Dynamic Reasoning Without Variables
Jan van Eijck

A variable free notation for dynamic logic is proposed which takes its cue 
from De Bruijn's variable free notation for lambda calculus. De Bruijn 
indexing replaces variables by indices which indicate the distance to their 
binders. We propose to use reverse De Bruijn indexing, which works almost the 
same, only now the indices refer to the depth of the binding operator in the 
formula. The resulting system is analysed at length and applied to a new 
rational reconstruction of discourse representation theory. It is argued that 
the present system of dynamic logic without variables provides an explicit 
account of anaphoric context and yields new insight into the dynamics of 
anaphoric linking in reasoning. A calculus for dynamic reasoning with anaphora 
is presented and its soundness and completeness are established.
Keywords and Phrases: dynamic semantics of natural language, complete calculus 
for dynamic reasoning with anaphora, anaphora and context.