Polynomial Event Semantics: Non-Montagovian Proper Treatment of Quantifiers

 

 

Introduction

We propose a simple extension of event semantics that naturally supports the compositional treatment of quantification. Our analyses require neither quantifier raising or other syntactic movements, nor type-lifting. Denotations are computed strictly compositionally, from lexical entries up, and quantifiers are analyzed in situ. We account for the universal, existential and counting quantification and the related distributive coordination, with the attendant quantifier ambiguity phenomena. The underlying machinery is not of lambda-calculus but of much simpler relational algebra, with the straightforward set-theoretic interpretation.

The source of quantifier ambiguity in our approach lies in two possible analyses for the existential and counting quantification. Their inherent ambiguity however becomes apparent only in the presence of another, non-existential quantification.

Version
The current version is March 2019
References
PolyEvent.pdf [289K]
The paper published in New Frontiers in Artificial Intelligence. JSAI-isAI 2018. Lecture Notes in Computer Science, 2019, vol 11717, pp 313-324. Springer.
doi:10.1007/978-3-030-31605-1_23

PolyEvent-talk.pdf [208K]
Talk at LENLS 2018, Kanagawa, Japan, November 13, 2018

poly.ml [18K]
The OCaml implementation of the model construction, to run all examples in the talk/paper

 

Negation

Polynomial event semantics is an interpretation of Neo-Davidsonian semantics in which the thorny event quantification problem does not even arise. Denotations are constructed strictly compositionally, from lexical entries up, and quantifiers are analyzed in situ. All advantages of event semantics, in particular, regarding entailment, are preserved. The previous work has dealt only with positive polarity phrases involving universal, existential and counting quantification.

We now extend the polynomial event semantics to sentences with negation and negative quantification, including adverbial quantification, with attendant ambiguities. The analysis remains compositional, and does not require positing of non-existing entities or events.

Version
The current version is March 2021
References
PolyNeg.pdf [259K]
The paper published in JSAI-isAI 2020: New Frontiers in Artificial Intelligence. Lecture Notes in Computer Science, vol 12758, 2021, pp 82-95. Springer.
doi:10.1007/978-3-030-79942-7_6

PolyNeg-talk.pdf [178K]
Talk at LENLS 2020, online, November 16, 2020

poly.ml [18K]
The OCaml implementation of the model construction, to run all examples in the talk/paper