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In concurrency theory—the branch of (theoretical) computer science that studies the logical and mathematical foundations of parallel computation—there are two main formal ways of modelling the behaviour of systems where multiple actions or events can happen independently and at the same time: either with interleaving or with partial order semantics. On the one hand, the interleaving semantics approach proposes to reduce concurrency to the nondeterministic, sequential computation of the events the system can perform independently. On the other hand, partial order semantics represent concurrency explicitly by means of an independence relation on the set of events that the system can execute in parallel; following this approach, the so-called ‘true concurrency’ approach, independence or concurrency is a primitive notion rather than a derived concept as in the interleaving framework. Using interleaving or partial order semantics is, however, more than a matter of taste. In fact, choosing one kind of semantics over the other can have important implications—both from theoretical and practical viewpoints—as making such a choice can raise different issues, some of which we investigate here. More specifically, this thesis studies concurrent systems with partial order semantics and focuses on their bisimulation and model-checking problems; the theories and techniques herein apply, in a uniform way, to different classes of Petri nets, event structures, and transition system with independence (TSI) models. Some results of this work are: a number of mu-calculi (in this case, fixpoint extensions of modal logic) that, in certain classes of systems, induce exactly the same identifications as some of the standard bisimulation equivalences used in concurrency. Secondly, the introduction of (infinite) higher-order logic games for bisimulation and for model-checking, where the players of the games are given (local) monadic second-order power on the sets of elements they are allowed to play. And, finally, the formalization of a new order-theoretic concurrent game model that provides a uniform approach to bisimulation and model-checking and bridges some mathematical concepts in order theory with the more operational world of games. In particular, we show that in all cases the logic games for bisimulation and model-checking developed in this thesis are sound and complete, and therefore, also determined—even when considering models of infinite state systems; moreover, these logic games are decidable in the finite case and underpin novel decision procedures for systems verification. Since the mu-calculi and (infinite) logic games studied here generalise well-known fixpoint modal logics as well as game-theoretic decision procedures for analysing concurrent systems with interleaving semantics, this thesis provides some of the groundwork for the design of a logic-based, game-theoretic framework for studying, in a uniform manner, several concurrent systems regardless of whether they have an interleaving or a partial order semantics.

The aim of this work is to use contemporary notation to build theory of Rosser logic, explain in detail its relation to Peano arithmetic, show its Kripke semantics and finally using plural self-reference show the proof of arithmetical completeness. In the last chapter we show some of the properties of Rosser sentences. Powered by TCPDF (www.tcpdf.org)

Motivées par de nombreuses applications allant du traitement XML à lavérification d'exécution de programmes, de nombreuses logiques sur les arbresde données et les flux de données ont été développées dans la littérature.Celles-ci offrent divers compromis entre expressivité et complexitéalgorithmique ; leur problème de satisfiabilité a souvent une complexité nonélémentaire ou peut même être indécidable.De plus, leur étude à travers des approches de théories des modèles ou dethéorie des automates peuvent être algorithmiquement impraticables ou manquerde modularité.Dans une première partie, nous étudions l'utilisation de systèmes de preuvecomme un moyen modulaire de résoudre le problème de satisfiabilité des données logiques sur des structures linéaires.Pour chaque logique considérée, nous développons un calcul d'hyperséquentscorrect et complet et décrivons une stratégie de recherche de preuve optimaledonnant une procédure de décision NP.En particulier, nous présentons un fragment NP-complet de la logique temporelle sur les ordinaux avec données, la logique complète étant indécidable, qui est exactement aussi expressif que le fragment à deux variables de la logique du premier ordre sur les ordinaux avec données.Dans une deuxième partie, nous menons une étude empirique des principaleslogiques à la XPath décidables proposées dans la littérature.Nous présentons un jeu de tests que nous avons développé à cette fin etexaminons comment ces logiques pourraient être étendues pour capturer davantage de requêtes du monde réel sans affecter la complexité de leur problème de satisfiabilité.Enfin, nous analysons les résultats que nous avons recueillis à partir de notre jeu de tests et identifions les nouvelles fonctionnalités à prendre en charge afin d’accroître la couverture pratique de ces logiques. / Motivated by applications ranging from XML processing to runtime verificationof