From Logical to Distributional Models

Preller, Anne

doi:10.4204/eptcs.171.11

Cited by 9 publications

(5 citation statements)

References 13 publications

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“…If the generating object I includes the semiring of positive rational numbers the 'counting property' of the predicates makes it possible to replace the canonical vector space model by a probabilistic vector space model where the basis vectors stand for arbitrarily chosen 'basic concepts', see [Preller, 2013]. A promising line of future investigations is the step from 'counting' predicates to measuring predicates in Hilbert spaces to capture the notion of 'truth in probability' and its relation to natural language.…”

Section: Resultsmentioning

confidence: 99%

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Natural language semantics in biproduct dagger categories

Preller

2014

Journal of Applied Logic

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Biproduct dagger categories serve as models for natural language. In particular, the biproduct dagger category of finite dimensional vector spaces over the field of real numbers accommodates both the extensional models of predicate calculus and the intensional models of quantum logic. The morphisms representing the extensional meanings of a grammatical string are translated to morphisms representing the intensional meanings such that truth is preserved. Pregroup grammars serve as the tool that transforms a grammatical string into a morphism. The chosen linguistic examples concern negation, relative noun phrases, comprehension and quantifiers.

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Section: Resultsmentioning

confidence: 99%

“…The suggested functor is partial, it is not defined for strings containing logical words, relative, determiners and so on. In fact, such a partial functor cannot be extended to the logical words expressing negation and implication, neither for classical logic nor for quantum logic, [Preller, 2013].…”

Section: Introductionmentioning

confidence: 99%

Natural language semantics in biproduct dagger categories

Preller

2014

Journal of Applied Logic

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“…Using a free compact closed category as opposed to a free pregroup is a solution suggested in Preller (2013) to the fact that there is no corresponding strongly monoidal functor on a free pregroup that assigns to atomic types, spaces of more than one dimension in the relational and distributional instantiations. In what follows, we drop the source category B and denote the semantics by (C, W, S, [[ ]]) in cases where the source category is fixed.…”

Section: Abstract Compact Closed Semantics Definition 4 An Abstract mentioning

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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“…Details can be found in [7,16], amongst others. We note only that instead of using a pregroup as our grammar category, we use the free compact closed category J = C (B) generated over a set of types B, as described in [24,23].…”

Section: Background 21 Categorical Compositional Distributional Seman...mentioning

confidence: 99%

Translating and Evolving: Towards a Model of Language Change in DisCoCat

Bradley

Lewis

Master

et al. 2018

Electron. Proc. Theor. Comput. Sci.

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The categorical compositional distributional (DisCoCat) model of meaning developed by [7] has been successful in modeling various aspects of meaning. However, it fails to model the fact that language can change. We give an approach to DisCoCat that allows us to represent language models and translations between them, enabling us to describe translations from one language to another, or changes within the same language. We unify the product space representation given in [7] and the functorial description in [16], in a way that allows us to view a language as a catalogue of meanings. We formalize the notion of a lexicon in DisCoCat, and define a dictionary of meanings between two lexicons. All this is done within the framework of monoidal categories. We give examples of how to apply our methods, and give a concrete suggestion for compositional translation in corpora.

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From Logical to Distributional Models

Cited by 9 publications

References 13 publications

Natural language semantics in biproduct dagger categories

Natural language semantics in biproduct dagger categories

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

Translating and Evolving: Towards a Model of Language Change in DisCoCat

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