How Much Expressive Power Is Needed for Natural Language Temporal Indexicality?
 Igor Yanovich
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Abstract
The paper studies how much expressive power beyond the capabilities of the simple Priorean temporal language K _{ t } is needed to give proper translation to natural language examples by Kamp and Vlach which are extensively used in the linguistic and philosophical literature as forcing the use of quite expressive languages, all the way up to full twosorted FOL. It turns out that when examined carefully, the examples in question only require a quite mild Kamp and Cresswellstyle system with now and then operators, or, equivalently, hybrid K _{ t } + ↓ + @. The paper generalizes the earlier results showing that in the propositional case, now and then do not increase the power of K _{ t }. For the firstorder case, a notion of FOL path bisimulation for firstorder \(\mathbf{K}_t^{FO}\) with untensed quantification and equality is defined, and it is demonstrated how to prove that a particular NL sentence cannot be expressed in \(\mathbf{K}_t^{FO}\) through nonpreservation under FOL path bisimulation. It is also shown that \(\mathbf{K}_t^{FO}\) plus now and then is still strictly less expressive than HL(↓, @), which is itself much less expressive than the strong systems that were claimed to be needed for NL translation. Thus the paper provides strict lower and upper bounds on the expressivity of the translation language forced by KampVlach NL sentences, and the upper bound turns out to be much lower than was widely believed in the linguistics community.
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 Title
 How Much Expressive Power Is Needed for Natural Language Temporal Indexicality?
 Book Title
 Logic, Language, Information and Computation
 Book Subtitle
 18th International Workshop, WoLLIC 2011, Philadelphia, PA, USA. Proceedings
 Pages
 pp 293309
 Copyright
 2011
 DOI
 10.1007/9783642209208_27
 Print ISBN
 9783642209192
 Online ISBN
 9783642209208
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 6642
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 Springer Berlin Heidelberg
 Additional Links
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 Editors

 Lev D. Beklemishev ^{(19)}
 Ruy de Queiroz ^{(20)}
 Editor Affiliations

 19. Steklov Mathematical Institute
 20. Centro de Informática, Universidade Federal de Pernambuco
 Authors

 Igor Yanovich ^{(21)}
 Author Affiliations

 21. MIT, USA
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