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Structural Control (1988)
| Venue: | SPECIFYING SYNTACTIC STRUCTURES, PATRICK BLACKBURN, MAARTEN DE RIJKE (EDS.) |
| Citations: | 45 - 9 self |
BibTeX
@ARTICLE{Kurtonina88structuralcontrol,
author = {Natasha Kurtonina and et al.},
title = {Structural Control},
journal = {SPECIFYING SYNTACTIC STRUCTURES, PATRICK BLACKBURN, MAARTEN DE RIJKE (EDS.)},
year = {1988},
volume = {98},
pages = {501--517}
}
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Abstract
In this paper we study Lambek systems as grammar logics: logics for reasoning about structured linguistic resources. The structural parameters of precedence, dominance and dependency generate a cube of resource-sensitive categorial type logics. From the pure logic of residuation NL, one obtains L, NLP and LP in terms of Associativity, Commutativity, and their combination. Each of these systems has a dependency variant, where the product is split up into a left-headed and a right-headed version. We develop a theory of systematic communication between these systems. The communication is two-way: we show how one can fully recover the structural discrimination of a weaker logic from within a system with a more liberal resource management regime, and how one can reintroduce the structural flexibility of a stronger logic within a system with a more articulate notion of structure-sensitivity. In executing this programme we follow the standard logical agenda: the categorial formula language is enriched with extra control operators, so-called structural modalities, and on the basis of these control operators, we prove embedding theorems for the two directions of substructural communication. But our results differ from the Linear Logic style of embedding with S4-like modalities in that we realize the communication in both directions in terms of a
Keyphrases
structural control linear logic style systematic communication substructural communication articulate notion lambek system resource-sensitive categorial type logic standard logical agenda pure logic right-headed version structural parameter categorial formula language control operator linguistic resource so-called structural modality s4-like modality residuation nl grammar logic extra control operator structural flexibility structural discrimination liberal resource management regime dependency variant
