Robin Cooper

Generalized quantifiers and natural language

In 1957, the Polish logician Andrej Mostowski pointed out that there are many mathematically interesting quantifiers that are not definable in terms of the first-order ∀, ∃ and initiated study of so-called generalized quantifiers (cf. Mostowski, 1957). Since then logicians have discovered and studied a large number of generalized quantifiers. At last count there were well over 200 research papers in this area. Most of this work has been directed toward cardinality quantifiers (e.g. Keisler, 1969) and topological quantifiers (e.g. Sgro, 1977) which are not particularly relevant to natural language, but even so, it has forced logicians to rethink the traditional theory of quantification.

Quantification and Syntactic Theory

I: Syntax and Model-Theoretic Semantics.- II: A Fragment of English.- III: Quantifier Storage.- IV: Storage and wh-Phenomena.- V: wh-Phenomena and the Theory of Grammar.- VI: Presupposition and Quantification.- VII: Gender Agreement.- Notes.- Answers to Selected Exercises.- Index of Names.- Index of Subjects.

Adapting Type Theory with Records for Natural Language Semantics

In this paper we will go through the version of type theory TTR (Type Theory with Records) that we have proposed in a number of publications (including, Cooper, Res Lang Comput, 3:333–362, 2005a, J Log Comput, 15(2):99–112, 2005b, Handbook of the philosophy of science, volume 14: Philosophy of linguistics, 2012) and discuss the motivation for some choices that we have made which make it differ from other more standard modern type theories. We will relate TTR to the kind of type theory used in traditional formal semantics, characterizing more modern type theories as rich type theories with a greater variety of types. TTR, unlike many rich type theories, allows objects to be of several types and introduces both a kind of intensionality and modality. While TTR uses the idea that propositions should be modelled by types, it does not complete follow the Curry-Howard Correspondence introducing intersection and union types for a more classical treatment of conjunction and disjunction. It uses record types in place of (varSigma )-types and uses dependent types for several aspects of linguistic analysis.

Interfacing language, spatial perception and cognition in Type Theory with Records

We argue that computational modelling of perception, action, language, and cognition introduces several requirements on a formal semantic theory and its practical implementations. Using examples of semantic representations of spatial descriptions we show how Type Theory with Records (TTR) satisfies these requirements.

Proper Names in Interaction

Proper names in natural languages seem very simple from a linguistic point of view although getting their semantics correct turns out to be something of a challenge. In this paper we will suggest that there is an important advantage in viewing proper names as something like Saussurean signs incorporated in a formal theory which takes account of linguistic utterances as actions enabling linguistic agents to interact.