arXiv subjects

Christian Retoré

Publications and source records attributed to Christian Retoré.

25 records · Page 2Linked to original sources

arXiv2013

Type-theoretical natural language semantics: on the system F for meaning assembly

This paper presents and extends our type theoretical framework for a compositional treatment of natural language semantics with some lexical features like coercions (e.g. of a town into a football club) and copredication (e.g. on a town as a set of people and as a location). The second order typed lambda calculus was shown to be a good framework, and here we discuss how to introduced predefined types and coercive subtyping which are much more natural than internally coded similar constructs. Linguistic applications of these new features are also exemplified.

cs.LO↗

arXiv2013

Some proof theoretical remarks on quantification in ordinary language

This paper surveys the common approach to quantification and generalised quantification in formal linguistics and philosophy of language. We point out how this general setting departs from empirical linguistic data, and give some hints for a different view based on proof theory, which on many aspects gets closer to the language itself. We stress the importance of Hilbert's oper- ator epsilon and tau for, respectively, existential and universal quantifications. Indeed, these operators help a lot to construct semantic representation close to natural language, in particular with quantified noun phrases as individual terms. We also define guidelines for the design of the proof rules corresponding to generalised quantifiers.

math.LO↗

arXiv2012

Variable types for meaning assembly: a logical syntax for generic noun phrases introduced by most

This paper proposes a way to compute the meanings associated with sentences with generic noun phrases corresponding to the generalized quantifier most. We call these generics specimens and they resemble stereotypes or prototypes in lexical semantics. The meanings are viewed as logical formulae that can thereafter be interpreted in your favourite models. To do so, we depart significantly from the dominant Fregean view with a single untyped universe. Indeed, our proposal adopts type theory with some hints from Hilbert ε-calculus (Hilbert, 1922; Avigad and Zach, 2008) and from medieval philosophy, see e.g. de Libera (1993, 1996). Our type theoretic analysis bears some resemblance with ongoing work in lexical semantics (Asher 2011; Bassac et al. 2010; Moot, Prévot and Retoré 2011). Our model also applies to classical examples involving a class, or a generic element of this class, which is not uttered but provided by the context. An outcome of this study is that, in the minimalism-contextualism debate, see Conrad (2011), if one adopts a type theoretical view, terms encode the purely semantic meaning component while their typing is pragmatically determined.

math.LO↗

arXiv2011

Specimens: "most of" generic NPs in a contextually flexible type theory

This paper proposes to compute the meanings associated to sentences with generic NPs corresponding to the most of generalized quantifier. We call these generics specimens and they resemble stereotypes or prototypes in lexical semantics. The meanings are viewed as logical formulae that can be thereafter interpreted in your favorite models. We rather depart from the dominant Fregean single untyped universe and go for type theory with hints from Hilbert epsilon calculus and from medieval philosophy. Our type theoretic analysis bears some resemblance with on going work in lexical semantics. Our model also applies to classical examples involving a class (or a generic element of this class) which is provided by the context. An outcome of this study is that, in the minimalism-contextualism debate, if one adopts a type theoretical view, terms encode the purely semantic meaning component while their typing is pragmatically determined.

math.LO↗

arXiv2011

On the system F as a glue language for natural-language compositional-semantics

In order to model in compositional framework some phenomena of lexical pragmatics and in particular the ones studied by Nicholas Asher several contributions developed in our team did use the system F of Jean-Yves Girard to construct logical formulae expressing the meaning of sentences --- while other authors prefer to use Per Martin-Löf's type theory In this note we explain the motivations supporting our preference for system F.

math.LO↗

arXiv2011

Quantification in ordinary language

We firstly show that the standard interpretation of natural quantification in mathematical logic does not provide a satisfying account of its original richness. In particular, it ignores the difference between generic and distributive readings. We claim that it is due to the use of a set theoretical framework. We therefore propose a proof theoretical treatment in terms of proofs and refutations. Thereafter we apply these ideas to quantifiers that are not first order definable like "the majority of".

math.LO↗

arXiv2010

Categorial Minimalist Grammar

We first recall some basic notions on minimalist grammars and on categorial grammars. Next we shortly introduce partially commutative linear logic, and our representation of minimalist grammars within this categorial system, the so-called categorial minimalist grammars. Thereafter we briefly present λμ-DRT (Discourse Representation Theory) an extension of λ-DRT (compositional DRT) in the framework of λμcalculus: it avoids type raising and derives different readings from a single semantic representation, in a setting which follows discourse structure. We run a complete example which illustrates the various structures and rules that are needed to derive a semantic representation from the categorial view of a transformational syntactic analysis.

cs.CL↗