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.
In the current work, we have restricted ourselves to grammatical composition, and in particular pregroup grammar. However, the categorical compositional scheme can be instantiated in a number of ways. The grammar can be changed from pregroup grammar to another categorial grammar, as in @cite_20 , or a compositional scheme that is not grammatically based may be used. Indeed, one of the challenges of this approach is to find a model of composition that accurately reflects human behaviour. One way of doing so would be to use an approach in which the syntactic scheme is generated by the semantics of the universe of discourse. Furthermore, since phrases and sentences are represented as sets equipped with a convex algebra, the model can in future work be extended to include logical composition.
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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, something which the other methods lack, 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 Lambekʼs pregroup grammar. Pregroup types form a poset al 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 Lambekʼs previous type-logic, the Lambek calculus. The latter and its extensions have been extensively used to formalise and reason about various linguistic phenomena. Hence, 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, and also reflects the structure of the parse trees of the Lambek calculus. Natural language parsing has typically been done with small sets of discrete categories such as NP and VP, but this representation does not capture the full syntactic nor semantic richness of linguistic phrases, and attempts to improve on this by lexicalizing phrases or splitting categories only partly address the problem at the cost of huge feature spaces and sparseness. Instead, we introduce a Compositional Vector Grammar (CVG), which combines PCFGs with a syntactically untied recursive neural network that learns syntactico-semantic, compositional vector representations. The CVG improves the PCFG of the Stanford Parser by 3.8 to obtain an F1 score of 90.4 . It is fast to train and implemented approximately as an efficient reranker it is about 20 faster than the current Stanford factored parser. The CVG learns a soft notion of head words and improves performance on the types of ambiguities that require semantic information such as PP attachments. While there is a growing body of work proposing grammars for music, there is little work testing analytical grammars in a generative setting. We explore the process of learning production probabilities for musical grammars from musical corpora and test the results using Kulitta, a recently developed framework for automated composition. To do this, we extend a well-known algorithm for learning production probabilities for context-free grammars (CFGs) to support various musical CFGs as well as an additional category of grammars called probabilistic temporal graph grammars. This paper illustrates a hierarchical generative model for representing and recognizing compositional object categories with large intra-category variance. In this model, objects are broken into their constituent parts and the variability of configurations and relationships between these parts are modeled by stochastic attribute graph grammars, which are embedded in an And-Or graph for each compositional object category. It combines the power of a stochastic context free grammar (SCFG) to express the variability of part configurations, and a Markov random field (MRF) to represent the pictorial spatial relationships between these parts. As a generative model, different object instances of a category can be realized as a traversal through the And-Or graph to arrive at a valid configuration (like a valid sentence in language, by analogy). The inference recognition procedure is intimately tied to the structure of the model and follows a probabilistic formulation consisting of bottom-up detection steps for the parts, which in turn recursively activate the grammar rules for top-down verification and searches for missing parts. We present experiments comparing our results to state of art methods and demonstrate the potential of our proposed framework on compositional objects with cluttered backgrounds using training and testing data from the public Lotus Hill and Caltech datasets. In this paper we explore the idea of characterizing sentences by the shapes of their structural descriptions only; for example, in the case of context free grammars, by the shapes of the derivation trees only. Such structural descriptions will be called skeletons . A skeleton exhibits all of the grouping structure (phrase structure) of the sentence without naming the syntactic categories used in the description. The inclusion of syntactic categories as variables is primarily a question of economy of description. Every context free grammar is strongly equivalent to a skelet al grammar, in a sense made precise in the paper. Besides clarifying the role of skeletons in mathematical linguistics, we show that skelet al automata provide a characterization of local sets, remedying a “defect” in the usual tree automata theory. We extend the method of skelet al structural descriptions to other forms of tree describing systems. We also suggest a theoretical basis for grammatical inference based on grouping structure only. Reusing syntax specifications without embedded arbitrary semantic actions is straightforward because the semantic analysis phases of new applications can feed off trees or other intermediate structures constructed by the pre-existing parser. The presence of arbitrary embedded semantic actions, however, makes reuse difficult with existing mechanisms such as grammar inheritance and modules. This short paper proposes a mechanism based upon prototype grammars that automatically pushes changes from prototypes to derived grammars even in the presence of semantic actions. The prototype mechanism alone would be unsuitable for creating a new grammar from multiple preexisting grammars. When combined with grammar composition, however, the prototype mechanism would improve grammar reuse because imported pre-existing grammars could be altered to suit each new application. We investigate several conceptions of linguistic structure to determine whether or not they can provide simple and "revealing" grammars that generate all of the sentences of English and only these. We find that no finite-state Markov process that produces symbols with transition from state to state can serve as an English grammar. Furthermore, the particular subclass of such processes that produce n -order statistical approximations to English do not come closer, with increasing n , to matching the output of an English grammar. We formalize-the notions of "phrase structure" and show that this gives us a method for describing language which is essentially more powerful, though still representable as a rather elementary type of finite-state process. Nevertheless, it is successful only when limited to a small subset of simple sentences. We