Representando o processo criativo da prova nos Grafos Existenciais

José Renato Salatiel

Resumo


Os Grafos Existenciais (GEs) de Charles S. Peirce são reconhecidos como o primeiro sistema lógico heterogêneo completo e correto equivalente à lógica predicativa de primeira ordem. Por sistema lógico heterogêneo entende-se aquele que combina uma sintaxe sentencial e diagramática. Neste artigo propomos a tese de que sistemas formais heterogêneos podem ser mais eficientes na investigação de estratégias de derivação e análise de hipóteses na prova, em razão dos elementos visuais presentes na linguagem diagramática. Como método de estudo sugere-se uma comparação do cálculo de dedução natural como os sistemas Alfa e Beta dos GEs, para a demonstração de alguns teoremas da lógica proposicional e de predicados. Justificamos a escolha em razão de ambos os métodos serem similares na composição de regras de inferências e nos propósitos por parte de seus autores (Peirce e Gentzen).

 

Abstract

The Charles S. Peirce's Existential Graphs (EGs) are recognized as the first complete and sound heterogeneous logical system equivalent to first order predicate logic. By heterogeneous logical system we mean one which combines a sentential and diagrammatical syntax. I propose in this paper the thesis that heterogeneous formal systems can be more effective inquiring strategies of derivation and in the analysis of assumptions in proofs, because of the visual aspects present in the diagrammatical language. As a method of study I suggest the comparison between the natural deduction calculus and the Alpha and Beta's systems of the EGs for demonstration of some theorems in the propositional and predicate logic. This choice is justified by the similarities found in the composition of rules of inference and purpose of the authors (Peirce and Gentzen) in both methods.

Recebido em novembro de 2014
Aprovado em março de 2015

Palavras-chave


Lógica; Diagramas; Charles Peirce; Grafos Existenciais; Dedução natural; Prova; Semiótica;Logic; Diagrams; Existential graphs; Natural deduction; Proof;Semiotic.

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Referências


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DOI: https://doi.org/10.35920/arf.2014.v18i1.133-160



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