulada, é incluído o quantificador do Plausível P, que engendra a formalização de um raciocínio indutivo de maneira que uma 'boa parte' dos indivíduos possui determinada propriedade. O presente trabalho introduz um novo sistema dedutivo para a Lógica do Plausível, denominado TLP, construído seguindo os princípios de tableaux semânticos clássicos. Na elaboração do sistema de tableaux TLP, há uma forma original de localizar pontos nos ramos de um dado tableau. Ademais, por meio do raciocínio indutivo engendrado por esta lógica, discussões sucederam acerca da indução ser considerada um processo genuinamente lógico, tendo por ponto de partida o problema epistemológico da indução. / The Logic of the Plausible was introduced in 1999 by Grácio as a particularization of a family of logical systems characterized by the inclusion of a generalized quantifier in the syntax of the classical logic of predicates, denominated the Modulated Logics, whose semantical interpretation is given by a subset of the power set of the universe. In this particularization of modulated logics, it is included the quantifier of Plausible P that engenders the formalization of a type of inductive reasoning so that a 'good' number of individuals possesses certain property . This work introduces a new deductive system for the Logic of the Plausible, denominated TLP, built according to the principles of the classical semantical tableaux. In the construction of the tableaux system TLP, an original form of locating points in the branches of any tableaux is presented. Besides, through the inductive reasoning engendered by this logic, the work also promotes discussions concerning the consideration of the induction as a genuinely logical process, beginning from the epistemological problem of the induction.

Orientador: Hércules de Araújo Feitosa / Banca: Edélcio Gonçalves de Souza / Banca: Mauri Cunha do Nascimento / Resumo: Dentre as diversas lógicas não-clássicas, que complementam o cálculo de predicados de primeira ordem, destacamos as lógicas moduladas. As lógicas moduladas são caracterizadas pela inclusão de um novo quantificador, chamado modulado, que tem a incumbência de interpretar aspectos indutivos de quantificadores das linguagens naturais. Como um caso particular de lógica modulada, a lógica do muito formaliza a noção intuitiva de "muitos". O quantificador do muito é representado por G. Assim, uma sentença do tipo Gxα(x) deve ser entendida como "muitos indivíduos satisfazem a propriedade α". Semanticamente, a noção de muitos está associada a uma estrutura matemática denominada família fechada superiormente e própria. Seja E um conjunto não vazio. Uma família própria fechada superiormente F em E é tal que: (i) F ⊆ P(E); (ii) E ∈ F; (iii) ∅ ∉ F; (iv) A ∈ F e A ⊆ B ⇒ B ∈ F. Intuitivamente, F caracteriza os conjuntos que possuem 'muitos' elementos. E, assim, o universo E possui muitos elementos; o ∅ não possui muitos elementos; e se A possui muitos elementos, então todo conjunto que contém A também possui muitos elementos. Com elementos sintáticos que caracterizam linguisticamente estas propriedades de F, pode-se verificar que a lógica do muito é correta e completa para uma estrutura de primeira ordem estendida por uma família própria fechada superiormente. A lógica do muito foi originalmente introduzida em um sistema dedutivo hilbertiano, baseado apenas em axiomas e regras de dedução. Neste trabalho, desenvolvemos um outro sistema dedutivo para a lógica do muito, porém num sistema de tablôs. Demonstramos, naturalmente, que esse novo sistema é equivalente ao sistema axiomático original. / Abstract: Among the several non classical logics that complement the classical first-order logic, we detach the Modulated Logics. This class of logics is characterized by extending the classical logic by the introduction of a new generalized quantifier, called modulated quantifier, that has the attribution of interpreting some inductive aspects of quantifiers in any natural language. As a particular case of Modulated Logic, the Logic of Many formalize the intuitive notion of "many". The quantifier of many is represented by G. Thus, a sentence of the type Gxα(x) must be understood like "many individuals satisfy the property α". Semantically, the notion of many is associated with a mathematical structure named proper superiorly closed family. Let E be a non empty set. A proper superiorly closed family F in E is such that: (i) F ⊆ P(E); (ii) E ∈ F; (iii) ∅ ∉ F; (iv) A ∈ F e A ⊆ B ⇒ B ∈ F. Intuitively, F characterizes the sets which have "many" elements. The empty set ∅ does not have many elements. And if A has many elements, then any set which contains A, also has many elements. The logic of many has syntactical elements that caracterize linguisticaly these properties of F. We can verify that the Logic of Many is correct and complete for a first order structure extended by a proper superiorly closed family. The Logic of Many was originally introduced in a Hilbertian deductive system, based only on axioms and rules. In this work, we developed another deductive system for the Logic of Many, but in a tableaux system. We proof that this new system is equivalent to the original one. / Mestre

