Paraconsistent probabilities: consistency, contradictions and bayes' theorem

2010/51038-0sem informaçãoThis paper represents the first steps towards constructing a paraconsistent theory of probability based on the Logics of Formal Inconsistency (LFIs). We show that LFIs encode very naturally an extension of the notion of probability able to express sophisticated probabilistic reasoning under contradictions employing appropriate notions of conditional probability and paraconsistent updating, via a version of Bayes' theorem for conditionalization. We argue that the dissimilarity between the notions of inconsistency and contradiction, one of the pillars of LFIs, plays a central role in our extended notion of probability. Some critical historical and conceptual points about probability theory are also reviewed.This paper represents the first steps towards constructing a paraconsistent theory of probability based on the logics of formal inconsistency (LFIs). We show that LFIs encode very naturally an extension of the notion of probability able to express sophisticated probabilistic reasoning under contradictions employing appropriate notions of conditional probability and paraconsistent updating, via a version of Bayes' theorem for conditionalization. We argue that the dissimilarity between the notions of inconsistency and contradiction, one of the pillars of LFIs, plays a central role in our extended notion of probability. Some critical historical and conceptual points about probability theory are also reviewed.189FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTIFICO E TECNOLOGICOFAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTIFICO E TECNOLOGICO2010/51038-0sem informaçã

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