How to link Semiotic Theory with Logical Deduction III

How to link Semiotic Theory with Logical Deduction III

Alfred Olszok

This talk will be the last one of a series of talks containing three in total, all organised by my colleagues from Brasil at PUCSP and UNICAMP. In my last talk titled How to Link Semiotic Theory with Logical Deduction II at the CLE in Campinas I presented the Existential Graphs of Charles Sanders Peirce from two points of view. On the one hand we are supposed to analyze them in relation to the Semiotic Theory also invented by Peirce and on the other hand we can reinterpret them from a more modern and thus mathematical viewpoint. For both, I outlined three topics:

1) the structure of the Semiotic Theory of C. S. Peirce,[2]

2) the way of deduction of Existential Graphs [4] and

3) the intersecting motivations of both.

A new System of Graphs for Intuitionistic Propositional Logic, called Granit, stands in the center of all this investigations. As shown by Oostra [1] and Pietarinen [3] Intuitionistic Propositional Logic can be evolved by enriching the original language of Existential Graphs by new signs and in result, also new rules. But since Granit utilizes only the signs invented by Peirce, it is closer to the Gamma Graphs of Peirce and its extension Gamma-4 constructed by Zeman.[5] As a result of which the rules of Granit are also closer to the original concept of Peirce, which is the reason why Granit, in contrast to the Graphs of Oostra and Pietarinen, can rather be rooted in Semiotic Theory. Respectively 3) I presented you three ideas concerning the intersection of Granit and Semiotics:

3.1) the link of the language of Granit and Semiotics,

3.2) the link of the semantics of Granit and Semiotics and

3.3) the link of the way of deduction of Granit and Semiotics.

Since the language of Granit presupposes its semantics and moreover, by inuencing its rules, also its way of deduction , the sub-items of 3) have to be examined together, which will be the main objective of my talk. For this purpose, I will give you a circumstantial overview of the signs, the semantics and the rules of Granit focused on their particular roots in the Semiotic Theory. By this, I hope to disclose the possibility, to arise Logical Deduction mainly from Semiotic Theory.