programs, many logics on data trees and data streams have been developed in the literature.These offer different trade-offs between expressiveness and computationalcomplexity; their satisfiability problem has often non-elementary complexity or is even undecidable.Moreover, their study through model-theoretic or automata-theoretic approaches can be computationally impractical or lacking modularity.In a first part, we investigate the use of proof systems as a modular way tosolve the satisfiability problem of data logics on linear structures.For each logic we consider, we develop a sound and complete hypersequentcalculus and describe an optimal proof search strategy yielding an NPdecision procedure.In particular, we exhibit an NP-complete fragment of the tense logic over data ordinals---the full logic being undecidable---, which is exactly as expressive as the two-variable fragment of the first-order logic on data ordinals.In a second part, we run an empirical study of the main decidable XPath-likelogics proposed in the literature.We present a benchmark we developed to that end, and examine how these logicscould be extended to capture more real-world queries without impacting thecomplexity of their satisfiability problem.Finally, we discuss the results we gathered from our benchmark, and identifywhich new features should be supported in order to increase the practicalcoverage of these logics.

The main theme shared by the two main parts of this thesis is EFFICIENT AUTOMATED REASONING.Part I is focussed on a general theory underpinning a number of efficient approximate algorithms for Constraint Satisfaction Problems (CSPs),the constraint propagation algorithms.In Chapter 3, we propose a Structured Generic Algorithm schema (SGI) for these algorithms. This iterates functions according to a certain strategy, i.e. by searching for a common fixpoint of the functions. A simple theory for SGI is developed by studying properties of functions and of the ways these influence the basic strategy. One of the primary objectives of our theorisation is thus the following: using SGI or some of its variations for DESCRIBINING and ANALISYING HOW the "pruning" and "propagation" process is carried through by constraint propagation algorithms.Hence, in Chapter 4, different domains of functions (e.g., domain orderings) are related to different classes of constraint propagation algorithms (e.g., arc consistency algorithms); thus each class of constraint propagation algorithms is associated with a "type" of function domains, and so separated from the others. Then we analys each such class: we distinguished functions on the same domains for their different ways of performing pruning (point or set based), and consequently differentiated between algorithms of the same class (e.g., AC-1 and AC-3 versus AC-4 or AC-5). Besides, we also show how properties of functions (e.g., commutativity or stationarity) are related to different strategies of propagation in constraint algorithms of the same class (see, for instance, AC-1 versus AC-3). In Chapter 5 we apply the SGI schema to the case of soft CSPs (a generalisation of CSPs with sort-of preferences), thereby clarifying some of the similarities and differences between the "classical" and soft constraint-propagation algorithms. Finally, in Chapter 6, we summarise and characterise all the functions used for constraint propagation; in fact, the other goal of our theorisation is abstracting WHICH functions, iterated as in SGI or its variations, perform the task of "pruning" or "propagation" of inconsistencies in constraint propagation algorithms.We focus on relations and relational structures in Part II of the thesis. More specifically, modal languages allow us to talk about various relational structures and their properties. Once the latter are formulated in a modal language, they can be passed to automated theorem provers and tested for satisfiability, with respect to certain modal logics. Our task, in this part, can be described as follows: determining the satisfiability of modal formulas in an efficient manner. In Chapter 8, we focus on one way of doing this: we refine the standard translation as the layered translation, and use existing theorem provers for first-order logic on the output of this refined translation. We provide ample experimental evidence on the improvements in performances that were obtained by means of the refinement.The refinement of the standard translation is based on the tree model property. This property is also used in the basic algorithm schema in Chapter 9 ---the original schema is due to~\cite{seb97}. The proposed algorithm proceeds layer by layer in the modal formula and in its candidate models, applying constraint propagation and satisfaction algorithms for finite CSPs at each layer. With Chapter 9, we wish to draw the attention of constraint programmers to modal logics, and of modal logicians to CSPs.Modal logics themselves express interesting problems in terms of relations and unary predicates, like temporal reasoning tasks. On the other hand, constraint algorithms manipulate relations in the form of constraints, and unary predicates in the form of domains or unary constraints, see Chapter 6. Thus the question of how efficiently those algorithms can be applied to modal reasoning problems seems quite natural and challenging.

