Updating Anaphoric Contexts
نویسنده
چکیده
An incremental semantics for a logic with dynamic binding is developed on the basis of a variable free notation for dynamic logic that 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 indexing mechanism guarantees that active registers are never overwritten by new quantiier actions. The resulting system is analysed and applied to a new rational reconstruction of discourse representation theory. It is argued that the present system of incremental dynamic logic 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. In recent developments of natural language semantics, problems of pronominal reference and anaphoric linking have inspired logicians to a dynamic turn in natural language semantics. This started with Discourse Representation Theory (Kamp 15]) and File Change Semantics (Heim 13]), and various attempts at rational reconstruction of these proposals, with Barwise 3] and Groenendijk and Stokhof 11] as the most prominent ones. The gist of these proposals is that the static variable binding regime from standard predicate logic gets replaced by a dynamic regime, where meanings are viewed as relations between variable states in a model. In the original version of thèdynamic shift', the basic ingredients are contexts and constraints on contexts. A Kamp-style representation for a piece of text (or: discourse) looks basically like this:
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