Composing causal orderings Speaker(s): Aleks Kissinger
Abstract: When studying (definite or indefinite) causal orderings of processes, it is often useful to consider higherorder processes, i.e. processes which take other processes as their input. However, as a recent nogo result of Guerin et al indicates, our naive firstorder notions of "composition" of processes become illdefined at higherorder. Unlike state spaces, there are multiple nonequivalent notions of "joint system" for process spaces and many different ways one might attempt to plug processes together, with only some giving welldefined (i.e. normalised) processes as outputs. While this starts to look a bit like the Wild West, I'll show in this talk that we can get quite a bit of mileage from considering just two kinds of joint systems: a "nonsignalling" tensor product, and a (de Morgan dual) "signalling" product. The interaction between these two products has in fact been wellunderstood by logicians since the 1980s in a very different disguise: multiplicative linear logic. Using this connection, I'll show how a set of "contractibility" criteria due to Danos and Regnier give a relatively simple, dimensionindependent technique for determining whether an arbitrary plugging of higherorder processes is welldefined.
Date: 09/12/2019  2:00 pm
Collection: Indefinite Causal Structure