Les contraintes arithmétiques sont largement utilisées dans les langages formels comme les expressions, les grammaires d'arbres et les chemins réguliers. Ces contraintes sont utilisées dans les modéles de contenu des types (XML Schemas) pour imposer des bornes sur le nombre d'occurrences de nœuds. Dans les langages de requêtes (XPath, XQuery), ces contraintes permettent de sélectionner les nœuds ayant un nombre limité de nœuds accessibles par une expression de chemin donnée. Les types et chemins étendus avec les contraintes de comptage constituent le prolongement naturel de leurs homologues sans comptage déjà considérés comme des constructions fondamentales dans les langages de programmation et les systèmes de type pour XML. Un des défis majeurs en programmation XML consiste à développer des techniques automatisées permettant d'assurer statiquement un typage correct et des optimisations de programmes manipulant les données XML. À cette fin, il est nécessaire de résoudre certaines tâches de raisonnement qui impliquent des constructions telles que les types et les expressions XPath avec des contraintes de comptage. Dans un futur proche, les compilateurs de programmes XML devront résoudre des problèmes de base tels que le sous-typage afin de s'assurer au moment de la compilation qu'un programme ne pourra jamais générer de documents non valides à l'exécution. Cette thèse étudie les logiques capables d'exprimer des contraintes de comptage sur les structures d'arbres. Il a été montré récemment que le mu-calcul sur les graphes, lorsqu'il est étendu à des contraintes de comptage portant exclusivement sur les nœuds successeurs immédiats est indécidable. Dans cette thèse, nous montrons que, sur les arbres finis, la logique avec contraintes de comptage est décidable en temps exponentiel. En outre, cette logique fournit des opérateurs de comptage selon des chemins plus généraux. En effet, la logique peut exprimer des contraintes numériques sur le nombre de nœuds descendants ou même ascendants. Nous présentons également des traductions linéaires d'expressions XPath et de types XML comportant des contraintes de comptage dans la logique. / Arithmetical constraints are widely used in formal languages like regular expressions, tree grammars and paths. In XML they are used to impose bounds on the number of occurrences described by content models of schema languages (XML Schema, RelaxNG). In query languages (XPath, XQuery), they allow selecting nodes that have a bounded number of nodes reachable by a given path expression. Counting types and paths are thus natural extensions of their countless counterparts already regarded as the core constructs in XML languages and type systems. One of the biggest challenges in XML is to develop automated techniques for ensuring static-type safety and optimization techniques. To this end, there is a need to solve some basic reasoning tasks that involve constructions such as counting XML schemas and XPath expressions. Every compiler of XML programs will have to routinely solve problems such as type and path type- checking, for ensuring at compile time that invalid documents can never arise as the output of XML processing code. This thesis studies efficient reasoning frameworks able to express counting constraints on tree structures. It was recently shown that the mu-calculus, when extended with counting constraints on immediate successor nodes is undecid able over graphs. Here we show that, when interpreted over finite trees, the logic with counting constraints is decidable in single exponential time. Furthermore, this logic allows more general counting operators. For example, the logic can pose numerical constraints on number of ancestors or descendants. We also present linear translations of counting XPath expressions and XML schemas into the logic.