study the formal properties of a set of grammatical transformations that carry sentences with phrase structure into new sentences with derived phrase structure, showing that transformational grammars are processes of the same elementary type as phrase-structure grammars; that the grammar of English is materially simplified if phrase structure description is limited to a kernel of simple sentences from which all other sentences are constructed by repeated transformations; and that this view of linguistic structure gives a certain insight into the use and understanding of language. This paper presents a series of experiments in applying compositional distributional semantic models to dialogue act classification. In contrast to the widely used bag-ofwords approach, we build the meaning of an utterance from its parts by composing the distributional word vectors using vector addition and multiplication. We investigate the contribution of word sequence, dialogue act sequence, and distributional information to the performance, and compare with the current state of the art approaches. Our experiment suggests that that distributional information is useful for dialogue act tagging but that simple models of compositionality fail to capture crucial information from word and utterance sequence; more advanced approaches (e.g. sequence- or grammar-driven, such as categorical, word vector composition) are required. We propose a grammar induction technique for AMR semantic parsing. While previous grammar induction techniques were designed to re-learn a new parser for each target application, the recently annotated AMR Bank provides a unique opportunity to induce a single model for understanding broad-coverage newswire text and support a wide range of applications. We present a new model that combines CCG parsing to recover compositional aspects of meaning and a factor graph to model non-compositional phenomena, such as anaphoric dependencies. Our approach achieves 66.2 Smatch F1 score on the AMR bank, significantly outperforming the previous state of the art. Algorithmic composition composing by means of formalizable methods has a century old tradition not only in occidental music history. This is the first book to provide a detailed overview of prominent procedures of algorithmic composition in a pragmatic way rather than by treating formalizable aspects in single works. In addition to an historic overview, each chapter presents a specific class of algorithm in a compositional context by providing a general introduction to its development and theoretical basis and describes different musical applications. Each chapter outlines the strengths, weaknesses and possible aesthetical implications resulting from the application of the treated approaches. Topics covered are: markov models, generative grammars, transition networks, chaos and self-similarity, genetic algorithms, cellular automata, neural networks and artificial intelligence are covered. The comprehensive bibliography makes this work ideal for the musician and the researcher alike. Cloth modeling and recognition is an important and challenging problem in both vision and graphics tasks, such as dressed human recognition and tracking, human sketch and portrait. In this paper, we present a context sensitive grammar in an And-Or graph representation which will produce a large set of composite graphical templates to account for the wide variabilities of cloth configurations, such as T-shirts, jackets, etc. In a supervised learning phase, we ask an artist to draw sketches on a set of dressed people, and we decompose the sketches into categories of cloth and body components: collars, shoulders, cuff, hands, pants, shoes etc. Each component has a number of distinct subtemplates (sub-graphs). These sub-templates serve as leafnodes in a big And-Or graph where an And-node represents a decomposition of the graph into sub-configurations with Markov relations for context and constraints (soft or hard), and an Or-node is a switch for choosing one out of a set of alternative And-nodes (sub-configurations) - similar to a node in stochastic context free grammar (SCFG). This representation integrates the SCFG for structural variability and the Markov (graphical) model for context. An algorithm which integrates the bottom-up proposals and the topdown information is proposed to infer the composite cloth template from the image. This paper presents a synchronous-graphgrammar-based approach for string-toAMR parsing. We apply Markov Chain Monte Carlo (MCMC) algorithms to learn Synchronous Hyperedge Replacement Grammar (SHRG) rules from a forest that represents likely derivations consistent with a fixed string-to-graph alignment. We make an analogy of string-toAMR parsing to the task of phrase-based machine translation and come up with an efficient algorithm to learn graph grammars from string-graph pairs. We propose an effective approximation strategy to resolve the complexity issue of graph compositions. We also show some useful strategies to overcome existing problems in an SHRG-based parser and present preliminary results of a graph-grammar-based approach. Categorical compositional distributional models unify compositional formal semantic models and distributional models by composing phrases with tensor-based methods from vector representations. For the tensor-based compositions, (2014) showed that word vectors obtained from the continuous bag-of-words (CBOW) model are competitive with those from co-occurrence based models. However, because word vectors from the CBOW model are trained assuming additive interactions between context words, the word composition used for the training mismatches to the tensor-based methods used for evaluating the actual compositions including pointwise multiplication and tensor product of context vectors. In this work, we show whether the word embeddings from extended CBOW models using multiplication or tensor product between context words, reflecting the actual composition methods, can show better performance than those from the baseline CBOW model in actual tasks of compositions with multiplication or tensor-based methods. Integrated Development Environments (IDEs) increase programmer productivity, providing rapid, interactive feedback based on the syntax and semantics of a language. Unlike conventional parsing algorithms, scannerless generalized-LR parsing supports the full set of context-free grammars, which is closed under composition, and hence can parse languages composed from separate grammar modules. To apply this algorithm in an interactive environment, this article introduces a novel error recovery mechanism. Our approach is language independent, and relies on automatic derivation of recovery rules from grammars. By taking layout information into consideration it can efficiently suggest natural recovery suggestions. Modelling the compositional process by which the meaning of an utterance arises from the meaning of its parts is a fundamental task of Natural Language Processing. In this paper we draw upon recent advances in the learning of vector space representations