Interacting Conceptual Spaces I : Grammatical Composition of Concepts

The categorical compositional approach to meaning has been successfully applied in natural language processing, outperforming other models in mainstream empirical language processing tasks. We show how this approach can be generalized to conceptual space models of cognition. In order to do this, first we introduce the category of convex relations as a new setting for categorical compositional semantics, emphasizing the convex structure important to conceptual space applications. We then show how to construct conceptual spaces for various types such as nouns, adjectives and verbs. Finally we show by means of examples how concepts can be systematically combined to establish the meanings of composite phrases from the meanings of their constituent parts. This provides the mathematical underpinnings of a new compositional approach to cognition.

Compositional Distributional Cognition

We accommodate the Integrated Connectionist/Symbolic Architecture (ICS) of [32] within the categorical compositional semantics (CatCo) of [13], forming a model of categorical compositional cognition (CatCog). This resolves intrinsic problems with ICS such as the fact that representations inhabit an unbounded space and that sentences with differing tree structures cannot be directly compared. We do so in a way that makes the most of the grammatical structure available, in contrast to strategies like circular convolution. Using the CatCo model also allows us to make use of tools developed for CatCo such as the representation of ambiguity and logical reasoning via density matrices, structural meanings for words such as relative pronouns, and addressing over- and under-extension, all of which are present in cognitive processes. Moreover the CatCog framework is sufficiently flexible to allow for entirely different representations of meaning, such as conceptual spaces. Interestingly, since the CatCo model was largely inspired by categorical quantum mechanics, so is CatCog.

Interacting Conceptual Spaces

We propose applying the categorical compositional scheme of [6] to conceptual space models of cognition. In order to do this we introduce the category of convex relations as a new setting for categorical compositional semantics, emphasizing the convex structure important to conceptual space applications. We show how conceptual spaces for composite types such as adjectives and verbs can be constructed. We illustrate this new model on detailed examples.

Proceedings of the 2016 Workshop on Semantic Spaces at the Intersection of NLP, Physics and Cognitive Science

This volume contains the Proceedings of the 2016 Workshop on Semantic Spaces at the Intersection of NLP, Physics and Cognitive Science (SLPCS 2016), which was held on the 11th of June at the University of Strathclyde, Glasgow, and was co-located with Quantum Physics and Logic (QPL 2016). Exploiting the common ground provided by the concept of a vector space, the workshop brought together researchers working at the intersection of Natural Language Processing (NLP), cognitive science, and physics, offering them an appropriate forum for presenting their uniquely motivated work and ideas. The interplay between these three disciplines inspired theoretically motivated approaches to the understanding of how word meanings interact with each other in sentences and discourse, how diagrammatic reasoning depicts and simplifies this interaction, how language models are determined by input from the world, and how word and sentence meanings interact logically. This first edition of the workshop consisted of three invited talks from distinguished speakers (Hans Briegel, Peter G\"ardenfors, Dominic Widdows) and eight presentations of selected contributed papers. Each submission was refereed by at least three members of the Programme Committee, who delivered detailed and insightful comments and suggestions.

Harmonic Grammar in a DisCo Model of Meaning

The model of cognition developed in (Smolensky and Legendre, 2006) seeks to unify two levels of description of the cognitive process: the connectionist and the symbolic. The theory developed brings together these two levels into the Integrated Connectionist/Symbolic Cognitive architecture (ICS). Clark and Pulman (2007) draw a parallel with semantics where meaning may be modelled on both distributional and symbolic levels, developed by Coecke et al, 2010 into the Distributional Compositional (DisCo) model of meaning. In the current work, we revisit Smolensky and Legendre (S&L)'s model. We describe the DisCo framework, summarise the key ideas in S&L's architecture, and describe how their description of harmony as a graded measure of grammaticality may be applied in the DisCo model.

Emerging Dimension Weights in a Conceptual Spaces Model of Concept Combination

We investigate the generation of new concepts from combinations of properties as an artificial language develops. To do so, we have developed a new framework for conjunctive concept combination. This framework gives a semantic grounding to the weighted sum approach to concept combination seen in the literature. We implement the framework in a multi-agent simulation of language evolution and show that shared combination weights emerge. The expected value and the variance of these weights across agents may be predicted from the distribution of elements in the conceptual space, as determined by the underlying environment, together with the rate at which agents adopt others' concepts. When this rate is smaller, the agents are able to converge to weights with lower variance. However, the time taken to converge to a steady state distribution of weights is longer.

The Utility of Hedged Assertions in the Emergence of Shared Categorical Labels

We investigate the emergence of shared concepts in a community of language users using a multi-agent simulation. We extend results showing that negated assertions are of use in developing shared categories, to include assertions modified by linguistic hedges. Results show that using hedged assertions positively affects the emergence of shared categories in two distinct ways. Firstly, using contraction hedges like `very' gives better convergence over time. Secondly, using expansion hedges such as `quite' reduces concept overlap. However, both these improvements come at a cost of slower speed of development.

Graded Entailment for Compositional Distributional Semantics

The categorical compositional distributional model of natural language provides a conceptually motivated procedure to compute the meaning of sentences, given grammatical structure and the meanings of its words. This approach has outperformed other models in mainstream empirical language processing tasks. However, until recently it has lacked the crucial feature of lexical entailment -- as do other distributional models of meaning. In this paper we solve the problem of entailment for categorical compositional distributional semantics. Taking advantage of the abstract categorical framework allows us to vary our choice of model. This enables the introduction of a notion of entailment, exploiting ideas from the categorical semantics of partial knowledge in quantum computation. The new model of language uses density matrices, on which we introduce a novel robust graded order capturing the entailment strength between concepts. This graded measure emerges from a general framework for approximate entailment, induced by any commutative monoid. Quantum logic embeds in our graded order. Our main theorem shows that entailment strength lifts compositionally to the sentence level, giving a lower bound on sentence entailment. We describe the essential properties of graded entailment such as continuity, and provide a procedure for calculating entailment strength.

A Label Semantics Approach to Linguistic Hedges

We introduce a model for the linguistic hedges `very' and `quite' within the label semantics framework, and combined with the prototype and conceptual spaces theories of concepts. The proposed model emerges naturally from the representational framework we use and as such, has a clear semantic grounding. We give generalisations of these hedge models and show that they can be composed with themselves and with other functions, going on to examine their behaviour in the limit of composition.

Concept Generation in Language Evolution

This thesis investigates the generation of new concepts from combinations of existing concepts as a language evolves. We give a method for combining concepts, and will be investigating the utility of composite concepts in language evolution and thence the utility of concept generation.