El objetivo de esta tesis es proponer mejoras en modelos existentes de razonamiento espacial cualitativo con relaciones cardinales, y proponer nuevos modelos y técnicas de razonamiento utilizando algunos resultados previos del razonamiento temporal cualitativo. Los modelos propuestos se basan en dos formalismos muy utilizados para razonamiento cualitativo: los Problemas de Satisfacción de Restricciones y las Lógicas Modales. / The main goal of this PhD Thesis is to propose improvements to existing models for qualitative spatial reasoning with cardinal direction relations, and to propose new models and reasoning techniques using some previous results from qualitative temporal reasoning. The proposed models are based on two widely used formalisms for Qualitative Reasoning: Constraint Satisfaction Problems and Modal Logics.

Les concepts d'action et de ressource sont omniprésents en informatique. La caractéristique principale d'une action est de changer l'état actuel du système modélisé. Une action peut ainsi être l'exécution d'une instruction dans un programme, l'apprentissage d'un fait nouveau, l'acte concret d'un agent autonome, l'énoncé d'un mot ou encore une tâche planifiée. La caractéristique principale d'une ressource est de pouvoir être divisée, par exemple pour être partagée. Il peut s'agir des cases de la mémoire d'un ordinateur, d'un ensemble d'agents, des différent sens d'une expression, d'intervalles de temps ou de droits d'accès. Actions et ressources correspondent souvent aux dimensions temporelles et spatiales du système modélisé. C'est le cas par exemple de l'exécution d'une instruction sur une case de la mémoire ou d'un groupe d'agents qui coopèrent. Dans ces cas, il est possible de modéliser les actions parallèles comme étant des actions opérant sur des parties disjointes des ressources disponibles. Les logiques modales permettent de modéliser les concepts d'action et de ressource. La sémantique relationnelle d'une modalité unaire est une relation binaire permettant d'accéder à un nouvel état depuis l'état courant. Ainsi une modalité unaire correspond à une action. De même, la sémantique d'une modalité binaire est une relation ternaire permettant d'accéder à deux états. En considérant ces deux états comme des sous-états de l'état courant, une modalité binaire modélise la séparation de ressources. Dans cette thèse, nous étudions des logiques modales utilisées pour raisonner sur les actions, les ressources et la concurrence. Précisément, nous analysons la décidabilité et la complexité du problème de satisfaisabilité de ces logiques. Ces problèmes consistent à savoir si une formule donnée peut être vraie. Pour obtenir ces résultats de décidabilité et de complexité, nous proposons des procédures de décision. Ainsi, nous étudions les logiques modales avec des modalités binaires, utilisées notamment pour raisonner sur les ressources. Nous nous intéressons particulièrement à l'associativité. Alors qu'il est généralement souhaitable que la modalité binaire soit associative, puisque la séparation de ressources l'est, cette propriété rend la plupart des logiques indécidables. Nous proposons de contraindre la valuation des variables propositionnelles afin d'obtenir des logiques décidables ayant une modalité binaire associative. Mais la majeure partie de cette thèse est consacrée à des variantes de la logique dynamique propositionnelle (PDL). Cette logiques possède une infinité de modalités unaires structurée par des opérateurs comme la composition séquentielle, l'itération et le choix non déterministe. Nous étudions tout d'abord des variantes de PDL comparables aux logiques temporelle avec branchement. Nous montrons que les problèmes de satisfaisabilité de ces variantes ont la même complexité que ceux des logiques temporelles correspondantes. Nous étudions ensuite en détails des variantes de PDL ayant un opérateur de composition parallèle de programmes inspiré des logiques de ressources. Cet opérateur permet d'exprimer la séparation de ressources et une notion intéressante d'actions parallèle est obtenue par la combinaison des notions d'actions et de séparation. En particulier, il est possible de décrire dans ces logiques des situations de coopération dans lesquelles une action ne peut être exécutée que simultanément avec une autre. Enfin, la contribution principale de cette thèse est de montrer que, dans certains cas intéressants en pratique, le problème de satisfaisabilité de ces logiques a la même complexité que PDL. / The concepts of action and resource are ubiquitous in computer science. The main characteristic of an action is to change the current state of the modeled system. An action may