Using conceptual metaphor and functional grammar to explore how language used in physics affects student learning

This paper introduces a theory about the role of language in learning physics. The theory is developed in the context of physics students' and physicists' talking and writing about the subject of quantum mechanics. We found that physicists' language encodes different varieties of analogical models through the use of grammar and conceptual metaphor. We hypothesize that students categorize concepts into ontological categories based on the grammatical structure of physicists' language. We also hypothesize that students over-extend and misapply conceptual metaphors in physicists' speech and writing. Using our theory, we will show how, in some cases, we can explain student difficulties in quantum mechanics as difficulties with language.Comment: Accepted for publication in Phys. Rev. ST:PE

A Study of Entanglement in a Categorical Framework of Natural Language

In both quantum mechanics and corpus linguistics based on vector spaces, the notion of entanglement provides a means for the various subsystems to communicate with each other. In this paper we examine a number of implementations of the categorical framework of Coecke, Sadrzadeh and Clark (2010) for natural language, from an entanglement perspective. Specifically, our goal is to better understand in what way the level of entanglement of the relational tensors (or the lack of it) affects the compositional structures in practical situations. Our findings reveal that a number of proposals for verb construction lead to almost separable tensors, a fact that considerably simplifies the interactions between the words. We examine the ramifications of this fact, and we show that the use of Frobenius algebras mitigates the potential problems to a great extent. Finally, we briefly examine a machine learning method that creates verb tensors exhibiting a sufficient level of entanglement.Comment: In Proceedings QPL 2014, arXiv:1412.810

Lambek vs. Lambek: Functorial Vector Space Semantics and String Diagrams for Lambek Calculus

The Distributional Compositional Categorical (DisCoCat) model is a mathematical framework that provides compositional semantics for meanings of natural language sentences. It consists of a computational procedure for constructing meanings of sentences, given their grammatical structure in terms of compositional type-logic, and given the empirically derived meanings of their words. For the particular case that the meaning of words is modelled within a distributional vector space model, its experimental predictions, derived from real large scale data, have outperformed other empirically validated methods that could build vectors for a full sentence. This success can be attributed to a conceptually motivated mathematical underpinning, by integrating qualitative compositional type-logic and quantitative modelling of meaning within a category-theoretic mathematical framework. The type-logic used in the DisCoCat model is Lambek's pregroup grammar. Pregroup types form a posetal compact closed category, which can be passed, in a functorial manner, on to the compact closed structure of vector spaces, linear maps and tensor product. The diagrammatic versions of the equational reasoning in compact closed categories can be interpreted as the flow of word meanings within sentences. Pregroups simplify Lambek's previous type-logic, the Lambek calculus, which has been extensively used to formalise and reason about various linguistic phenomena. The apparent reliance of the DisCoCat on pregroups has been seen as a shortcoming. This paper addresses this concern, by pointing out that one may as well realise a functorial passage from the original type-logic of Lambek, a monoidal bi-closed category, to vector spaces, or to any other model of meaning organised within a monoidal bi-closed category. The corresponding string diagram calculus, due to Baez and Stay, now depicts the flow of word meanings.Comment: 29 pages, pending publication in Annals of Pure and Applied Logi

Types and forgetfulness in categorical linguistics and quantum mechanics

The role of types in categorical models of meaning is investigated. A general scheme for how typed models of meaning may be used to compare sentences, regardless of their grammatical structure is described, and a toy example is used as an illustration. Taking as a starting point the question of whether the evaluation of such a type system 'loses information', we consider the parametrized typing associated with connectives from this viewpoint. The answer to this question implies that, within full categorical models of meaning, the objects associated with types must exhibit a simple but subtle categorical property known as self-similarity. We investigate the category theory behind this, with explicit reference to typed systems, and their monoidal closed structure. We then demonstrate close connections between such self-similar structures and dagger Frobenius algebras. In particular, we demonstrate that the categorical structures implied by the polymorphically typed connectives give rise to a (lax unitless) form of the special forms of Frobenius algebras known as classical structures, used heavily in abstract categorical approaches to quantum mechanics.Comment: 37 pages, 4 figure

Gender representation in different languages and grammatical marking on pronouns: when beauticians, musicians, and mechanics remain men

Gygax, Gabriel, Sarrasin, Oakhill, and Garnham (2008) showed that readers form a mental representation of gender that is based on grammatical gender in French and German (i.e., masculine supposedly interpretable as a generic form) but is based on stereotypical information in English. In this study, a modification of their stimulus material was used to examine the additional potential influence of pronouns. Across the three languages, pronouns differ in their grammatical gender marking: The English they is gender neutral, the French ils is masculine, and the German sie, although interpretable as generic, is morphologically feminine. Including a later pronominal reference to a group of people introduced by a plural role name significantly altered the masculine role name’s grammatical influence only in German, suggesting that grammatical cues that match (as in French) do not have a cumulative impact on the gender representation, whereas grammatical cues that mismatch (as in German) do counteract one another. These effects indicate that subtle morphological relations between forms actually used in a sentence and other forms have an immediate impact on language processing, although information about the other forms is not necessary for comprehension and may, in some cases, be detrimental to it

Handling non-compositionality in multilingual CNLs

In this paper, we describe methods for handling multilingual non-compositional constructions in the framework of GF. We specifically look at methods to detect and extract non-compositional phrases from parallel texts and propose methods to handle such constructions in GF grammars. We expect that the methods to handle non-compositional constructions will enrich CNLs by providing more flexibility in the design of controlled languages. We look at two specific use cases of non-compositional constructions: a general-purpose method to detect and extract multilingual multiword expressions and a procedure to identify nominal compounds in German. We evaluate our procedure for multiword expressions by performing a qualitative analysis of the results. For the experiments on nominal compounds, we incorporate the detected compounds in a full SMT pipeline and evaluate the impact of our method in machine translation process.Comment: CNL workshop in COLING 201