Applicability of fair simulation

AbstractIn this paper we compare four notions of fair simulation: direct [9], delay [12], game [19], and exists [16]. Our comparison refers to three main aspects: The time complexity of constructing the fair simulation, the ability to use it for minimization, and the relationship between the fair simulations and universal branching-time logics. We developed a practical application that is based on this comparison. The application is a new implementation for the assume-guarantee modular framework presented By Grumberg at al. in [ACM Transactions on Programming Languages and Systems (TOPLAS), 16 (1994) 843]. The new implementation significantly improves the complexity of the framework

Interpolation in Fragments of Intuitionistic Propositional Logic

We show in this paper that all fragments of intuitionistic propositional logic based on a subset of the connective ∧, ∨, →, ¬ satisfy interpolation. Fragments containing ↔ or ¬¬ are briefly considered

The interpolation theorem in fragments of logics

In the first part of this paper, we prove that there are continuously many fragments of intuitionistic propositional calculus (IpC) which fail to have the interpolation property, thereby extending an earlier result. Our proof makes use of the Rieger-Nishimura lattice. The second part is devoted to transferring this result to fragments of classical predicate calculus (CPC): this is done by giving a translation T of fragments of IpC in fragments of CPC which preserves the interpolation property

Paraconsistent modalities as a basis for treating epistemic-doxastic paradoxes

Orientador: Itala Maria Loffredo D'OttavianoDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciências HumanasResumo: Pretende-se nesta dissertação analisar sistemas de lógicas modais paraconsistentes que sirvam de base para o tratamento formal de Paradoxos no âmbito das Lógicas Epistêmico-Doxásticas, lógicas modais que formalizam as noções de conhecimento e crença. Estas por sua vez são interpretações de lógicas modais baseadas na lógica clássica, na qual demonstra-se o Princípio Ex Falso Sequitur Quodlibet, conhecido também como Princípio de Explosão. A demonstração deste Princípio nestas lógicas contribui para resultados indesejados como o Paradoxo da Cognoscibilidade (ou Paradoxo de Fitch), e o Paradoxo da Credibilidade, ambos resultados que levam aos colapsos dos operadores de crença e conhecimento, respectivamente. Algumas soluções têm sido propostas para lidar com os Paradoxos, dentre elas rejeitar certas hipóteses assumidas, tais como o Princípio de Cognoscibilidade. A presente dissertação segue outra linha, a saber, que busca investigar os efeitos decorrentes de dotar de bases paraconsistentes os sistemas nos quais os Paradoxos ocorrem. O aparato lógico que utilizaremos para esta tarefa são os chamados sistemas catódicos, introduzidos em [Bueno-Soler, 2009]. Estes são sistemas modais que contêm negações subclássicas em suas linguagens e podem ser vistos como combinações entre lógicas modais e paraconsistentes. Especificamente investigamos a possibilidade de que Lógicas da Inconsistência Formal (LFIs), introduzidas em [Carnielli e Marcos, 2002] e desenvolvidas em [Carnielli, Coniglio e Marcos, 2007] possam constituir sistemas catódicos promissores para o tratamento dos Paradoxos Epistêmico-DoxásticosAbstract: The aim of this dissertation is to analyze paraconsistent modal logic systems that serve as the basis for the formal treatment of Paradoxes within the framework of Epistemic-Doxastic Logics, modal logics that formalize the notions of knowledge and belief. These, in turn, are interpretations of modal logics based on classical logic, in which the Ex Falso Sequitur Quodlibet Principle, also known as the Explosion Principle, is demonstrable. The demonstration of this Principle in these logics contributes to unwanted outcomes such as the Paradox of Knowability (or Fitch Paradox), and the Credibility Paradox, both of which results in the collapse of belief and knowledge operators, respectively. Some solutions have been proposed to deal with the Paradoxes, among them rejecting certain assumed hypotheses, such as the Principle of Knowability. The present dissertation follows another line, namely, that seeks to investigate the effects of providing paraconsistent bases with the systems in which Paradoxes occur. The logical apparatus that we will use for this task are the so-called cathodic systems, introduced in [Bueno-Soler, 2009]. These are modal systems that contain subclassic negations in their languages and can be seen as combinations of modal and paraconsistent logics. Specifically, we investigated the possibility that Logics of Formal Inconsistency (LFIs), introduced in [Carnielli and Marcos, 2002] and developed in [Carnielli, Coniglio and Marcos, 2007] may constitute promising cathodic systems for the treatment of Epistemic-Doxastic ParadoxesMestradoFilosofiaMestre em Filosofia161480CAPE