be the execution of an instruction in a program, the learning of a new fact, a concrete act of an autonomous agent, a spoken word or a planned task. The main characteristic of resources is to be divisible, for instance in order to be shared. Resources may be memory cells in a computer, performing agents, different meanings of a phrase, time intervals or access rights. Together, actions and resources often constitute the temporal and spatial dimensions of a modeled system. Consider for instance the instructions of a computer executed at memory cells or a set of cooperating agents. We observe that in these cases, an interesting modeling of concurrency arises from the combination of actions and resources: concurrent actions are actions performed simultaneously on disjoint parts of the available resources. Modal logics have been successful in modeling both concepts of actions and resources. The relational semantics of a unary modality is a binary relation which allows to access another state from the current state. Hence, unary modalities are convenient to model actions. Similarly, the relational semantics of a binary modality is a ternary relation which allows to access two states from the current state. By interpreting these two states as substates of the current state, binary modalities allow to divide states. Hence, binary modalities are convenient to model resources. In this thesis, we study modal logics used to reason about actions, resources and concurrency. Specifically, we analyze the decidability and complexity of the satisfiability problem of these logics. These problems consist in deciding whether a given formula can be true in any model. We provide decision procedures to prove the decidability and state the complexity of these problems. Namely, we study modal logics with a binary modality used to reason about resources. We are particularly interested in the associativity property of the binary modality. This property is desirable since the separation of resources is usually associative too. But the associativity of a binary modality generally makes the logic undecidable. We propose in this thesis to constrain the valuation of propositional variables to make modal logics with an associative binary modality decidable. The main part of the thesis is devoted to the study of variants of the Propositional Dynamic Logic (PDL). These logics features an infinite set of unary modalities representing actions, structured by some operators like sequential composition, iteration and non-deterministic choice. We first study branching time variants of PDL and prove that the satisfiability problems of these logics have the same complexity as the corresponding branching-time temporal logics. Then we thoroughly study extensions of PDL with an operator for parallel composition of actions called separating parallel composition and based on the semantics of binary modalities. This operator allows to reason about resources, in addition to actions. Moreover, the combination of actions and resources provides a convenient expression of concurrency. In particular, these logics can express situations of cooperation where some actions can be executed only in parallel with some other actions. Finally, our main contribution is to prove that the complexity of the satisfiability problem of a practically useful variant of PDL with separating parallel composition is the same as the satisfiability problem of plain PDL.

Made available in DSpace on 2015-03-03T15:47:48Z (GMT). No. of bitstreams: 1 AdrianoAD_DISSERT.pdf: 771338 bytes, checksum: 06adea5feab9914c5a48eb146511b556 (MD5) Previous issue date: 2013-11-19 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / I thank to my advisor, Jo?o Marcos, for the intellectual support and patience that devoted me along graduate years. With his friendship, his ability to see problems of the better point of view and his love in to make Logic, he became a great inspiration for me. I thank to my committee members: Claudia Nalon, Elaine Pimentel and Benjamin Bedregal. These make a rigorous lecture of my work and give me valuable suggestions to make it better. I am grateful to the Post-Graduate Program in Systems and Computation that accepted me as student and provided to me the propitious environment to develop my research. I thank also to the CAPES for a 21 months fellowship. Thanks to my research group, LoLITA (Logic, Language, Information, Theory and Applications). In this group I have the opportunity to make some friends. Someone of them I knew in my early classes, they are: Sanderson, Haniel and Carol Blasio. Others I knew during the course, among them I?d like to cite: Patrick, Claudio, Flaulles