This paper is an attempt to solve the following problem: given a logic, how to turn it into a paraconsistent one? In other words, given a logic in which ex falso quodlibet holds, how to convert it into a logic not satisfying this principle? We use a framework provided by category theory in order to define a category of consequence structures. Then, we propose a functor to transform a logic not able to deal with contradictions into a paraconsistent one. Moreover, (...) we study the case of paraconsistentization of propositional classical logic. (shrink)

Some strategies to turn any logic into a paraconsistent system are examined. In the environment of universal logic, we show how to paraconsistentize logics at the abstract level using a transformation in the class of all abstract logics called paraconsistentization by consistent sets. Moreover, by means of the notions of paradeduction and paraconsequence we go on applying the process of changing a logic converting it into a paraconsistent system. We also examine how this transformation can be performed using multideductive abstract (...) logics. To conclude, the conceptual notion paraconsistent orbit of a logic is proposed. (shrink)

This paper analyzes the problem of implication and attempts to characterize conditionals by a criterion of adequacy. A definition of implication based on the notion of limit of an infinite sequence is proposed.

This article introduces some concepts that help exploring the ontological import of universal logic. It studies the notions of an antilogic and counterlogic associated to each logic and shows some of their properties. It presents the notion of galaxy, as the class of possible worlds compatible with a given logic.We explore some consequences of these developments.

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 paper shows how to transform explosive many-valued systems into paraconsistent logics. We investigate mainly the case of three-valued systems exhibiting how non-explosive three-valued logics can be obtained from them.

This paper is about the concept of semantically closed languages. Roughly speaking, those are languages which can name their own sentences and apply to them semantic predicates, such as the truth or satisfaction predicates. Hence, they are “self-referential languages,” in the sense that they are capable of producing sentences about themselves or other sentences in the same language. In section one, we introduce the concept informally; in section two, we provide the formal definition of first-order semantically closed languages, which is (...) the Tarskian definition with some technical modifications. Then, we construct a semantic for this kind of language, and prove that the language is indeed semantically closed (according to Definition 1). Finally, we discuss whether the logic underlying the construction is classical, and future goals of this research. (shrink)

O objetivo deste trabalho é apresentar uma definição materialmente adequada de verdade, no sentido de Tarski, para uma classe de linguagens formais capaz de expressar as proposições categóricas da lógica aristotélica.The aim of this paper is to put forward a materially adequate definition of truth, in Tarski's sense, for a class of formal languages that would be able to represent the categorical propositions of Aristotelian logic.

Resumo: No presente artigo, discutiremos os aspectos filosóficos de teorias de conjuntos paraconsistentes. A fim de ilustrar nossas considerações de modo mais concreto, abordaremos uma nova teoria de conjuntos baseada em um sistema bem conhecido de Quine e em um cálculo paraconsistente.Palavras-chave: existência, contradição, lógica e paraconsistência.: In the present paper we deal with the philosophical aspects of paraconsistent set theories. In order to illustrate our points more concretely, we will discuss new paraconsistent set theory based both on Quine's well-known (...) system and on a paraconsistent calculus.Keywords: existence, contradiction, logic and paraconsistency. (shrink)

Resumo: Apresentamos uma abordagem geral da demonstração de completude de cálculos lógicos abstratos por meio da noção de valoração e de um resultado devido a A. Lindenbaum.: We present a general approach to the proof the completeness of abstract logical calculi through the notion of valuation and of a result due to A. Lindenbaum.

We present a kind of logic named multideductive logic and outline an application of it in the problem of theoretic-formal unification of physical theories dealing with the Bohr atom theory. This is just a preliminary study that will be developed in future papers.

Resumo: Examinar-se á o conceito de verdade pragmática em uma perspectiva que poderia ser denominada de pragmática. Assim, pretende-se apresentar, de um ponto de vista lógico-formal, a idéia de verdade pragmática num sentido de que uma proposição é pragmaticamente verdadeira se e somente se, em determinado contexto, tudo se passa como se ela fosse verdadeira do ponto de vista correspondencial. Ora, A. Tarski, em 1933, ao examinar o conceito de verdade nas linguagens formalizadas forneceu uma definição precisa de verdade inaugurando (...) assim os estudos semânticos e criando o que hoje entendemos por teoria dos modelos. Da mesma forma, Mikemberg, Chuaqui e da Costa, em um trabalho de 1986, forneceram uma noção precisa de quase verdade que pode ser considerada uma espécie de versão do conceito pragmático de verdade. Apresentar-se-á, em linhas gerais, o conceito formal de quase-verdade, junto com alguns desenvolvimentos que foram obtidos a partir do mesmo em problemas de filosofia da ciência.: It's our goal to analyze the concept of pragmatic truth in a perspective that could be called pragmatic. Therefore, we intend to present, from a formal=logic point of view, the idea of pragmatic truth, as meaning a proposition which Is pragmactilly truthful, if and only if, in a determinate context, everything runs as it was truthful in a correspondential perspective. In 1933, A Tarski, while examining the truth concept in formalized languages, gave a precise definition of truth inaugurating with it the semantic studies and creating what we understand, in our days, as theory of models. In the same way, Mikenberg, Chuaqui and da Costa, in a work of 1986, conceived a precise notion of almost-truth, which can be considered as a version of pragmatic truth conception. We intend to show, in general ways, the formal concept of almost-truth among some developments obtained from this same concept in philosophy of science. (shrink)

Resumo: Pretendemos esboçar o conceito de lógica multidedutiva que constitui um sistema lógico subjacente à noção de verdade pragmática. Com base em lógicas multidedutivas, delineamos um aparato formal para o tratamento apropriado de inconsistências em teorias físicas.: we intend to delineate the concept of multideductive logic that constitutes a subjacent logical system for the pragmatic notion of truth. Based upon the multideductive logic we have pictured a formal apparatus used as an appropriate treatment to the inconsistencies in Physics theories.

Infinitary languages are used to prove that any strong isomorphism of substructures of isomorphic structures can be extended to an isomorphism of the structures. If the structures are models of a theory that has quantifier elimination, any isomorphism of substructures is strong. This theorem is a partial generalization of Steinitz’s theorem for algebraically closed fields and has as special case the analogous theorem for differentially closed fields. In this note, we announce results which will be proved elsewhere.

We present a kind of logic named multideductive logic and outline an application of it in the problem of theoretic-formal unification of physical theories dealing with the Bohr atom theory. This is just a preliminary study that will be developed in future papers.

Resumo: A partir de um raciocínio equivocado acerca do significado dos teoremas de completude e incompletude de Gödel, apresentamos alguns importantes conceitos de lógica matemática e, com base em uma análise dos teoremas acima, concluímos mencionando a existência de modelos não standard da Aritmética de Peano.Palavras-chave: Completude. Incompletude. Teoremas de Gödel: From a mistaken reasoning about the completeness and incompleteness Gödel's theorems, we show important concepts of mathematical logic and, based on above theorems, we conclude showing the existence of non (...) standard models for Peano's Arithmetic.Keywords: Completeness. Incompleteness. Gödel's theorems. (shrink)