Comparing and evaluating extended Lambek calculi

Lambeks Syntactic Calculus, commonly referred to as the Lambek calculus, was innovative in many ways, notably as a precursor of linear logic. But it also showed that we could treat our grammatical framework as a logic (as opposed to a logical theory). However, though it was successful in giving at least a basic treatment of many linguistic phenomena, it was also clear that a slightly more expressive logical calculus was needed for many other cases. Therefore, many extensions and variants of the Lambek calculus have been proposed, since the eighties and up until the present day. As a result, there is now a large class of calculi, each with its own empirical successes and theoretical results, but also each with its own logical primitives. This raises the question: how do we compare and evaluate these different logical formalisms? To answer this question, I present two unifying frameworks for these extended Lambek calculi. Both are proof net calculi with graph contraction criteria. The first calculus is a very general system: you specify the structure of your sequents and it gives you the connectives and contractions which correspond to it. The calculus can be extended with structural rules, which translate directly into graph rewrite rules. The second calculus is first-order (multiplicative intuitionistic) linear logic, which turns out to have several other, independently proposed extensions of the Lambek calculus as fragments. I will illustrate the use of each calculus in building bridges between analyses proposed in different frameworks, in highlighting differences and in helping to identify problems.Comment: Empirical advances in categorial grammars, Aug 2015, Barcelona, Spain. 201

Robust Processing of Natural Language

Previous approaches to robustness in natural language processing usually treat deviant input by relaxing grammatical constraints whenever a successful analysis cannot be provided by ``normal'' means. This schema implies, that error detection always comes prior to error handling, a behaviour which hardly can compete with its human model, where many erroneous situations are treated without even noticing them. The paper analyses the necessary preconditions for achieving a higher degree of robustness in natural language processing and suggests a quite different approach based on a procedure for structural disambiguation. It not only offers the possibility to cope with robustness issues in a more natural way but eventually might be suited to accommodate quite different aspects of robust behaviour within a single framework.Comment: 16 pages, LaTeX, uses pstricks.sty, pstricks.tex, pstricks.pro, pst-node.sty, pst-node.tex, pst-node.pro. To appear in: Proc. KI-95, 19th German Conference on Artificial Intelligence, Bielefeld (Germany), Lecture Notes in Computer Science, Springer 199

Big data and the SP theory of intelligence

This article is about how the "SP theory of intelligence" and its realisation in the "SP machine" may, with advantage, be applied to the management and analysis of big data. The SP system -- introduced in the article and fully described elsewhere -- may help to overcome the problem of variety in big data: it has potential as "a universal framework for the representation and processing of diverse kinds of knowledge" (UFK), helping to reduce the diversity of formalisms and formats for knowledge and the different ways in which they are processed. It has strengths in the unsupervised learning or discovery of structure in data, in pattern recognition, in the parsing and production of natural language, in several kinds of reasoning, and more. It lends itself to the analysis of streaming data, helping to overcome the problem of velocity in big data. Central in the workings of the system is lossless compression of information: making big data smaller and reducing problems of storage and management. There is potential for substantial economies in the transmission of data, for big cuts in the use of energy in computing, for faster processing, and for smaller and lighter computers. The system provides a handle on the problem of veracity in big data, with potential to assist in the management of errors and uncertainties in data. It lends itself to the visualisation of knowledge structures and inferential processes. A high-parallel, open-source version of the SP machine would provide a means for researchers everywhere to explore what can be done with the system and to create new versions of it.Comment: Accepted for publication in IEEE Acces

Structure Unification Grammar: A Unifying Framework for Investigating Natural Language

This thesis presents Structure Unification Grammar and demonstrates its suitability as a framework for investigating natural language from a variety of perspectives. Structure Unification Grammar is a linguistic formalism which represents grammatical information as partial descriptions of phrase structure trees, and combines these descriptions by equating their phrase structure tree nodes. This process can be depicted by taking a set of transparencies which each contain a picture of a tree fragment, and overlaying them so they form a picture of a complete phrase structure tree. The nodes which overlap in the resulting picture are those which are equated. The flexibility with which information can be specified in the descriptions of trees and the generality of the combination operation allows a grammar writer or parser to specify exactly what is known where it is known. The specification of grammatical constraints is not restricted to any particular structural or informational domains. This property provides for a very perspicuous representation of grammatical information, and for the representations necessary for incremental parsing. The perspicuity of SUG\u27s representation is complemented by its high formal power. The formal power of SUG allows other linguistic formalisms to be expressed in it. By themselves these translations are not terribly interesting, but the perspicuity of SUG\u27s representation often allows the central insights of the other investigations to be expressed perspicuously in SUG. Through this process it is possible to unify the insights from a diverse collection of investigations within a single framework, thus furthering our understanding of natural language as a whole. This thesis gives several examples of how insights from investigations into natural language can be captured in SUG. Since these investigations come from a variety of perspectives on natural language, these examples demonstrate that SUG can be used as a unifying framework for investigating natural language

Calibrating Generative Models: The Probabilistic Chomsky-Schützenberger Hierarchy

A probabilistic Chomsky–Schützenberger hierarchy of grammars is introduced and studied, with the aim of understanding the expressive power of generative models. We offer characterizations of the distributions definable at each level of the hierarchy, including probabilistic regular, context-free, (linear) indexed, context-sensitive, and unrestricted grammars, each corresponding to familiar probabilistic machine classes. Special attention is given to distributions on (unary notations for) positive integers. Unlike in the classical case where the "semi-linear" languages all collapse into the regular languages, using analytic tools adapted from the classical setting we show there is no collapse in the probabilistic hierarchy: more distributions become definable at each level. We also address related issues such as closure under probabilistic conditioning