DisCoCat for Donkey Sentences

We demonstrate how to parse Geach's Donkey sentences in a compositional distributional model of meaning. We build on previous work on the DisCoCat (Distributional Compositional Categorical) framework, including extensions that model discourse, determiners, and relative pronouns. We present a type-logical syntax for parsing donkey sentences, for which we define both relational and vector space semantics.

The Causal Structure of Semantic Ambiguities

Ambiguity is a natural language phenomenon occurring at different levels of syntax, semantics, and pragmatics. It is widely studied; in Psycholinguistics, for instance, we have a variety of competing studies for the human disambiguation processes. These studies are empirical and based on eyetracking measurements. Here we take first steps towards formalizing these processes for semantic ambiguities where we identified the presence of two features: (1) joint plausibility degrees of different possible interpretations, (2) causal structures according to which certain words play a more substantial role in the processes. The novel sheaf-theoretic model of definite causality developed by Gogioso and Pinzani in QPL 2021 offers tools to model and reason about these features. We applied this theory to a dataset of ambiguous phrases extracted from Psycholinguistics literature and their human plausibility judgements collected by us using the Amazon Mechanical Turk engine. We measured the causal fractions of different disambiguation orders within the phrases and discovered two prominent orders: from subject to verb in the subject-verb and from object to verb in the verb object phrases. We also found evidence for delay in the disambiguation of polysemous vs homonymous verbs, again compatible with Psycholinguistic findings.

On the Quantum-like Contextuality of Ambiguous Phrases

Language is contextual as meanings of words are dependent on their contexts. Contextuality is, concomitantly, a well-defined concept in quantum mechanics where it is considered a major resource for quantum computations. We investigate whether natural language exhibits any of the quantum mechanics' contextual features. We show that meaning combinations in ambiguous phrases can be modelled in the sheaf-theoretic framework for quantum contextuality, where they can become possibilistically contextual. Using the framework of Contextuality-by-Default (CbD), we explore the probabilistic variants of these and show that CbD-contextuality is also possible.