(Feitosa, Grácio, Nascimento, 2007) introduziram uma nova lógica, a Lógica TK, que foi apresentada inicialmente no estilo hilbertiano. O objetivo deste trabalho é apresentar a Lógica TK em sistemas de dedução natural, cálculo de sequentes e tableaux assim como demonstrar a equivalência entre esses novos sistemas e o original.

Este texto apresenta um breve histórico da lógica TK, originalmente motivada pelo conceito de operador de consequência de Tarski, a sua adequação segundo os Espaços de Tarski e uma caracterização como uma lógica modal não normal. Como novidade, mostra como interpretar suas fórmulas em polinômios sobre uma TK-álgebra e discorre sobre a decidibilidade algébrica de TK segundo esta interpretação polinomial.

The logic TK was introduced as a propositional logic extending the classical propositional calculus with a new unary operator which interprets some conceptions of Tarski’s consequence operator. TK-algebras were introduced as models to TK. Thus, by using algebraic tools, the adequacy of TK relatively to the TK-algebras was proved. This work presents a neighbourhood semantics for TK, which turns out to be deductively equivalent to the non-normal modal logic EMT4.

Tarski presented his definition of consequence operator to explain the most important notions which any logical consequence concept must contemplate. A Tarski space is a pair constituted by a nonempty set and a consequence operator. This structure characterizes an almost topological space. This paper presents an algebraic view of the Tarski spaces and introduces a modal propositional logic which has as a model exactly the closed sets of a Tarski space. • DOI:10.5007/1808-1711.2010v14n1p47.

Apresentamos conceitos algébricos básicos e fundamentais como conjuntos ordenados, reticulados, álgebra de Boole e as TK-álgebras. Destacamos os espaços de Tarski, associados ao conceito de sistema dedutivo e sua apresentação quase topológica. Então, apresentamos a Lógica da Dedutibilidade, vinda da formalização lógica dos espaços de Tarski. A seguir, trazemos os pares de funções de Galois, que surgem em muitos tópicos da Matemática. Como resultado original, além de alguns desenvolvimentos teóricos, destacamos uma conexão de Galois com os espaços de (...) Tarski. (shrink)

Dewey’s understanding of democratic school life is regarded as the early foundation of democratic education (Cohen et al. 2009). Similarly, Biesta (2007) underlines the significant role of schools...

Over the past 50 years, Nelson algebras have been extensively studied by distinguished scholars as the algebraic counterpart of Nelson's constructive logic with strong negation. Despite these studies, a comprehensive survey of the topic is currently lacking, and the theory of Nelson algebras remains largely unknown to most logicians. This paper aims to fill this gap by focussing on the essential developments in the field over the past two decades. Additionally, we explore generalisations of Nelson algebras, such as N4-lattices which (...) correspond to the paraconsistent version of Nelson's logic, as well as their applications to other areas of interest to logicians, such as duality and rough set theory. A general representation theorem states that each Nelson algebra is isomorphic to a subalgebra of a rough set-based Nelson algebra induced by a quasiorder. Furthermore, a formula is a theorem of Nelson logic if and only if it is valid in every finite Nelson algebra induced by a quasiorder. (shrink)

En las primeras páginas de la Ciencia de la lógica, el pensar tiene la pretensión de iniciar su propio movimiento sin aceptar ningún pensamiento dado o presuposición como la paradójica y pura autorreferencia del vínculo de ser y nada. De acuerdo conesto, proponemos una lectura que afirma la presencia de una negatividad que explica la actividad inmanente del pensar en el inicio de la Ciencia de la lógica.

The 'Perutilis logica' is both by its content and its didactic value the most paradigmatic logical compendium of the 14th century. The study presented here tries to show on the basis of an interpretative analysis of the second treatise that the doctrine of the properties of terms is stated in a unusually developed form in the 'Perutilis logica' and that suggestions that it lacks originality must be revised.