TY - GEN
T1 - Scope as syntactic abstraction
AU - Barker, Chris
N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2015.
PY - 2015
Y1 - 2015
N2 - What is the logic of scope? By “scope”, I mean scopetaking in natural languages such as English, as illustrated by the sentence Ann saw everyone. In this example, the quantifier denoted by everyone takes scope over the rest of the sentence, that is, it takes the denotation of the rest of the sentence as its semantic argument: everyone(λx.saw(x)(ann)). The answer I will give here will be to provide a substructural logic whose two modes are related by a single structural postulate. This postulate can be interpreted as constituting a kind of lambda-abstraction over structures, where the abstracted structures are interpreted as delimited continuations. I discuss soundness and completeness results, as well as cut elimination. I also compare the logic to a number of alternative approaches, including the standard technique of Quantifier Raising, and mention applications to scope ambiguity and parasitic scope.
AB - What is the logic of scope? By “scope”, I mean scopetaking in natural languages such as English, as illustrated by the sentence Ann saw everyone. In this example, the quantifier denoted by everyone takes scope over the rest of the sentence, that is, it takes the denotation of the rest of the sentence as its semantic argument: everyone(λx.saw(x)(ann)). The answer I will give here will be to provide a substructural logic whose two modes are related by a single structural postulate. This postulate can be interpreted as constituting a kind of lambda-abstraction over structures, where the abstracted structures are interpreted as delimited continuations. I discuss soundness and completeness results, as well as cut elimination. I also compare the logic to a number of alternative approaches, including the standard technique of Quantifier Raising, and mention applications to scope ambiguity and parasitic scope.
KW - Continuations
KW - Natural language quantification
KW - Parasitic scope
KW - Quantifier raising
KW - Scope
KW - Substructural logic
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U2 - 10.1007/978-3-662-48119-6_14
DO - 10.1007/978-3-662-48119-6_14
M3 - Conference contribution
AN - SCOPUS:84945550656
SN - 9783662481189
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 184
EP - 199
BT - New Frontiers in Artificial Intelligence - JSAI-isAI 2014 Workshops, LENLS, JURISIN, and GABA, Revised Selected Papers
A2 - Murata, Tsuyoshi
A2 - Mineshima, Koji
A2 - Bekki, Daisuke
PB - Springer Verlag
T2 - 6th International Symposium on Artificial Intelligence, JSAI 2014
Y2 - 27 October 2014 through 28 October 2014
ER -