|
|
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. |
|
|