We define a linear pregroup parser, by applying some key modifications to the minimal parser defined in (Preller, 2007). These include handling words as separate blocks, and thus respecting their syntactic role in the sentence. We prove correctness of our algorithm with respect to parsing sentences in a subclass of pregroup grammars. The algorithm was specifically designed for a seamless implementation in Python. This facilitates its integration within the DisCopy module for QNLP and vastly increases the applicability of pregroup grammars to parsing real-world text data.

While the DisCoCat model (Coecke et al., 2010) has been proved a valuable tool for studying compositional aspects of language at the level of semantics, its strong dependency on pregroup grammars poses important restrictions : first, it prevents large-scale experimentation due to the absence of a pregroup parser ; and second, it limits the expressibility of the model to context-free grammars. In this paper we solve these problems by reformulating DisCoCat as a passage from Combinatory Categorial Grammar (CCG) to a category of semantics. We start by showing that standard categorial grammars can be expressed as a biclosed category, where all rules emerge as currying / uncurrying the identity ; we then proceed to model permutation-inducing rules by exploiting the symmetry of the compact closed category encoding the word meaning. We provide a proof of concept for our method, converting Alice in Wonderland into DisCoCat form, a corpus that we make available to the community.

Diagrammatically speaking, grammatical calculi such as pregroups provide wires between words in order to elucidate their interactions, and this enables one to verify grammatical correctness of phrases and sentences. In this paper we also provide wirings within words. This will enable us to identify grammatical constructs that we expect to be either equal or closely related. Hence, our work paves the way for a new theory of grammar, that provides novel ‘grammatical truths’. We give a nogo-theorem for the fact that our wirings for words make no sense for preordered monoids, the form which grammatical calculi usually take. Instead, they require diagrams or equivalently, (free) monoidal categories.

We propose a framework to model an operational conversational negation by applying worldly context (prior knowledge) to logical negation in compositional distributional semantics. Given a word, our framework can create its negation that is similar to how humans perceive negation. The framework corrects logical negation to weight meanings closer in the entailment hierarchy more than meanings further apart. The proposed framework is flexible to accommodate different choices of logical negations, compositions, and worldly context generation. In particular, we propose and motivate a new logical negation using matrix inverse. We validate the sensibility of our conversational negation framework by performing experiments, leveraging density matrices to encode graded entailment information. We conclude that the combination of subtraction negation and phaser in the basis of the negated word yields the highest Pearson correlation of 0.635 with human ratings.

In distributional compositional models of meaning logical words require special interpretations, that specify the way in which other words in the sentence interact with each other. So far within the DisCoCat framework, conjunctions have been implemented as merging both conjuncts into a single output, however in the new framework of DisCoCirc merging between nouns is no longer possible. We provide an account of conjunction and an interpretation for the word ‘and’ that solves this, and moreover ensures certain intuitively similar sentences can be given the same interpretations.