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Jeudi 22 Novembre
| Heure: |
10:30 - 12:00 |
| Lieu: |
Salle B107, bâtiment B, Université de Villetaneuse |
| Résumé: |
Soft modalities as prices: a game model for intuitionistic linear logic with subexponentials |
| Description: |
Carlos Olarte We look at substructural calculi from a game semantic point of view,
guided by certain intuitions about resource conscious and, more
specifically, cost conscious reasoning. To this aim, we start with a
game for aILL (affine intuitionistic linear logic), where player I
defends a claim corresponding to a (single-conclusion) sequent, while
player II tries to refute that claim. Branching rules for additive
connectives are modeled by choices of II, while branching for
multiplicative connectives leads to splitting the game into parallel
subgames, all of which have to be won by player I to succeed. The game
comes into full swing by using subexponentials for representing two
types of options - volatile and permanent - for purchasing
resources. This leads to a new type of subexponetial calculus where
costs are attached to sequents. Different proofs are interpreted as
more or less expensive strategies to obtain a certain resource from a
bunch of resources (priced options). Finally, we generalize the
concept of costs and option's prices in proofs by using a semiring
structure. This general framework allows us to
interpret a wider range of subexponential systems and give meaning
to the use of resources in proofs in a more flexible way. |
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