Learning to Prove Theorems via Interacting with Proof Assistants

Humans prove theorems by relying on substantial high-level reasoning and problem-specific insights. Proof assistants offer a formalism that resembles human mathematical reasoning, representing theorems in higher-order logic and proofs as high-level tactics. However, human experts have to construct proofs manually by entering tactics into the proof assistant. In this paper, we study the problem of using machine learning to automate the interaction with proof assistants. We construct CoqGym, a large-scale dataset and learning environment containing 71K human-written proofs from 123 projects developed with the Coq proof assistant. We develop ASTactic, a deep learning-based model that generates tactics as programs in the form of abstract syntax trees (ASTs). Experiments show that ASTactic trained on CoqGym can generate effective tactics and can be used to prove new theorems not previously provable by automated methods. Code is available at https://github.com/princeton-vl/CoqGym.Comment: Accepted to ICML 201

Jointly Multiple Events Extraction via Attention-based Graph Information Aggregation

Event extraction is of practical utility in natural language processing. In the real world, it is a common phenomenon that multiple events existing in the same sentence, where extracting them are more difficult than extracting a single event. Previous works on modeling the associations between events by sequential modeling methods suffer a lot from the low efficiency in capturing very long-range dependencies. In this paper, we propose a novel Jointly Multiple Events Extraction (JMEE) framework to jointly extract multiple event triggers and arguments by introducing syntactic shortcut arcs to enhance information flow and attention-based graph convolution networks to model graph information. The experiment results demonstrate that our proposed framework achieves competitive results compared with state-of-the-art methods.Comment: accepted by EMNLP 201

Advanced Knowledge Technologies at the Midterm: Tools and Methods for the Semantic Web

The University of Edinburgh and research sponsors are authorised to reproduce and distribute reprints and on-line copies for their purposes notwithstanding any copyright annotation hereon. The views and conclusions contained herein are the author’s and shouldn’t be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of other parties.In a celebrated essay on the new electronic media, Marshall McLuhan wrote in 1962:Our private senses are not closed systems but are endlessly translated into each other in that experience which we call consciousness. Our extended senses, tools, technologies, through the ages, have been closed systems incapable of interplay or collective awareness. Now, in the electric age, the very instantaneous nature of co-existence among our technological instruments has created a crisis quite new in human history. Our extended faculties and senses now constitute a single field of experience which demands that they become collectively conscious. Our technologies, like our private senses, now demand an interplay and ratio that makes rational co-existence possible. As long as our technologies were as slow as the wheel or the alphabet or money, the fact that they were separate, closed systems was socially and psychically supportable. This is not true now when sight and sound and movement are simultaneous and global in extent. (McLuhan 1962, p.5, emphasis in original)Over forty years later, the seamless interplay that McLuhan demanded between our technologies is still barely visible. McLuhan’s predictions of the spread, and increased importance, of electronic media have of course been borne out, and the worlds of business, science and knowledge storage and transfer have been revolutionised. Yet the integration of electronic systems as open systems remains in its infancy.Advanced Knowledge Technologies (AKT) aims to address this problem, to create a view of knowledge and its management across its lifecycle, to research and create the services and technologies that such unification will require. Half way through its sixyear span, the results are beginning to come through, and this paper will explore some of the services, technologies and methodologies that have been developed. We hope to give a sense in this paper of the potential for the next three years, to discuss the insights and lessons learnt in the first phase of the project, to articulate the challenges and issues that remain.The WWW provided the original context that made the AKT approach to knowledge management (KM) possible. AKT was initially proposed in 1999, it brought together an interdisciplinary consortium with the technological breadth and complementarity to create the conditions for a unified approach to knowledge across its lifecycle. The combination of this expertise, and the time and space afforded the consortium by the IRC structure, suggested the opportunity for a concerted effort to develop an approach to advanced knowledge technologies, based on the WWW as a basic infrastructure.The technological context of AKT altered for the better in the short period between the development of the proposal and the beginning of the project itself with the development of the semantic web (SW), which foresaw much more intelligent manipulation and querying of knowledge. The opportunities that the SW provided for e.g., more intelligent retrieval, put AKT in the centre of information technology innovation and knowledge management services; the AKT skill set would clearly be central for the exploitation of those opportunities.The SW, as an extension of the WWW, provides an interesting set of constraints to the knowledge management services AKT tries to provide. As a medium for the semantically-informed coordination of information, it has suggested a number of ways in which the objectives of AKT can be achieved, most obviously through the provision of knowledge management services delivered over the web as opposed to the creation and provision of technologies to manage knowledge.AKT is working on the assumption that many web services will be developed and provided for users. The KM problem in the near future will be one of deciding which services are needed and of coordinating them. Many of these services will be largely or entirely legacies of the WWW, and so the capabilities of the services will vary. As well as providing useful KM services in their own right, AKT will be aiming to exploit this opportunity, by reasoning over services, brokering between them, and providing essential meta-services for SW knowledge service management.Ontologies will be a crucial tool for the SW. The AKT consortium brings a lot of expertise on ontologies together, and ontologies were always going to be a key part of the strategy. All kinds of knowledge sharing and transfer activities will be mediated by ontologies, and ontology management will be an important enabling task. Different applications will need to cope with inconsistent ontologies, or with the problems that will follow the automatic creation of ontologies (e.g. merging of pre-existing ontologies to create a third). Ontology mapping, and the elimination of conflicts of reference, will be important tasks. All of these issues are discussed along with our proposed technologies.Similarly, specifications of tasks will be used for the deployment of knowledge services over the SW, but in general it cannot be expected that in the medium term there will be standards for task (or service) specifications. The brokering metaservices that are envisaged will have to deal with this heterogeneity.The emerging picture of the SW is one of great opportunity but it will not be a wellordered, certain or consistent environment. It will comprise many repositories of legacy data, outdated and inconsistent stores, and requirements for common understandings across divergent formalisms. There is clearly a role for standards to play to bring much of this context together; AKT is playing a significant role in these efforts. But standards take time to emerge, they take political power to enforce, and they have been known to stifle innovation (in the short term). AKT is keen to understand the balance between principled inference and statistical processing of web content. Logical inference on the Web is tough. Complex queries using traditional AI inference methods bring most distributed computer systems to their knees. Do we set up semantically well-behaved areas of the Web? Is any part of the Web in which semantic hygiene prevails interesting enough to reason in? These and many other questions need to be addressed if we are to provide effective knowledge technologies for our content on the web

Using Neural Networks for Relation Extraction from Biomedical Literature

Using different sources of information to support automated extracting of relations between biomedical concepts contributes to the development of our understanding of biological systems. The primary comprehensive source of these relations is biomedical literature. Several relation extraction approaches have been proposed to identify relations between concepts in biomedical literature, namely, using neural networks algorithms. The use of multichannel architectures composed of multiple data representations, as in deep neural networks, is leading to state-of-the-art results. The right combination of data representations can eventually lead us to even higher evaluation scores in relation extraction tasks. Thus, biomedical ontologies play a fundamental role by providing semantic and ancestry information about an entity. The incorporation of biomedical ontologies has already been proved to enhance previous state-of-the-art results.Comment: Artificial Neural Networks book (Springer) - Chapter 1