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workshop_2 [2014/05/30 08:45]
mellies
workshop_2 [2014/05/30 08:45] (current)
mellies
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 //​Polarities and classical constructiveness//​ //​Polarities and classical constructiveness//​
  
-> I will recall what constructive can mean in the context of classical logic, as accounted for by double negation translations and control operators in programming. +> I will recall what constructive can mean in the context of classical logic, as accounted for by double negation translations and control operators in programming. Girard proposed a few years back a classical sequent calculus where negation is strictly involutive (¬¬A = A) by taking formally into account the polarity of connectives. I will show that this idea is very natural from the point of view of control operators, leading us to a natural deduction where negation is involutive (¬¬A ≅ A). One of the main aspect is that we do not consider that composition needs to be associative when the middle map is from positives to negatives. In a second time I will therefore introduce duploids, which characterises this non-associative composition directly, and relate them to adjunctions.
-Girard proposed a few years back a classical sequent calculus where negation is strictly involutive (¬¬A = A) by taking formally into account the polarity of connectives. I will show that this idea is very natural from the point of view of control operators, leading us to a natural deduction where negation is involutive (¬¬A ≅ A). +
-One of the main aspect is that we do not consider that composition needs to be associative when the middle map is from positives to negatives. In a second time I will therefore introduce duploids, which characterises this non-associative composition directly, and relate them to adjunctions.+
  
 **Palmgren**\\ **Palmgren**\\
workshop_2.txt · Last modified: 2014/05/30 08:45 by mellies
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