NDLI: The Soundness of Internalized Polarity Marking

Content Provider	Springer Nature Link
Author	Moss, Lawrence S.
Copyright Year	2012
Abstract	This paper provides a foundation for the polarity marking technique introduced by David Dowty [3] in connection with monotonicity reasoning in natural language and in linguistic analyses of negative polarity items based on categorial grammar. Dowty’s work is an alternative to the better-known algorithmic approach first proposed by Johan van Benthem [11], and elaborated by Víctor Sánchez Valencia [10]. Dowty’s system internalized the monotonicity/polarity markings by generating strings using a categorial grammar whose categories already contain the markings that the earlier system would obtain by separate steps working on an already-derived string. Despite the linguistic advantages of the internalized system, no soundness proof has yet been given for it. This paper offers an account. The leading mathematical idea is to interpret categorial types as preorders (in order to talk about monotonicity in the first place), and then to add a primitive operation to the type hierarchy of taking the opposite of a preorder (in order to capture monotone decreasing functions). At the same time, the use of internalized categories also raises issues. Although these will not be addressed in full, the paper points out possible approaches to them.
Starting Page	683
Ending Page	704
Page Count	22
File Format	PDF
ISSN	00393215
Journal	Studia Logica
Volume Number	100
Issue Number	4
e-ISSN	15728730
Language	English
Publisher	Springer Netherlands
Publisher Date	2012-08-08
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Categorial grammar Monotonicity Natural logic Polarity Logic Computational Linguistics Mathematical Logic and Foundations
Content Type	Text
Resource Type	Article
Subject	Logic History and Philosophy of Science

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