An Account of Natural Language Coordination in Type Theory with Coercive Subtyping

Chatzikyriakidis, Stergios; Zhang, Luo

doi:10.1007/978-3-642-41578-4_3

Cited by 12 publications

(22 citation statements)

References 28 publications

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“…6 This stands as part of the study of linguistic semantics using MTTs rather than simply typed ones. These issues have already been discussed in [16,17,1,2,4] among others. In what follows I provide a brief discussion on some of the features of MTTs relevant to the paper.…”

Section: Mtt Semantics: a Brief Intromentioning

confidence: 94%

“…12 Interesting applications of the use of universes can be proposed. For example, we can propose types for quantifiers and VP adverbs that extend over the universe cn [20] as well as a type for coordination extending over the universe of all linguistic types LType [1]. We will see the relevance of universes further on in this paper, when VP-adverbs are going to be discussed.…”

Section: Dependent Typing and Universesmentioning

confidence: 99%

“…According to this classification, there are three basic classes of adverbials with further subclassifications for each class: a) predicational, b) participant oriented and c) functional adverbials. 1 Note that this classification is for adverbials in general, and not adverbs only. In this paper, we concentrate on a subset of predicational adverbs that constitute the main bulk of adverbs.…”

Section: Introductionmentioning

confidence: 99%

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Adverbs in a Modern Type Theory

Chatzikyriakidis

2014

Logical Aspects of Computational Linguistics

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Abstract. This paper is the first attempt to deal with aspects of the semantics of adverbs within a modern type theoretical setting. A number of issues pertaining to the semantics of different classes of adverbs like verididality and intensionality will be discussed and further shown to be captured straightforwardly within a modern type theoretical setting. In particular, I look at the issue of veridicality and show that the inferences associated with veridical adverbs can be dealt with via typing alone, i.e. without the aid of meaning postulates. In case of intensional adverbs like intentionally or allegedly, I show that these can be captured by making use of the type theoretical notion of context, i.e. without the use of possible worlds.

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Section: Mtt Semantics: a Brief Intromentioning

confidence: 94%

Section: Dependent Typing and Universesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Adverbs in a Modern Type Theory

Chatzikyriakidis

2014

Logical Aspects of Computational Linguistics

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“…For instance, let cn be the type universe of (the interpretations of) common nouns. 3 Then, for N 1 and N 2 in cn, N 1 =⇒ cn N 2 if, and only if,…”

Section: A =⇒ B If and Only If A ≤ Bmentioning

confidence: 99%

“…For A : CN and n : N at, V ec(A, n) is the inductive type of vectors whose lengths are n. Vector types may be used to deal with some linguistic features such as those involve collective verbs [3]. For instance, we may interpret meet as of the following type:…”

Section: Dependent Products (π-Types)mentioning

confidence: 99%

Monotonicity Reasoning in Formal Semantics Based on Modern Type Theories

Lungu

Zhang

2014

Logical Aspects of Computational Linguistics

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Abstract. Modern type theories (MTTs) have been developed as a powerful foundation for formal semantics. In particular, it provides a useful platform for natural language inference (NLI) where proof assistants can be used for inference on computers. In this paper, we consider how monotonicity reasoning can be dealt in MTTs, so that it can contribute to NLI based on the MTT-semantics. We show that subtyping is crucial in monotonicity reasoning in MTTs because CNs are interpreted as types and therefore the monotonicity relations between CNs should be represented by the subtyping relations. In the past, monotonicity reasoning has only been considered for the arrow-types in the Montagovian setting of simple type theory. In MTT-semantics, richer type constructors involving dependent types and inductive types are employed in semantic representations. We show how to consider monotonicity reasoning that involve such type constructors and how this offers new useful mechanisms in monotonicity reasoning in MTTs.

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