Finding Resolution in unexpected places: Girard’s formula outside its usual setting

Peter Hines

Date(s) : 02/07/2020   iCal
10 h 00 min - 11 h 00 min


Abstract: This is not a talk about Linear Logic or the Geometry of Interaction; these feature, very briefly, as historical background & motivation. Rather, the aim is to consider a key part of these topics — Girard’s « Resolution Formula » — in a more general context, and examine both where it appears in other settings and why this is the case.

These ‘other settings’ range across several distinct fields of theoretical computer science and mathematics. From a Theoretical Computer Science perspective, they include automata & Turing machines, domain theory, the low-level / high-level distinction, and the halting problem for quantum computers. The mathematical tools required include categorical closure & reflexivity, pointless topologies, categorical coherence, and inverse semigroups & categories.

The talk concludes by discussing possible future directions : in particular, whether we can identify / construct problems that we may prove are not solvable by certain classes of machines.

Peter Hines (YCCSA, York, UK)



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