Variables as Stacks: A Case Study in Dynamic Model Theory

The development of the dynamic semantics of natural language has put issues of variable control on the agenda of formal semantics. In this paper we regard variables as names for stacks of values and make explicit several control actions as push and pop actions on stacks. We apply this idea both to s...

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Bibliographic Details
Published in:Journal of logic, language, and information language, and information, 2000-04, Vol.9 (2), p.143-167
Main Author: Vermeulen, C. F. M.
Format: Article
Language:English
Subjects:
Denotational semantics
Dynamic games
Dynamic model theory
Games
Model theory
Natural language
Pebbles
Predicate logic
Pronouns
Semantics
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Summary:The development of the dynamic semantics of natural language has put issues of variable control on the agenda of formal semantics. In this paper we regard variables as names for stacks of values and make explicit several control actions as push and pop actions on stacks. We apply this idea both to static and dynamic languages and compare their finite variable hierarchies, i.e., the relation between the number of variable stacks that is available and the expressivity of the language. This can be compared in natural languages with relating the number of pronouns available to the expressivity of the language. The results are obtained using techniques from static and dynamic model theory: model theoretic games, transition systems and bisimulation.
ISSN:0925-8531
1572-9583
DOI:10.1023/A:1008332604642