## 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.