Our thesis investigates a mechanism for representing schema mapping by tabular forms and checking utility of the new representation. Schema mapping is a high-level specification that describes the relationship between two database schemas. Schema mappings constitute essential building blocks of data integration, data exchange and peer-to-peer data sharing systems. Global-and-local-as-view (GLAV) is one of the approaches for specifying the schema mappings. Tableaux are used for expressing queries and functional dependencies on a single database in a tabular form. In our thesis, we first introduce a tabular representation of GLAV mappings. We find that this tabular representation helps to solve many mapping-related algorithmic and semantic problems. For example, a well-known problem is to find the minimal instance of the target schema for a given instance of the source schema and a set of mappings between the source and the target schema. Second, we show that our proposed tabular mapping can be used as an operator on an instance of the source schema to produce an instance of the target schema which is `minimal' and `most general' in nature. There exists a tableaux-based mechanism for finding equivalence of two queries. Third, we extend that mechanism for deducing equivalence between two schema mappings using their corresponding tabular representations. Sometimes, there exist redundant conjuncts in a schema mapping which causes data exchange, data integration and data sharing operations more time consuming. Fourth, we present an algorithm that utilizes the tabular representations for reducing number of constraints in the schema mappings. At present, either schema-level mappings or data-level mappings are used for data sharing purposes. Fifth, we introduce and give the semantics of bi-level mapping that combines the schema-level and data-level mappings. We also show that bi-level mappings are more effective for data sharing systems. Finally, we implemented our algorithms and developed a software prototype to evaluate our proposed strategies.

Our thesis investigates a mechanism for representing schema mapping by tabular forms and checking utility of the new representation. Schema mapping is a high-level specification that describes the relationship between two database schemas. Schema mappings constitute essential building blocks of data integration, data exchange and peer-to-peer data sharing systems. Global-and-local-as-view (GLAV) is one of the approaches for specifying the schema mappings. Tableaux are used for expressing queries and functional dependencies on a single database in a tabular form. In our thesis, we first introduce a tabular representation of GLAV mappings. We find that this tabular representation helps to solve many mapping-related algorithmic and semantic problems. For example, a well-known problem is to find the minimal instance of the target schema for a given instance of the source schema and a set of mappings between the source and the target schema. Second, we show that our proposed tabular mapping can be used as an operator on an instance of the source schema to produce an instance of the target schema which is `minimal' and `most general' in nature. There exists a tableaux-based mechanism for finding equivalence of two queries. Third, we extend that mechanism for deducing equivalence between two schema mappings using their corresponding tabular representations. Sometimes, there exist redundant conjuncts in a schema mapping which causes data exchange, data integration and data sharing operations more time consuming. Fourth, we present an algorithm that utilizes the tabular representations for reducing number of constraints in the schema mappings. At present, either schema-level mappings or data-level mappings are used for data sharing purposes. Fifth, we introduce and give the semantics of bi-level mapping that combines the schema-level and data-level mappings. We also show that bi-level mappings are more effective for data sharing systems. Finally, we implemented our algorithms and developed a software prototype to evaluate our proposed strategies.

We consider the overlap between reasoning involved in <em>conjunctive query optimization</em> (CQO) and in tableaux-based approaches to reasoning about subsumption in <em>description logics</em> (DLs). In both cases, an underlying graph is created, searched and modified. This process is determined by a given <em>query</em> and <em>database schema</em> in the first case and by a given <em>description</em> and <em>terminology</em> in the second. The opportunities for overlap derive from an abundance of reductions of various schema languages to terminologies for common DL dialects, and from the fact that descriptions can in turn be viewed as queries that compute a single column. <br /><br /> Our main contributions are as follows. We present the design and implementation of a common graph utility that integrates the requirements for both CQO and DL reasoning. We then verify this model by also presenting the design and implementation for two drivers, one that implements a query optimizer for a conjunctive query language extended with descriptions, and one that implements a complete DL reasoner for a feature based DL dialect.

We consider the overlap between reasoning involved in <em>conjunctive query optimization</em> (CQO) and in tableaux-based approaches to reasoning about subsumption in <em>description logics</em> (DLs). In both cases, an underlying graph is created, searched and modified. This process is determined by a given <em>query</em> and <em>database schema</em> in the first case and by a given <em>description</em> and <em>terminology</em> in the second. The opportunities for overlap derive from an abundance of reductions of various schema languages to terminologies for common DL dialects, and from the fact that descriptions can in turn be viewed as queries that compute a single column. <br /><br /> Our main contributions are as follows. We present the design and implementation of a common graph utility that integrates the requirements for both CQO and DL reasoning. We then verify this model by also presenting the design and implementation for two drivers, one that implements a query optimizer for a conjunctive query language extended with descriptions, and one that implements a complete DL reasoner for a feature based DL dialect.

Sergei Vasilievich Rachmaninoff (1873-1943) is one of the greatest representatives of Russian classical music in the early twentieth century. In addition to being a successful composer, Rachmaninoff was also a great concert pianist and a conductor. He had written 237 musical compositions, including piano, instrumental, orchestral, and vocal music. As an outstanding pianist, he had well-received tours in Russia, America, and Switzerland. He conducted many operas and orchestral works in Russia. This paper will discuss the compositional background and the compositional techniques in Rachmaninoff¡¦s¡qEtudes-Tableaux, Op.39.¡r, with a special focus on the images that inspired Rachmaninoff to compose these etudes. ¡qEtudes-Tableaux, Op.39.¡rwas composed between 1916 and 1917; these etudes enriched the genre of piano etudes initiated by the previous romantic composers. This composition contains abundant expressive images rather than merely monotonous piano techniques which increase the artistic value of this composition.