Type-theoretical semantics with coercive subtyping

Zhang, Luo

doi:10.3765/salt.v0i20.2580

Cited by 5 publications

(12 citation statements)

References 6 publications

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“…Coercive subtyping [14,19] provides an adequate framework to be employed for MTT-based formal semantics [15,18]. 13 …”

Section: Subtypingmentioning

confidence: 99%

“…π 1 (ADV (A, v)) This line of approach, as the authors show, can effectively take care of the inferences associated with veridical adverbs. 15 In what follows, I present an account of different types of adverbs, concentrating on predicational adverbs and a number of their properties. The veridical/non-veridical distinction is first discussed, followed by a discussion on various other issues associated with the semantics of adverbs like opacity and rich typing.…”

Section: Adverbs In Mttsmentioning

confidence: 99%

“…I consider this to be nonsatisfactory for at least two reasons a) redundancy, i.e. every adverb will need 15 It has to be noted that the inference associated with manner adverbs like the one discussed, has been tried out in the Coq proof-assistant [3,4]. There it was shown that using a lexical entry for on time like the one proposed in (17), one can formally verify/prove that (13) is a valid inference.…”

Section: Veridical Adverbsmentioning

confidence: 99%

“…type theories within the tradition of Martin-Löf. In particular, an expressive and computationally attractive language, that of UTT with coercive subtyping [16,15,18] will be used in order to present an account of various aspects of adverbial modification that, as it will 3 Within the simple type theory used in Montague Grammar, e is the type of individuals, t is the type of truth-values and s the type of world-time pairs. 4 An example in case would involve a VP-adverb like intentionally in a sentence like Oedipus intentionally married Jocaste.…”

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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“…Coercive subtyping [14,19] provides an adequate framework to be employed for MTT-based formal semantics [15,18]. 13 …”

Section: Subtypingmentioning

confidence: 99%

Section: Adverbs In Mttsmentioning

confidence: 99%

Section: Veridical Adverbsmentioning

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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“…These types are not inductive types found in traditional MTTs. They were introduced to model the linguistic feature of copredication [12]. If A and B are types do not share common components, then we can form a dot-type A • B for which we have two coercions from A • B to A and from A • B to B.…”

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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Adjectival and Adverbial Modification: The View from Modern Type Theories

Chatzikyriakidis

Zhang

2017

J of Log Lang and Inf

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In this paper we present a study of adjectival/adverbial modification using modern type theories (MTTs), i.e. type theories within the tradition of Martin-Löf. We present an account of various issues concerning adjectival/adverbial modification and argue that MTTs can be used as an adequate language for interpreting NL semantics. MTTs are not only expressive enough to deal with a range of modification phenomena, but are furthermore well-suited to perform reasoning tasks that can be easily implemented (e.g. in proof-assistants) given their proof-theoretic nature. In MTT-semantics, common nouns are interpreted as types rather than predicates. Therefore, in order to capture the semantics of adjectives adequately, one needs to meet the challenge of modeling CNs modified by adjectives as types. To explicate that this can be done successfully, we first look at the mainstream classification of adjectives, i.e. intersective, subsective and non-subsective adjectives. There, we show that the rich type structure available in MTTs, along with a suitable subtyping framework, offers an adequate mechanism to model these cases. In particular, this modelling naturally takes care of the characterising inferences associated with each class of adjectives. Then, more advanced issues on adjectival modification are discussed: (a) degree adjectives, (b) comparatives and (c) multidimensional adjectives. There, it is shown that the use of indexed types can be usefully applied in order to deal with these cases. In the same vein, the issue of adverbial modification is discussed. We study two general typings for sentence and VP adverbs respectively. It is shown that the rich type structure in MTTs further provides useful organisational mechanisms in giving formal semantics for adverbs. In particular, we discuss the use of Σ-types to capture the veridicality/nonveridicality distinction and further discuss cases of intensional adverbs using the type theoretic notion of context (i.e. without resorting to intensional typing). We also look at manner, subject and speech act adverbials and propose solutions using MTTs. Finally, we show that the current proof technology can help mechanically check the associated inferences. A number of our proposals concerning adjectival and adverbial modification have been formalised in the proof assistant Coq and many of the associated inference patterns are checked to be correctly captured.

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Type-theoretical semantics with coercive subtyping

Cited by 5 publications

References 6 publications

Adverbs in a Modern Type Theory

Adverbs in a Modern Type Theory

Monotonicity Reasoning in Formal Semantics Based on Modern Type Theories

Adjectival and Adverbial Modification: The View from Modern Type Theories

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