Fuzzy Mathematics

This book provides a timely overview of topics in fuzzy mathematics. It lays the foundation for further research and applications in a broad range of areas. It contains break-through analysis on how results from the many variations and extensions of fuzzy set theory can be obtained from known results of traditional fuzzy set theory. The book contains not only theoretical results, but a wide range of applications in areas such as decision analysis, optimal allocation in possibilistics and mixed models, pattern classification, credibility measures, algorithms for modeling uncertain data, and numerical methods for solving fuzzy linear systems. The book offers an excellent reference for advanced undergraduate and graduate students in applied and theoretical fuzzy mathematics. Researchers and referees in fuzzy set theory will find the book to be of extreme value

Verification in the Hierarchical Development of Reactive Systems

In many approaches to the verification of reactive systems, operational semantics are used to model systems whereas specifications are expressed in temporal logics. Most approaches however fail to handle changes of the specification but assume, that the initial specification is indeed the intended one. Changing the specification thus necessitates to find an accordingly adapted system and to carry out the verification from scratch. During a systems life cycle however, changes of the requirements and resources necessitate repeated adaptations of specifications. We here propose a method that supports syntactic action refinement (in the process algebra TCSP and the Modal Mu-Calculus) and allows to automatically obtain (a priori) correct reactive systems by hierarchically adding details to the according specifications

Multimodalidades anodicas e catodicas : a negação controlada em logicas multimodais e seu poder expressivo

Orientador: Itala Maria Loffredo D'OttavianoTese (doutorado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciencias HumanasResumo: O presente trabalho tem por objetivo investigar o papel da negação no âmbito das modalidades, de forma a poder esclarecer até que ponto a negação pode ser atenuada, controlada ou mesmo totalmente eliminada em favor da melhor expressabilidade lógica de certas teorias, asserções ou raciocínios que sofrem os efeitos da negação. Contudo, atenuar ou eliminar a negação tem um alto preço: métodos tradicionais em lógica podem deixar de ser válidos e certos resultados, como teoremas de completude para sistemas lógicos, podem ser derrogados. Do ponto de vista formal, a questão central que investigamos aqui e até que ponto tais métodos podem ser restabelecidos. Com tal finalidade, iniciamos nosso estudo a partir do que denominamos sistemas anódicos" (sem negação) e, a posteriori, introduzimos gradativamente o elemento catódico" (negações, com diversas gradações e diferentes características) nos sistemas modais por meio de combinações com certas lógicas paraconsistentes, as chamadas lógicas da inconsistência formal (LFIs). Todos os sistemas tratados são semanticamente caracterizados por semânticas de mundos possíveis; resultados de incompletude são também obtidos e discutidos. Obtemos ainda semânticas modais de traduções possíveis para diversos desses sistemas. Avançamos na direção das multimodalidades, investigando os assim chamados sistemas multimodais anódicos e catódicos. Finalmente, procuramos avaliar criticamente o alcance e o interesse dos resultados obtidos na direção da racionalidade sensível à negação.Abstract: The present work aims to investigate the role of negations in the scope of modalities and in the reasoning expressed by modalities. The investigation starts from what we call anodic" systems (without any form of negation) and gradually reaches the cathodic" elements, where negations are introduced by means of combining modal logics with certain paraconsistent logics known as logics of formal inconsistency (LFIs). We obtain completeness results for all treated systems, and also show that certain incompleteness results can be obtained. The class of the investigated systems includes all normal modal logics that are extended by means of the schema Gk;l;m;n due to E. J. Lemmon and D. Scott combined with LFIs. We also tackle the question of obtaining modal possible-translations semantics for these systems. Analogous results are analyzed in the scope of multimodalities, where anodic as much as cathodic logics are studied. Finally, we advance a critical evaluation of the reach and scope of all the results obtained to what concerns expressibility of reasoning considered to be sensible to negation. We also critically assess the obtained results in contrast with problems of rationality that are sensible to negation.DoutoradoDoutor em Filosofi