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## Section: New Results

### Hybrid Linear Logic, revisited

Participant : Kaustuv Chaudhuri.

Hybrid Linear Logic (HyLL) was proposed by Chaudhuri and Despeyroux in 2010 as a meta-logic for reasoning about constrained transition systems, with applications to a number of domains including formal molecular biology  [36]. This logic is an extension of (intuitionistic) linear logic with hybrid connectives that can reason about monoidal constraint domains such as instants of time or rate functions. Linear logic with subexponential is a different extension of linear logic that has been proposed as a mechanism for capturing certain well known constrained settings such as bigraphs  [39] or concurrent constraint programming  [65]. In a paper accepted to MSCS [5] we show how to relate these two extensions of linear logic by giving an embedding of HyLL into linear logic with subexponentials. Furthermore, we show that subexponentials are able to give an adequate encoding of CTL$*$, which is beyond the expressive power of HyLL. Thus, subexponentials appear to be the better choice as a foundation for constraints in linear logic.