Linguistic Grammar as Dynamic Logic
Johan van Benthem

Abstract:
Natural language is the primary vehicle of human communication. It involves
a series of interlocked processes at various levels of aggregation. Proof
theory and dynamic logic provide two paradigms for dealing with this variety.
This paper gives an analysis of some main issues that arise in merging the
two viewpoints towards this broader goal. Topics discussed include: proof
as discourse, interfacing low­level fast and high­level slow systems, merging
lambda dynamics and modal state dynamics, strategies that create feasible
proof calculi. Overall prospects for broad 'dynamic architectures' look good.