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.