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

Abstract

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.

Lambek pregroups are Frobenius spiders in preorders

“…The reason is that the sequents used to analyze syntax can be reduced to contractions along the counits of adjoint pairs of syntactic types. 8 Ongoing work suggests that data analysis, concept mining, and even communication in general evolve as adjunctions [30,33,54,58]. What is the impact of the presented results on these observations?…”

“…The algebraic equivalence of the two different presentations of the syntactic process does seem to have repercussions on the original epistemological analyses of language, and possibly on the present computational applications, but they are far from clear at present. 8 Since the adjunction units are never used in syntactic analyses, the question whether the actual adjunctions are really needed has been raised from the outset. In [38], pregroups were introduced only after an extended discussion about "protogroups", which are partially ordered monoids with left and right "protoinverses" x ℓ and x r equipped with contractions ι ← x ℓ x and (ι ← xx r ), but no expansions that would make them adjoint to x.…”

“…Pregroups and spiders have been used together in computational linguistics, one for presenting the syntax, the other for assigning the vector space semantics [49,62,63]. The string diagram notation has been instrumental in combining these two structures of disjoint origins, at different levels of language modeling, to open an alley towards reconciling the two leading paradigms of natural language processing, the distributional and the compositional [8,18,24,28].…”

Lambek pregroups are Frobenius spiders in preorders

“…Pregroups and spiders have been used together in computational linguistics, one for presenting the syntax, the other for assigning the vector space semantics [48,60,61]. The string diagram notation has been instrumental in combining these two structures of disjoint origins, at different levels of language modeling, to open an alley towards reconciling the two leading paradigms of natural language processing, the distributional and the compositional [8,19,24,27].…”