Natural language semantics in biproduct dagger categories

Preller, Anne

doi:10.1016/j.jal.2013.08.001

Cited by 3 publications

(6 citation statements)

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“…Extending the theory to other sets of subsets, for example, down or up sets, rather than the full powerset is a future direction, as is developing a logic based on any of these collections (powerset vs down or up sets). Extending the grammar to more expressive fragments of English and addressing advanced language phenomena such as co-reference resolution, following the work of Preller (2014), are other future directions.…”

Section: Discussionmentioning

confidence: 99%

A generalised quantifier theory of natural language in categorical compositional distributional semantics with bialgebras

Hedges

Sadrzadeh

2019

Math. Struct. Comp. Sci.

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Categorical compositional distributional semantics is a model of natural language; it combines the statistical vector space models of words with the compositional models of grammar. We formalise in this model the generalised quantifier theory of natural language, due to Barwise and Cooper. The underlying setting is a compact closed category with bialgebras. We start from a generative grammar formalisation and develop an abstract categorical compositional semantics for it, then instantiate the abstract setting to sets and relations and to finite dimensional vector spaces and linear maps. We prove the equivalence of the relational instantiation to the truth theoretic semantics of generalised quantifiers. The vector space instantiation formalises the statistical usages of words and enables us to, for the first time, reason about quantified phrases and sentences compositionally in distributional semantics.

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Section: Discussionmentioning

confidence: 99%

A generalised quantifier theory of natural language in categorical compositional distributional semantics with bialgebras

Hedges

Sadrzadeh

2019

Math. Struct. Comp. Sci.

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“…We write G for the free rigid category that it generates, also called the lexical category in [6]. An arrow r : u → s for an utterance u ∈ List(V ) is a proof that u is a grammatical sentence, i.e.…”

Section: Definition 11mentioning

confidence: 99%

“…Note that our de nition of the lexical category G di ers slightly from [6] in that we take not only basic types b ∈ B but also words w ∈ V as generating objects. This allows us to capture both type assignment and reduction as a single arrow as well as to de ne the semantics of pregroup grammars as a functor, see de nition 3.2 where we will also make use of the following lemma.…”

Section: Definition 18 Parsingmentioning

confidence: 99%

“…Hence, a concrete RelCoCat model F : G → Rel is fully speci ed by a nite set of triples { w : t :: F (w → t) } (w,t)∈∆ , called a pregroup lexicon in [6]. This allows us to de ne Semantics as a function problem with RelCoCat models as input.…”

Section: Relcocat Semantics and Natural Language Entailmentmentioning

confidence: 99%

“…Building on previous work [4], we then show that the QuestionAnswering problem is NP − complete. Logical semantics for pregroups has been developped in a line of work by Preller [5,6,7], however the corresponding reasoning problems were undecidable.…”

Section: Introductionmentioning

confidence: 99%

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Functorial Question Answering

Felice

Meichanetzidis

Toumi

2020

Electron. Proc. Theor. Comput. Sci.

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We study the relational variant of the categorical compositional distributional (DisCoCat) models of Coecke et al. [1], where we replace vector spaces and linear maps by sets and relations. We show that RelCoCat models factorise through Cartesian bicategories, as a corollary we get logspace reductions from semantics and entailment to evaluation and containment of conjunctive queries respectively.Finally, we de ne question answering as an NP − complete problem.

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Categorical Vector Space Semantics for Lambek Calculus with a Relevant Modality

et al. 2023

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We develop a categorical compositional distributional semantics for Lambek Calculus with a Relevant Modality !L∗, a modality that allows for the use of limited editions of contraction and permutation in the logic. Lambek Calculus has been introduced to analyse syntax of natural language and the linguistic motivation behind this modality is to extend the domain of the applicability of the calculus to fragments which witness the discontinuity phenomena. The categorical part of the semantics is a monoidal biclosed category with a !-functor, very similar to the structure of a Differential Category. We instantiate this category to finite dimensional vector spaces and linear maps via "quantisation" functors and work with three concrete interpretations of the !-functor. We apply the model to construct categorical and concrete semantic interpretations for the motivating example of !L∗: the derivation of a phrase with a parasitic gap. The efficacy of the concrete interpretations are evaluated via a disambiguation task, on an extension of a sentence disambiguation dataset to parasitic gap phrase one, using BERT, Word2Vec, and FastText vectors and relational tensors.

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Natural language semantics in biproduct dagger categories

Cited by 3 publications

References 10 publications

A generalised quantifier theory of natural language in categorical compositional distributional semantics with bialgebras

A generalised quantifier theory of natural language in categorical compositional distributional semantics with bialgebras

Functorial Question Answering

Categorical Vector Space Semantics for Lambek Calculus with a Relevant Modality

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