Semantic Composition via Probabilistic Model Theory

Semantic composition remains an open problem for vector space models of semantics. In this paper, we explain how the probabilistic graphical model used in the framework of Functional Distributional Semantics can be interpreted as a probabilistic version of model theory. Building on this, we explain how various semantic phenomena can be recast in terms of conditional probabilities in the graphical model. This connection between formal semantics and machine learning is helpful in both directions: it gives us an explicit mechanism for modelling context-dependent meanings (a challenge for formal semantics), and also gives us well-motivated techniques for composing distributed representations (a challenge for distributional semantics). We present results on two datasets that go beyond word similarity, showing how these semantically-motivated techniques improve on the performance of vector models.Schiff Foundatio

"Not not bad" is not "bad": A distributional account of negation

With the increasing empirical success of distributional models of compositional semantics, it is timely to consider the types of textual logic that such models are capable of capturing. In this paper, we address shortcomings in the ability of current models to capture logical operations such as negation. As a solution we propose a tripartite formulation for a continuous vector space representation of semantics and subsequently use this representation to develop a formal compositional notion of negation within such models.Comment: 9 pages, to appear in Proceedings of the 2013 Workshop on Continuous Vector Space Models and their Compositionalit

Don't Blame Distributional Semantics if it can't do Entailment

Distributional semantics has had enormous empirical success in Computational Linguistics and Cognitive Science in modeling various semantic phenomena, such as semantic similarity, and distributional models are widely used in state-of-the-art Natural Language Processing systems. However, the theoretical status of distributional semantics within a broader theory of language and cognition is still unclear: What does distributional semantics model? Can it be, on its own, a fully adequate model of the meanings of linguistic expressions? The standard answer is that distributional semantics is not fully adequate in this regard, because it falls short on some of the central aspects of formal semantic approaches: truth conditions, entailment, reference, and certain aspects of compositionality. We argue that this standard answer rests on a misconception: These aspects do not belong in a theory of expression meaning, they are instead aspects of speaker meaning, i.e., communicative intentions in a particular context. In a slogan: words do not refer, speakers do. Clearing this up enables us to argue that distributional semantics on its own is an adequate model of expression meaning. Our proposal sheds light on the role of distributional semantics in a broader theory of language and cognition, its relationship to formal semantics, and its place in computational models.Comment: To appear in Proceedings of the 13th International Conference on Computational Semantics (IWCS 2019), Gothenburg, Swede

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

Lexical and Derivational Meaning in Vector-Based Models of Relativisation

Sadrzadeh et al (2013) present a compositional distributional analysis of relative clauses in English in terms of the Frobenius algebraic structure of finite dimensional vector spaces. The analysis relies on distinct type assignments and lexical recipes for subject vs object relativisation. The situation for Dutch is different: because of the verb final nature of Dutch, relative clauses are ambiguous between a subject vs object relativisation reading. Using an extended version of Lambek calculus, we present a compositional distributional framework that accounts for this derivational ambiguity, and that allows us to give a single meaning recipe for the relative pronoun reconciling the Frobenius semantics with the demands of Dutch derivational syntax.Comment: 10 page version to appear in Proceedings Amsterdam Colloquium, updated with appendi

A Context-theoretic Framework for Compositionality in Distributional Semantics

Techniques in which words are represented as vectors have proved useful in many applications in computational linguistics, however there is currently no general semantic formalism for representing meaning in terms of vectors. We present a framework for natural language semantics in which words, phrases and sentences are all represented as vectors, based on a theoretical analysis which assumes that meaning is determined by context. In the theoretical analysis, we define a corpus model as a mathematical abstraction of a text corpus. The meaning of a string of words is assumed to be a vector representing the contexts in which it occurs in the corpus model. Based on this assumption, we can show that the vector representations of words can be considered as elements of an algebra over a field. We note that in applications of vector spaces to representing meanings of words there is an underlying lattice structure; we interpret the partial ordering of the lattice as describing entailment between meanings. We also define the context-theoretic probability of a string, and, based on this and the lattice structure, a degree of entailment between strings. We relate the framework to existing methods of composing vector-based representations of meaning, and show that our approach generalises many of these, including vector addition, component-wise multiplication, and the tensor product.Comment: Submitted to Computational Linguistics on 20th January 2010 for revie

Experimental Support for a Categorical Compositional Distributional Model of Meaning

Modelling compositional meaning for sentences using empirical distributional methods has been a challenge for computational linguists. We implement the abstract categorical model of Coecke et al. (arXiv:1003.4394v1 [cs.CL]) using data from the BNC and evaluate it. The implementation is based on unsupervised learning of matrices for relational words and applying them to the vectors of their arguments. The evaluation is based on the word disambiguation task developed by Mitchell and Lapata (2008) for intransitive sentences, and on a similar new experiment designed for transitive sentences. Our model matches the results of its competitors in the first experiment, and betters them in the second. The general improvement in results with increase in syntactic complexity showcases the compositional power of our model.Comment: 11 pages, to be presented at EMNLP 2011, to be published in Proceedings of the 2011 Conference on Empirical Methods in Natural Language Processin