A* CCG Parsing with a Supertag-factored Model

We introduce a new CCG parsing model which is factored on lexical category as-signments. Parsing is then simply a de-terministic search for the most probable category sequence that supports a CCG derivation. The parser is extremely simple, with a tiny feature set, no POS tagger, and no statistical model of the derivation or dependencies. Formulating the model in this way allows a highly effective heuris-tic for A ∗ parsing, which makes parsing extremely fast. Compared to the standard C&C CCG parser, our model is more ac-curate out-of-domain, is four times faster, has higher coverage, and is greatly simpli-fied. We also show that using our parser improves the performance of a state-of-the-art question answering system.

Trustworthy Formal Natural Language Specifications

Interactive proof assistants are computer programs carefully constructed to check a human-designed proof of a mathematical claim with high confidence in the implementation. However, this only validates truth of a formal claim, which may have been mistranslated from a claim made in natural language. This is especially problematic when using proof assistants to formally verify the correctness of software with respect to a natural language specification. The translation from informal to formal remains a challenging, time-consuming process that is difficult to audit for correctness. This paper shows that it is possible to build support for specifications written in expressive subsets of natural language, within existing proof assistants, consistent with the principles used to establish trust and auditability in proof assistants themselves. We implement a means to provide specifications in a modularly extensible formal subset of English, and have them automatically translated into formal claims, entirely within the Lean proof assistant. Our approach is extensible (placing no permanent restrictions on grammatical structure), modular (allowing information about new words to be distributed alongside libraries), and produces proof certificates explaining how each word was interpreted and how the sentence's structure was used to compute the meaning. We apply our prototype to the translation of various English descriptions of formal specifications from a popular textbook into Lean formalizations; all can be translated correctly with a modest lexicon with only minor modifications related to lexicon size.Comment: arXiv admin note: substantial text overlap with arXiv:2205.0781

Unsupervised grammar induction with Combinatory Categorial Grammars

Language is a highly structured medium for communication. An idea starts in the speaker's mind (semantics) and is transformed into a well formed, intelligible, sentence via the specific syntactic rules of a language. We aim to discover the fingerprints of this process in the choice and location of words used in the final utterance. What is unclear is how much of this latent process can be discovered from the linguistic signal alone and how much requires shared non-linguistic context, knowledge, or cues. Unsupervised grammar induction is the task of analyzing strings in a language to discover the latent syntactic structure of the language without access to labeled training data. Successes in unsupervised grammar induction shed light on the amount of syntactic structure that is discoverable from raw or part-of-speech tagged text. In this thesis, we present a state-of-the-art grammar induction system based on Combinatory Categorial Grammars. Our choice of syntactic formalism enables the first labeled evaluation of an unsupervised system. This allows us to perform an in-depth analysis of the system’s linguistic strengths and weaknesses. In order to completely eliminate reliance on any supervised systems, we also examine how performance is affected when we use induced word clusters instead of gold-standard POS tags. Finally, we perform a semantic evaluation of induced grammars, providing unique insights into future directions for unsupervised grammar induction systems

Combined distributional and logical semantics

Understanding natural language sentences requires interpreting words, and combining the meanings of words into the meanings of sentences. Despite much work on lexical and compositional semantics individually, existing approaches are unlikely to offer a complete solution. This thesis introduces a new approach, which combines the benefits of distributional lexical semantics and logical compositional semantics. Linguistic theories of compositional semantics have shown how logical forms can be built for sentences, and how to represent semantic operators such as negatives, quantifiers and modals. However, computational implementations of such theories have shown poor performance on applications, mainly due to a reliance on incomplete hand-built ontologies for the meanings of content words. Conversely, distributional semantics has been shown to be effective in learning the representations of content words based on collocations in large unlabelled corpora, but there are major outstanding challenges in representing function words and building representations for sentences. I introduce a new model which captures the main advantages of logical and distributional approaches. The proposal closely follows formal semantics, except for changing the definitions of content words. In traditional formal semantics, each word would express a different symbol. Instead, I allow multiple words to express the same symbol, corresponding to underlying concepts. For example, both the verb write and the noun author can be made to express the same relation. These symbols can be learnt by clustering symbols based on distributional statistics—for example, write and author will share many similar arguments. Crucially, the clustering means that the representations are symbolic, so can easily be incorporated into standard logical approaches. The simple model proves insufficient, and I develop several extensions. I develop an unsupervised probabilistic model of ambiguity, and show how this model can be built into compositional derivations to produce a distribution over logical forms. The flat clustering approach does not model relations between concepts, for example that buying implies owning. Instead, I show how to build graph structures over the clusters, which allows such inferences. I also explore if the abstract concepts can be generalized cross-lingually, for example mapping French verb ecrire to the same cluster as the English verb write. The systems developed show good performance on question answering and entailment tasks, and are capable of both sophisticated multi-sentence inferences involving quantifiers, and subtle reasoning about lexical semantics. These results show that distributional and formal logical semantics are not mutually exclusive, and that a combined model can be built that captures the advantages of each

