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workshop_2 [2014/05/30 08:33] streicher [Lectures] |
workshop_2 [2014/05/30 08:45] (current) mellies |
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| ^Monday 2 June||| | ^Monday 2 June||| | ||
| |10h30-12h00|Per Martin-Löf|//Sample space-time //|| | |10h30-12h00|Per Martin-Löf|//Sample space-time //|| | ||
| - | |14h00-15h30|Peter Dybjer|//What is a model of type theory//| | + | |14h00-15h30|Peter Dybjer|//What is a model of intuitionistic type theory//| |
| |16h00-17h30|Steve Awodey|//Natural Models of Type Theory//| | |16h00-17h30|Steve Awodey|//Natural Models of Type Theory//| | ||
| ^Tuesday 3 June||| | ^Tuesday 3 June||| | ||
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| //Polarities and classical constructiveness// | //Polarities and classical constructiveness// | ||
| - | > I will recall what constructive can mean in the context of classical | + | > 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. |
| - | 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 (not not 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 (not not 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**\\ | ||