Caríssimos amigos, mestres e colegas,

Quando encontro um artigo de que gosto, faço questão de o divulgar. E este 
inclusive é de autoria da estimada Valéria de Paiva que participa desta lista. 
O texto encontra-se no sítio academia.edu.

A Short Note on Intuitionistic Propositional Logic with Multiple Conclusions
By Valeria de Paiva
Manuscrito, 2005

It is a common misconception among logicians to think that intuition-ism is 
necessarily tied-up with single conclusion (sequent or Natural Deduction) 
calculi. Single conclusion calculi can be used and are convenient, but they are 
by no means necessary, as shown by such influential authors as Kleene, Takeuti 
and Dummett, to cite only three. If single conclusions are not necessary, how 
do we guarantee that only intuitionistic derivations are allowed? Traditionally 
one insists on restrictions on particular rules: implication right, negation 
right and universal quantification right are required to be single conclusion 
rules. In this note we show that instead of a cardinality restrictionm such as 
one conclusion only, we can use a notion of dependency between formulae to 
enforce the constructive character of derivations.











Most problems of teaching are not problems of growth but helping cultivate 
growth. As far as I know, and this is only from personal experience in 
teaching, I think about ninety percent of the problem in teaching, or maybe 
ninety-eight percent, is just to help the students get interested. 
Noam Chomsky 

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