copredication in homotopy type theory: a homotopical approach to formal semantics of natural...
TRANSCRIPT
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Copredication in Homotopy Type Theory
Hamidreza Bahramian1
Indiana University Bloomington
Presentation based on a joint work with NargesNematollahi2 and Amr Sabry3
1 Department of Computer Science2 Department of Linguistics3 Department of Computer Science
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IntroductionCopredication: the phenomenon where two or more predicates with different requirements on their arguments are applied to a single argument
a) The lunch was delicious but took forever. (Asher, 2011)
b) The heavy book is easy to understand. (Gotham, 2014)
c) John picked up and mastered three books.(Asher 2011)
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History� Asher(2011), nouns as “dot objects”(Pustejovsky, 1995)
◦ i.e., objects that can be viewed under different “aspects”
� Cooper (2011)
◦ nouns as functions from “records” to “record types”
� Luo (2012), Chatzikyriakidisand Luo (2012, 2013, 2015)
◦ common nouns as types
◦ dot types + coercive subtyping
� Gotham(2014)
◦ `book' denotes the set of composite objects physical+informational
◦ criteria of individuation are combined during semantic composition
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Montague semantics
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Montague semantics
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Montague semantics
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In Luo’s framework
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In Luo’s framework
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In Luo’s framework
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In Luo’s framework
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In Luo’s framework
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In Luo’s framework
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In Luo’s framework
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In Luo’s framework
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In Luo’s framework
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The problem
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The problem
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Homotopy Type Theory� intensional version of Martin-Löf’s type theory [ML75]
� a proof-relevant interpretation of equality
� propositions-as-types principle
� a full cumulative hierarchy of universes
� judgmental vs propositional equality ◦ “=” vs “ ”≡
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Homotopy Type Theory
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Homotopy Theory
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Homotopy Theory
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Homotopy Theory
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Homotopy Theory
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Homotopy Theory
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Homotopy Theory
Johnson, Chris. " Path Homotopy Animation." Youtube. Youtube, 11 May 2009. Web. 9 July 2016.
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Homotopy Theory
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Homotopy Theory
Rowland, Todd. "Homotopic." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. http://mathworld.wolfram.com/Homotopic.html
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Homotopy Theory
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Homotopy Theory
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CN as identifications
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CN as identifications
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CN as identifications
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CN as identifications
Sameness
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CN as identifications
Sameness Unlikeness
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CN as identifications
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CN as identifications
TreePT TreePT = TreePT
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CN as identifications
TreePT = TreePT
TreePT TreePT
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CN as identifications
TreePT = TreePT
TreePT TreePT
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CN as identifications
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CN as identifications
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CN as identifications
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CN as identifications
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CN as identifications
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Heim and Kratzer’s framework
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Heim and Kratzer’s framework
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Heim and Kratzer’s framework
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Heim and Kratzer’s framework
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Heim and Kratzer’s framework
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Heim and Kratzer’s framework
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Heim and Kratzer’s framework
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Heim and Kratzer’s framework
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Heim and Kratzer’s framework
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Heim and Kratzer’s framework
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Semantic computation using HoTTlogic
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Future work� Formal semantics of natural languages◦ “possible world”?
� HoTT◦ subtyping?
� Homotopy◦ Prefiguration as theorem?
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References