An incremental semantics for a logic with dynamic binding is developed on the basis of a variable free notation for dynamic logic. The variable free indexing mechanism guarantees that active registers are never overwritten by new quantifier actions. The resulting system has the same expressive power as Dynamic Predicate Logic or Discourse Representation Theory, but comes with a more well behaved consequence relation. A calculus for dynamic reasoning with anaphora is presented and its soundness and completeness are established. Incremental dynamic logic provides an explicit account of anaphoric context and yields new insight into the dynamics of anaphoric linking in reasoning.

Specifying and Verifying and Reasoning about Programs (acm F.3.1), Semantics of Programming Languages (acm F.3.2), Knowledge Representation Formalisms and Methods (acm I.2.4), Natural Language Processing (acm I.2.7)
Logic of natural languages (msc 03B65), Semantics (msc 68Q55)
Information Systems [INS]
Standardization and Knowledge Transfer

van Eijck, D.J.N. (1998). Incremental dynamics. Information Systems [INS]. CWI.