Abstract

room subject to change

In this talk, I will introduce a new EPSRC -funded project on “Resources and co-Resources: A junction between semantics and descriptive complexity” which I jointly lead with Samson Abramsky.

The project seeks to explore ways in which methods from the study of logic and algorithms (specifically finite model theory and descriptive complexity) can be combined with methods from semantics (such as category theory) to build a cohesive algebraic theory of resources. This builds on recent work obtaining categorical accounts of essential constructions in finite model theory (by Abramsky, Dawar and Wang and Abramsky and Shah), as well as categorical accounts of quantum resources (by Abramsky, Barbosa, de Silva and Zapata). This work made essential use of monads—seen as encapsulating quantum and other resources—and of comonads, which encapsulate “co-resources”, i.e. ways of limiting access to a structure corresponding to definability in various logics. The project will seek to apply these new tools to major results in descriptive complexity, to expand them to cover other important constructions, to find ways of combining accounts of quantum resources and logical co-resources, and to build a general theory of these.