A Survey on Retrieval of Mathematical Knowledge

We present a short survey of the literature on indexing and retrieval of mathematical knowledge, with pointers to 72 papers and tentative taxonomies of both retrieval problems and recurring techniques.Comment: CICM 2015, 20 page

Specifying Reusable Components

Reusable software components need expressive specifications. This paper outlines a rigorous foundation to model-based contracts, a method to equip classes with strong contracts that support accurate design, implementation, and formal verification of reusable components. Model-based contracts conservatively extend the classic Design by Contract with a notion of model, which underpins the precise definitions of such concepts as abstract equivalence and specification completeness. Experiments applying model-based contracts to libraries of data structures suggest that the method enables accurate specification of practical software

HOL(y)Hammer: Online ATP Service for HOL Light

HOL(y)Hammer is an online AI/ATP service for formal (computer-understandable) mathematics encoded in the HOL Light system. The service allows its users to upload and automatically process an arbitrary formal development (project) based on HOL Light, and to attack arbitrary conjectures that use the concepts defined in some of the uploaded projects. For that, the service uses several automated reasoning systems combined with several premise selection methods trained on all the project proofs. The projects that are readily available on the server for such query answering include the recent versions of the Flyspeck, Multivariate Analysis and Complex Analysis libraries. The service runs on a 48-CPU server, currently employing in parallel for each task 7 AI/ATP combinations and 4 decision procedures that contribute to its overall performance. The system is also available for local installation by interested users, who can customize it for their own proof development. An Emacs interface allowing parallel asynchronous queries to the service is also provided. The overall structure of the service is outlined, problems that arise and their solutions are discussed, and an initial account of using the system is given

The MMT API: A Generic MKM System

The MMT language has been developed as a scalable representation and interchange language for formal mathematical knowledge. It permits natural representations of the syntax and semantics of virtually all declarative languages while making MMT-based MKM services easy to implement. It is foundationally unconstrained and can be instantiated with specific formal languages. The MMT API implements the MMT language along with multiple backends for persistent storage and frontends for machine and user access. Moreover, it implements a wide variety of MMT-based knowledge management services. The API and all services are generic and can be applied to any language represented in MMT. A plugin interface permits injecting syntactic and semantic idiosyncrasies of individual formal languages.Comment: Conferences on Intelligent Computer Mathematics (CICM) 2013 The final publication is available at http://link.springer.com

Formal models, usability and related work in IR (editorial for special edition)

The Glasgow IR group has carried out both theoretical and empirical work, aimed at giving end users efficient and effective access to large collections of multimedia data

Towards MKM in the Large: Modular Representation and Scalable Software Architecture

MKM has been defined as the quest for technologies to manage mathematical knowledge. MKM "in the small" is well-studied, so the real problem is to scale up to large, highly interconnected corpora: "MKM in the large". We contend that advances in two areas are needed to reach this goal. We need representation languages that support incremental processing of all primitive MKM operations, and we need software architectures and implementations that implement these operations scalably on large knowledge bases. We present instances of both in this paper: the MMT framework for modular theory-graphs that integrates meta-logical foundations, which forms the base of the next OMDoc version; and TNTBase, a versioned storage system for XML-based document formats. TNTBase becomes an MMT database by instantiating it with special MKM operations for MMT.Comment: To appear in The 9th International Conference on Mathematical Knowledge Management: MKM 201

Escaping the Trap of too Precise Topic Queries

At the very center of digital mathematics libraries lie controlled vocabularies which qualify the {\it topic} of the documents. These topics are used when submitting a document to a digital mathematics library and to perform searches in a library. The latter are refined by the use of these topics as they allow a precise classification of the mathematics area this document addresses. However, there is a major risk that users employ too precise topics to specify their queries: they may be employing a topic that is only "close-by" but missing to match the right resource. We call this the {\it topic trap}. Indeed, since 2009, this issue has appeared frequently on the i2geo.net platform. Other mathematics portals experience the same phenomenon. An approach to solve this issue is to introduce tolerance in the way queries are understood by the user. In particular, the approach of including fuzzy matches but this introduces noise which may prevent the user of understanding the function of the search engine. In this paper, we propose a way to escape the topic trap by employing the navigation between related topics and the count of search results for each topic. This supports the user in that search for close-by topics is a click away from a previous search. This approach was realized with the i2geo search engine and is described in detail where the relation of being {\it related} is computed by employing textual analysis of the definitions of the concepts fetched from the Wikipedia encyclopedia.Comment: 12 pages, Conference on Intelligent Computer Mathematics 2013 Bath, U