Students´ language in computer-assisted tutoring of mathematical proofs

Truth and proof are central to mathematics. Proving (or disproving) seemingly simple statements often turns out to be one of the hardest mathematical tasks. Yet, doing proofs is rarely taught in the classroom. Studies on cognitive difficulties in learning to do proofs have shown that pupils and students not only often do not understand or cannot apply basic formal reasoning techniques and do not know how to use formal mathematical language, but, at a far more fundamental level, they also do not understand what it means to prove a statement or even do not see the purpose of proof at all. Since insight into the importance of proof and doing proofs as such cannot be learnt other than by practice, learning support through individualised tutoring is in demand. This volume presents a part of an interdisciplinary project, set at the intersection of pedagogical science, artificial intelligence, and (computational) linguistics, which investigated issues involved in provisioning computer-based tutoring of mathematical proofs through dialogue in natural language. The ultimate goal in this context, addressing the above-mentioned need for learning support, is to build intelligent automated tutoring systems for mathematical proofs. The research presented here has been focused on the language that students use while interacting with such a system: its linguistic propeties and computational modelling. Contribution is made at three levels: first, an analysis of language phenomena found in students´ input to a (simulated) proof tutoring system is conducted and the variety of students´ verbalisations is quantitatively assessed, second, a general computational processing strategy for informal mathematical language and methods of modelling prominent language phenomena are proposed, and third, the prospects for natural language as an input modality for proof tutoring systems is evaluated based on collected corpora

Broad-coverage model of prediction in human sentence processing

The aim of this thesis is to design and implement a cognitively plausible theory of sentence processing which incorporates a mechanism for modeling a prediction and verification process in human language understanding, and to evaluate the validity of this model on specific psycholinguistic phenomena as well as on broad-coverage, naturally occurring text. Modeling prediction is a timely and relevant contribution to the field because recent experimental evidence suggests that humans predict upcoming structure or lexemes during sentence processing. However, none of the current sentence processing theories capture prediction explicitly. This thesis proposes a novel model of incremental sentence processing that offers an explicit prediction and verification mechanism. In evaluating the proposed model, this thesis also makes a methodological contribution. The design and evaluation of current sentence processing theories are usually based exclusively on experimental results from individual psycholinguistic experiments on specific linguistic structures. However, a theory of language processing in humans should not only work in an experimentally designed environment, but should also have explanatory power for naturally occurring language. This thesis first shows that the Dundee corpus, an eye-tracking corpus of newspaper text, constitutes a valuable additional resource for testing sentence processing theories. I demonstrate that a benchmark processing effect (the subject/object relative clause asymmetry) can be detected in this data set (Chapter 4). I then evaluate two existing theories of sentence processing, Surprisal and Dependency Locality Theory (DLT), on the full Dundee corpus. This constitutes the first broad-coverage comparison of sentence processing theories on naturalistic text. I find that both theories can explain some of the variance in the eye-movement data, and that they capture different aspects of sentence processing (Chapter 5). In Chapter 6, I propose a new theory of sentence processing, which explicitly models prediction and verification processes, and aims to unify the complementary aspects of Surprisal and DLT. The proposed theory implements key cognitive concepts such as incrementality, full connectedness, and memory decay. The underlying grammar formalism is a strictly incremental version of Tree-adjoining Grammar (TAG), Psycholinguistically motivated TAG (PLTAG), which is introduced in Chapter 7. I then describe how the Penn Treebank can be converted into PLTAG format and define an incremental, fully connected broad-coverage parsing algorithm with associated probability model for PLTAG. Evaluation of the PLTAG model shows that it achieves the broad coverage required for testing a psycholinguistic theory on naturalistic data. On the standardized Penn Treebank test set, it approaches the performance of incremental TAG parsers without prediction (Chapter 8). Chapter 9 evaluates the psycholinguistic aspects of the proposed theory by testing it both on a on a selection of established sentence processing phenomena and on the Dundee eye-tracking corpus. The proposed theory can account for a larger range of psycholinguistic case studies than previous theories, and is a significant positive predictor of reading times on broad-coverage text. I show that it can explain a larger proportion of the variance in reading times than either DLT integration cost or Surprisal

Proceedings

Proceedings of the Ninth International Workshop on Treebanks and Linguistic Theories. Editors: Markus Dickinson, Kaili Müürisep and Marco Passarotti. NEALT Proceedings Series, Vol. 9 (2010), 268 pages. © 2010 The editors and contributors. Published by Northern European Association for Language Technology (NEALT) http://omilia.uio.no/nealt . Electronically published at Tartu University Library (Estonia) http://hdl.handle.net/10062/15891