Inference in Action

Johan van Benthem

Substructural logics arise whenever classical logic is put to new uses, and logicians from Serbia have been in the fore-front here. In this paper, we join the substructural tradition with another recent trend, viz. dynamic logic of information update. We show how these two approaches fit together, in particular, through a number of representation theorems concerning structural rules. The proper background for these results turn out to be modal and dynamic logics of cross-model relations. We connect this finding with recent accounts of generalized inference, interpolation, and preservation results.