of sentential semantics and the transparent interface between syntax and semantics provided by Combinatory Categorial Grammar to introduce Combinatory Categorial Autoencoders. This model leverages the CCG combinatory operators to guide a non-linear transformation of meaning within a sentence. We use this model to learn high dimensional embeddings for sentences and evaluate them in a range of tasks, demonstrating that the incorporation of syntax allows a concise model to learn representations that are both effective and general. We present a general learning-based approach for phrase-level sentiment analysis that adopts an ordinal sentiment scale and is explicitly compositional in nature. Thus, we can model the compositional effects required for accurate assignment of phrase-level sentiment. For example, combining an adverb (e.g., "very") with a positive polar adjective (e.g., "good") produces a phrase ("very good") with increased polarity over the adjective alone. Inspired by recent work on distributional approaches to compositionality, we model each word as a matrix and combine words using iterated matrix multiplication, which allows for the modeling of both additive and multiplicative semantic effects. Although the multiplication-based matrix-space framework has been shown to be a theoretically elegant way to model composition (Rudolph and Giesbrecht, 2010), training such models has to be done carefully: the optimization is non-convex and requires a good initial starting point. This paper presents the first such algorithm for learning a matrix-space model for semantic composition. In the context of the phrase-level sentiment analysis task, our experimental results show statistically significant improvements in performance over a bag-of-words model. As robots become more ubiquitous and capable, it becomes ever more important for untrained users to easily interact with them. Recently, this has led to study of the language grounding problem, where the goal is to extract representations of the meanings of natural language tied to the physical world. We present an approach for joint learning of language and perception models for grounded attribute induction. The perception model includes classifiers for physical characteristics and a language model based on a probabilistic categorial grammar that enables the construction of compositional meaning representations. We evaluate on the task of interpreting sentences that describe sets of objects in a physical workspace, and demonstrate accurate task performance and effective latent-variable concept induction in physical grounded scenes. Attempto Controlled English (ACE) is a language specifically designed to write specifications. ACE is a controlled natural language, i.e. a subset of English with a domain specific vocabulary and a restricted grammar in the form of a small set of construction and interpretation principles. This means that all ACE sentences are correct English, but that not all English sentences are allowed in ACE. The restriction of full natural language to a controlled subset is essential for ACE to be suitable for specification purposes. The main goals of this restriction are: to support the writing of precise specifications, to reduce ambiguity and vagueness inherent in full natural language, to encourage domain specialists to deliberately choose a clear and unambiguous writing style so that readers of a specification understand it in the same way as the writer, to make specifications computer processable, to render specifications unambiguously translatable into formal specification languages, particularly into first-order logic, and to make specifications executable. In brief, ACE allows domain specialists to express specifications in familiar natural language and to combine this with the rigor of formal specification languages. ACE has been used to specify a simple automatic teller machine, Kemmerer''s library data base problem, Schubert''s steamroller, and a number of smaller problems. Recently, ACE has also been used as the input language of a theorem prover, and first attempts have been made to interface it to a program synthesiser. Clearly, ACE can be adapted and extended for other purposes requiring precise input, e.g. writing technical documentation or updating databases. The use of ACE presupposes only basic knowledge of English grammar. Note however, that because ACE is a controlled natural language not all standard grammatical notions are directly applicable or suitable for the description of the ACE grammar. Some grammatical notions have a restricted meaning in ACE, while other notions are especially coined for an effective description of the language. The divergences are kept to a minimum so that ACE can be easily learned extending basic grammatical knowledge. Grounded language learning, the task of mapping from natural language to a representation of meaning, has attracted more and more interest in recent years. In most work on this topic, however, utterances in a conversation are treated independently and discourse structure information is largely ignored. In the context of language acquisition, this independence assumption discards cues that are important to the learner, e.g., the fact that consecutive utterances are likely to share the same referent (, 2013). The current paper describes an approach to the problem of simultaneously modeling grounded language at the sentence and discourse levels. We combine ideas from parsing and grammar induction to produce a parser that can handle long input strings with thousands of tokens, creating parse trees that represent full discourses. By casting grounded language learning as a grammatical inference task, we use our parser to extend the work of (2012), investigating the importance of discourse continuity in children’s language acquisition and its interaction with social cues. Our model boosts performance in a language acquisition task and yields good discourse segmentations compared with human annotators. Parsers are ubiquitous in computing, and many applications depend on their performance for decoding data efficiently. Parser combinators are an intuitive tool for writing parsers: tight integration with the host language enables grammar specifications to be interleaved with processing of parse results. Unfortunately, parser combinators are typically slow due to the high overhead of the host language abstraction mechanisms that enable composition. We present a technique for eliminating such overhead. We use staging, a form of runtime code generation, to dissociate input parsing from parser composition, and eliminate intermediate data structures and computations associated with parser composition at staging time. A key challenge is to maintain support for input dependent grammars, which have no clear stage distinction. Our approach applies to top-down recursive-descent parsers as well as bottom-up non-deterministic parsers with key applications in dynamic programming on sequences, where we auto-generate code for parallel hardware. We achieve performance comparable to specialized, hand-written parsers.