Departing from basic concepts in abstract logics, this paper introduces two concepts: conjunctive and disjunctive limits. These notions are used to formalize levels of modal operators.

This book explores the interplay between logic and science, describing new trends, new issues and potential research developments.

This paper briefly outlines some advancements in paraconsistent logics for modelling knowledge representation and reasoning. Emphasis is given on the so-called Logics of Formal Inconsistency (LFIs), a class of paraconsistent logics that formally internalize the very concept(s) of consistency and inconsistency. A couple of specialized systems based on the LFIs will be reviewed, including belief revision and probabilistic reasoning. Potential applications of those systems in the AI area of KRR are tackled by illustrating some examples that emphasizes the importance of (...) a fine-tuned treatment of consistency in modelling reputation systems, preferences, argumentation, and evidence. (shrink)

O objetivo geral da pesquisa da qual esse artigo faz parte é investigar o sistema metafísico que emerge dos trabalhos de David Lewis. Esse sistema pode ser decomposto em pelo menos duas teorias. A primeira nomeada como realismo modal genuíno (RMG) e a segunda como mosaico neo-humeano. O RMG é, sem dúvida, mais popular e defende a hipótese metafísica da existência de uma pluralidade de mundos possíveis. A principal razão em favor dessa hipótese é a sua aplicabilidade na discussão de (...) problemas losó cos, esse motivo não será diretamente abordado neste artigo. Pois, o foco está em compreender o mosaico neo-humea- no e como ele relaciona-se com a metafísica de mundos possíveis. Em outras palavras, o meu objetivo é entender as bases losó cas que sus- tentam o realismo modal genuíno. (shrink)

De modo geral, este texto é uma incursão em lógica filosófica e filosofia da lógica. Ele contém reflexões originais acerca dos conceitos de paraconsistência, modalidades e cognoscibilidade e suas possíveis relações. De modo específico, o texto avança em quatro direções principais: inicialmente, uma definição genérica de lógicas não clássicas utilizando a ideia de lógica abstrata é sugerida. Em seguida, é mostrado como técnicas manuais de paraconsistentização de lógicas são usadas para gerar sistemas particulares de lógicas paraconsistentes. Depois, uma definição de (...) possibilidade lógica é proposta por meio da ideia de limites de sequências de fórmulas. Por fim, muitas abordagens distintas ao paradoxo de Fitch e, consequentemente, aos limites do conhecimento são apresentadas considerando as reflexões anteriores. (shrink)

The terms “model” and “model-building” have been used to characterize the field of formal philosophy, to evaluate philosophy’s and philosophical logic’s progress and to define philosophical logic itself. A model is an idealization, in the sense of being a deliberate simplification of something relatively complex in which several important aspects are left aside, but also in the sense of being a view too perfect or excellent, not found in reality, of this thing. Paraconsistent logic is a branch of philosophical logic. (...) It is however not clear how paraconsistent logic can be seen as model-building. What exactly is modeled? In this paper I adopt the perspective of looking at a particular instance of paraconsistent logic—paranormal modal logic—which might be seen as a model of a specific kind of agent: inductive agents. After ntroducing what I call the highlevel and low-level models of inductive agents, I analyze the extent to which the above-mentioned idealizing features of model-building appear in paranormal modal logic and how they affect its philosophical significance. (shrink)

The purpose of this paper is twofold. First we want to extent a specific paranormal modal logic in such a way as obtain a paraconsistent and paracomplete multimodal logic able to formalize the notions of plausibility and certainty. With this logic at hand, and this is our second purpose, we shall use a modified version of Reiter‘s default logic to build a sort of inductive logic of plausibility and certainty able to represent some basic principles of epistemic inductive reasoning, such (...) as a negative autoepistemic principle, an `error-prone feature of induction' principle and a confirmation by enumeration principle. (shrink)

An overcomplete logic is a logic that ‘ceases to make the difference’: According to such a logic, all inferences hold independently of the nature of the statements involved. A negation-inconsistent logic is a logic having at least one model that satisfies both some statement and its negation. A negation-incomplete logic has at least one model according to which neither some statement nor its negation are satisfied. Paraconsistent logics are negation-inconsistent yet non-overcomplete; paracomplete logics are negation-incomplete yet non-overcomplete. A paranormal logic (...) is simply a logic that is both paraconsistent and paracomplete. -/- Despite being perfectly consistent and complete with respect to classical negation, nearly every normal modal logic, in its ordinary language and interpretation, admits to some latent paranormality: It is paracomplete with respect to a negation defined as an impossibility operator, and paraconsistent with respect to a negation defined as non-necessity. In fact, as it will be shown here, even in languages without a primitive classical negation, normal modal logics can often be alternatively characterized directly by way of their paranormal negations and related operators. So, instead of talking about ‘necessity’, ‘possibility’, and so on, modal logics could be seen just as devices tailored for the study of (modal) negation. This paper shows how and to what extent this alternative characterization of modal logics can be realized. (shrink)

We present a philosophical motivation for the logics of formal inconsistency, a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language. We shall defend the view according to which logics of formal inconsistency are theories of logical consequence of normative and epistemic character. This approach not only allows us to make inferences in the presence of contradictions, but offers a philosophically acceptable account of paraconsistency.