Incremental processing. Proof nets, considered statically as graphs satisfying certain correctness criteria, remove spurious choices relating to the order of rule applications in sequent calculi: in this respect, they represent a purely ‘declarative’ view on categorial deductions. Johnson (1998) and Morrill (2000) have pointed out that an alternative, ‘procedural’ view on the actual process of constructing a net makes perfect sense as well, and offers an attractive perspective on performance phenomena. Under this interpretation, a net is built in a left-to-right incremental fashion by establishing possible linkings between the input/output literals of the partial proof nets associated with lexical items as they occur in real time. This suggests a simple complexity measure on an incremental traversal, given by the number of unresolved dependencies between literals.  This complexity measure correlates nicely with a number of well-attested processing issues, such as the difficulty of center embedding, garden path effects, attachment preferences, and preferred scope construals in ambiguous constructions.