Niveau: Supérieur, Doctorat, Bac+8
MELL in a Free Compact Closure Etienne Duchesne Laboratoire d'Informatique de Paris Nord Abstract. We present a step by step construction of the exponential modality in the context of the free compact closure Int(PInj) of sets and partial functions. Each step provides a key feature necessary to compute the exponential formula of Mellies, Tabareau & Tasson [MTT09]. We obtain a denotational model of multi- plicative and exponential linear logic based on the geometry of interaction. 1 Introduction Linear logic relies on a policy of hypothesis consumption: when proving a sequent A1, . . . , An B, each hypothesis Ai is used exactly once in the course of the reason- ing. This restriction restores the idempotency of double negation A?? = A, and in particular the linear implication A( B can be defined by means of linear conjunction (the tensor product ?) and negation: A( B = (A?B?)?. However most reasonings need the duplication or the discarding of the hypothesis. The role of the exponential modality !A is to provide this expressivity: we explicitly denote !A the formula A on which we want to perform such non-linear reasonings. The logic obtained from these connectives is called multiplicative and exponential linear logic (MELL). The general structure shared by the various models of MELL can be expressed synthetically with the language of category theory (see [Mel02] for a survey).
- trace operator
- category having
- a?u ?
- free compact
- m? ?
- ip-pairs m?
- exponential
- category
- injection-projection pair
- tive comonoid