and Ronildo. I thank to Severino Linhares and Maria Linhares who gently hosted me at your home in my first months in Natal. This couple jointly with my colleagues of student flat Fernado, Don?tila and Aline are my nuclear family in Natal. I thank my fianc?e Lucl?cia for her precious a ective support and to understand my absence at home during my master. I thank also my parents Manoel and Zenilda, my siblings Alexandre, Paulo and Paula.Without their confidence and encouragement I wouldn?t achieve success in this journey. If you want the hits, be prepared for the misses Carl Yastrzemski / Esta disserta??o trata do enriquecimento de l?gicas modais. O termo enriquecimento ? usado em dois sentidos distintos. No primeiro deles, de fundo sem?ntico, propomos uma sem?ntica difusa para diversas l?gicas modais normais e demonstramos um resultado de completude para uma extensa classe dessas l?gicas enriquecidas com m?ltiplas inst?ncias do axioma da conflu?ncia. Um fato curioso a respeito dessa sem?ntica ? que ela se comporta como as sem?nticas de Kripke usuais. O outro enriquecimento diz respeito ? expressividade da l?gica e se d? por meio da adi??o de novos conectivos, especialmente de nega??es modais. Neste sentido, estudamos inicialmente o fragmento da l?gica cl?ssica positiva estendido com uma nega??o modal paraconsistente e mostramos que essa linguagem ? forte o suficiente para expressar as linguagens modais normais. Vemos que tamb?m ? poss?vel definir uma nega??o modal paracompleta e conectivos de restaura??o que internalizam as no??es de consist?ncia e determina??o a n?vel da linguagem-objeto. Esta l?gica constitui-se em uma L?gica da Inconsist?ncia Formal e em uma L?gica da Indetermina??o Formal. Em tais l?gicas, com o objetivo de recuperar infer?ncias cl?ssicas perdidas, demonstram-se Teoremas de Ajuste de Derivabilidade. No caso da l?gica estendida com uma nega??o paraconsistente, se removermos a implica??o ainda lidaremos com uma linguagem bastante rica, com ambas nega??es paranormais e seus respectivos conectivos de restaura??o. Sobre esta linguagem estudamos a l?gica modal normal minimal definida por meio de um c?lculo de Gentzen apropriado, ? diferen?a dos demais sistemas estudados at? ent?o, que s?o apresentados via c?lculo de Hilbert. Em seguida ap?s demonstrarmos a completude do sistema dedutivo associado a este c?lculo, introduzimos algumas extens?es desse sistema e buscamos Teoremas de Ajuste de Derivabilidade adequados

Automated deduction procedures for modal logics, and related decidable fragments of first-order logic, are used in many real-world applications. A popular way of obtaining decision procedures for these logics is to base them on semantic tableau calculi. We focus on calculi that use unification, instead of the more widely employed approach of generating ground instantiations over the course of a derivation. The most common type of tableaux with unification are so-called free-variable tableaux, where variables are treated as global to the entire tableau. A long-standing open problem for procedures based on free-variable tableaux is how to ensure fairness, in the sense that "equivalent" applications of the closure rule are prevented from being done over and over again. Some solutions such as using depth-first iterative deepening are known, but those are unnecessary in theory, and not very efficient in practice. This is a main reason why there are hardly any decision procedures for modal logics based on free-variable tableaux. In this thesis, we review existing work on incorporating unification into first-order and modal tableau procedures, show how the closure fairness problem arises, and discuss existing solutions to it. For the first-order case, we outline a calculus which addresses the closure fairness problem. As opposed to free-variable tableaux, closure fairness is much easier to achieve in disconnection tableaux and similar clausal calculi. We therefore focus on using clausal first-order tableau calculi for decidable classes, in particular the two-variable fragment. Using the so-called unrestricted blocking mechanism for enforcing termination, we present the first ground tableau decision procedure for this fragment. Even for such a ground calculus, guaranteeing that depth-first terminations terminate is highly non-trivial. We parametrise our procedure by a so-called lookahead amount, and prove that this parameter is crucial for determining whether depth-first derivations terminate or not. Extending these ideas to tableaux with unification, we specify a preliminary disconnection tableau procedure which uses a non-grounding version of the unrestricted blocking rule.