Variables as stacks

The development of the dynamic semantics of natural languagehas put issues of variable control on the agenda of formal semantics. Inthis paper we regard variables as names for stacks of values and makeexplicit several control actions as push and pop actions on stacks. Weapply this idea both to static and dynamic languages and compare theirfinite variable hierarchies, i.e., the relation between the number ofvariable stacks that is available and the expressivity of the language.This can be compared in natural languages with relating the number ofpronouns available to the expressivity of the language.The results are obtained using techniques from static and dynamic modeltheory: model theoretic games, transition systems and bisimulation.
Keywords dynamic semantics  finite variable hierarchy  games  model theory
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DOI 10.1023/A:1008332604642
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Alastair Butler (2007). Scope Control and Grammatical Dependencies. Journal of Logic, Language and Information 16 (3):241-264.

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