Open AccessA Weakly-Intuitionistic Logic I1
Author(s) -
Я. Чючюра
Publication year - 2015
Publication title -
logičeskie issledovaniâ
Language(s) - English
Resource type - Journals
eISSN - 2413-2713
pISSN - 2074-1472
DOI - 10.21146/2074-1472-2015-21-2-53-60
Subject(s) - duality (order theory) , propositional calculus , calculus (dental) , mathematics , intuitionistic logic , dual (grammatical number) , translation (biology) , function (biology) , paraconsistent logic , pure mathematics , algebra over a field , discrete mathematics , computer science , linguistics , philosophy , higher order logic , artificial intelligence , medicine , dentistry , biochemistry , chemistry , evolutionary biology , biology , messenger rna , description logic , gene
In 1995, Sette and Carnielli presented a calculus, $I1$, which is intended to be dual to the paraconsistent calculus $P1$. The duality between $I1$ and $P1$ is reflected in the fact that both calculi are maximal with respect to classical propositional logic and they behave in a special, non-classical way, but only at the level of variables. Although some references are given in the text, the authors do not explicitly define what they mean by ‘duality’ between the calculi. For instance, no definition of the translation function from the language of $I1$ into the language of $P1$ (or from $P1$ to $I1$) was provided (see [4], pp. 88–90) nor was it shown that the calculi were functionally equivalent (see [13], pp. 260–261).The purpose of this paper is to present a new axiomatization of $I1$ and briefly discuss some results concerning the issue of duality between the calculi.