## About

15

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## Publications

Publications (15)

OpenDreamKit – “Open Digital Research Environment Toolkit for the Advancement of Mathematics” – is an H2020 EU Research Infrastructure project that aims at supporting, over the period 2015–2019, the ecosystem of open-source mathematical software systems. OpenDreamKit will deliver a flexible toolkit enabling research groups to set up Virtual Researc...

Mathematical vernacular – the everyday language we use to communicate about mathematics is characterized by a special vocabulary. If we want to support humans with mathematical documents, we need to extract their semantics and for that we need a resource that captures the terminological, linguistic, and ontological aspects of the mathematical vocab...

In the traditional knowledge dissemination process in mathematics and sciences, authors write semi-selfcontained articles which are then published in journals, conference proceedings, preprint archives, and/or given as talks. Other scientists read these, extract the new knowledge, integrate it into their personal mental model of the field, and use...

Mathematicians integrate acquired knowledge into a mental model. For trained mathematicians, the mental model seems to include not just the bare facts, but various induced forms of knowledge, and the amount of this and the ability to perform all reasoning and knowledge operations taking that into account can be seen as a measure of mathematical tra...

Representation formats based on theory graphs have been successful in formalized mathematics as they provide valuable logic-compatible modularity and foster reuse. Theories – sets of symbols and axioms – serve as modules and theory morphisms – truth-preserving mappings from the (language of the) source theory to the target theory – formalize inheri...

There is an interesting duality between the forms and extents of mathematical knowledge that is verbally expressed (published in articles, scribbled on blackboards, or presented in talks/discussions) and the forms that are needed to successfully extend and apply mathematics. To “do mathematics”, we need to judge the veracity, extract the relevant s...

We present the MathHub.info system, a development environment for active mathematical documents and an archive for flexiformal mathematics. It offers a rich interface for reading, writing, and interacting with mathematical documents and knowledge. The core of the MathHub.info system is an archive for flexiformal mathematical documents and libraries...

Due to the high degree of interconnectedness of formal mathematical statements and theories, human authors often have difficulties anticipating and tracking the effects of a change in large bodies of symbolic mathematical knowledge. Therefore, the automation of change management is often desirable. But while computers can in principle detect and pr...

Over recent decades there has been a trend towards formalised mathematics, and a number of sophisticated systems have been developed both to support the formalisation process and to verify the results mechanically. However, each tool is based on a specific foundation of mathematics, and formalisations in different systems are not necessarily compat...

The Mizar Mathematical Library is one of the largest libraries of formalized mathematics. Its language is highly optimized for authoring by humans. As in natural languages, the meaning of an expression is influenced by its (mathematical) context in a way that is natural to humans, but harder to specify for machine manipulation. Thus its custom file...

The Mizar Mathematical Library is one of the largest libraries of formalized and mechanically verified mathematics. Its language is highly optimized for authoring by humans. As in natural languages, the meaning of an expression is influenced by its (mathematical) context in a way that is natural to humans, but harder to specify for machine manipula...

We discuss formula search in highly modular libraries, such as the LATIN atlas. In such libraries, statements can be inherited (and thus need not be explicitly represented) via morphisms that can include translations. This is good for knowledge management as the number of induced (i.e. not explicitly represented) statements can grow exponen-tially...

The MMT language constitutes a scalable representation and interchange format for formal math-ematical knowledge. It is foundation-independent and permits natural representations of the syntax and semantics of virtually all declarative languages. This is leveraged in the MMT API, which pro-vides a variety of generic logical and knowledge management...

## Projects

Project (1)

Language and System for the Uniform Representation of Knowledge
http://uniformal.github.io/