DeepAI AI Chat
Log In Sign Up

Typed Hilbert Epsilon Operators and the Semantics of Determiner Phrases (Invited Lecture)

by   Christian Retoré, et al.

The semantics of determiner phrases, be they definite de- scriptions, indefinite descriptions or quantified noun phrases, is often as- sumed to be a fully solved question: common nouns are properties, and determiners are generalised quantifiers that apply to two predicates: the property corresponding to the common noun and the one corresponding to the verb phrase. We first present a criticism of this standard view. Firstly, the semantics of determiners does not follow the syntactical structure of the sentence. Secondly the standard interpretation of the indefinite article cannot ac- count for nominal sentences. Thirdly, the standard view misses the linguis- tic asymmetry between the two properties of a generalised quantifier. In the sequel, we propose a treatment of determiners and quantifiers as Hilbert terms in a richly typed system that we initially developed for lexical semantics, using a many sorted logic for semantical representations. We present this semantical framework called the Montagovian generative lexicon and show how these terms better match the syntactical structure and avoid the aforementioned problems of the standard approach. Hilbert terms rather differ from choice functions in that there is one polymorphic operator and not one operator per formula. They also open an intriguing connection between the logic for meaning assembly, the typed lambda calculus handling compositionality and the many-sorted logic for semantical representations. Furthermore epsilon terms naturally introduce type-judgements and confirm the claim that type judgment are a form of presupposition.


page 1

page 2

page 3

page 4


Petrarch 2 : Petrarcher

PETRARCH 2 is the fourth generation of a series of Event-Data coders ste...

Ultimate approximations in nonmonotonic knowledge representation systems

We study fixpoints of operators on lattices. To this end we introduce th...

Proof-Theory and Semantics for a Theory of Definite Descriptions

This paper presents a sequent calculus and a dual domain semantics for a...

Semantics and Axiomatization for Stochastic Differential Dynamic Logic

Building on previous work by André Platzer, we present a formal language...

Decidability of Intuitionistic Sentential Logic with Identity via Sequent Calculus

The aim of our paper is twofold: firstly we present a sequent calculus f...

Definite Descriptions in Intuitionist Positive Free Logic

This paper presents rules of inference for a binary quantifier I for the...

Understanding the Expressive Power of Unhygienic Substitution in Metaprogramming via Combinatory Logic

Recent work on combinatory logic demonstrates a compositional translatio...