304 research outputs found
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
Towards an Interaction-based Integration of MKM Services into End-User Applications
The Semantic Alliance (SAlly) Framework, first presented at MKM 2012, allows
integration of Mathematical Knowledge Management services into typical
applications and end-user workflows. From an architecture allowing invasion of
spreadsheet programs, it grew into a middle-ware connecting spreadsheet, CAD,
text and image processing environments with MKM services. The architecture
presented in the original paper proved to be quite resilient as it is still
used today with only minor changes.
This paper explores extensibility challenges we have encountered in the
process of developing new services and maintaining the plugins invading
end-user applications. After an analysis of the underlying problems, I present
an augmented version of the SAlly architecture that addresses these issues and
opens new opportunities for document type agnostic MKM services.Comment: 14 pages, 7 figure
Search Interfaces for Mathematicians
Access to mathematical knowledge has changed dramatically in recent years,
therefore changing mathematical search practices. Our aim with this study is to
scrutinize professional mathematicians' search behavior. With this
understanding we want to be able to reason why mathematicians use which tool
for what search problem in what phase of the search process. To gain these
insights we conducted 24 repertory grid interviews with mathematically inclined
people (ranging from senior professional mathematicians to non-mathematicians).
From the interview data we elicited patterns for the user group
"mathematicians" that can be applied when understanding design issues or
creating new designs for mathematical search interfaces.Comment: conference article "CICM'14: International Conference on Computer
Mathematics 2014", DML-Track: Digital Math Libraries 17 page
Interoperability in the OpenDreamKit Project: The Math-in-the-Middle Approach
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. From that, OpenDreamKit will deliver
a flexible toolkit enabling research groups to set up Virtual Research
Environments, customised to meet the varied needs of research projects in pure
mathematics and applications.
An important step in the OpenDreamKit endeavor is to foster the
interoperability between a variety of systems, ranging from computer algebra
systems over mathematical databases to front-ends. This is the mission of the
integration work package (WP6). We report on experiments and future plans with
the \emph{Math-in-the-Middle} approach. This information architecture consists
in a central mathematical ontology that documents the domain and fixes a joint
vocabulary, combined with specifications of the functionalities of the various
systems. Interaction between systems can then be enriched by pivoting off this
information architecture.Comment: 15 pages, 7 figure
Realms: A Structure for Consolidating Knowledge about Mathematical Theories
Since there are different ways of axiomatizing and developing a mathematical
theory, knowledge about a such a theory may reside in many places and in many
forms within a library of formalized mathematics. We introduce the notion of a
realm as a structure for consolidating knowledge about a mathematical theory. A
realm contains several axiomatizations of a theory that are separately
developed. Views interconnect these developments and establish that the
axiomatizations are equivalent in the sense of being mutually interpretable. A
realm also contains an external interface that is convenient for users of the
library who want to apply the concepts and facts of the theory without delving
into the details of how the concepts and facts were developed. We illustrate
the utility of realms through a series of examples. We also give an outline of
the mechanisms that are needed to create and maintain realms.Comment: As accepted for CICM 201
Which one is better: presentation-based or content-based math search?
Mathematical content is a valuable information source and retrieving this
content has become an important issue. This paper compares two searching
strategies for math expressions: presentation-based and content-based
approaches. Presentation-based search uses state-of-the-art math search system
while content-based search uses semantic enrichment of math expressions to
convert math expressions into their content forms and searching is done using
these content-based expressions. By considering the meaning of math
expressions, the quality of search system is improved over presentation-based
systems
A Universal Machine for Biform Theory Graphs
Broadly speaking, there are two kinds of semantics-aware assistant systems
for mathematics: proof assistants express the semantic in logic and emphasize
deduction, and computer algebra systems express the semantics in programming
languages and emphasize computation. Combining the complementary strengths of
both approaches while mending their complementary weaknesses has been an
important goal of the mechanized mathematics community for some time. We pick
up on the idea of biform theories and interpret it in the MMTt/OMDoc framework
which introduced the foundations-as-theories approach, and can thus represent
both logics and programming languages as theories. This yields a formal,
modular framework of biform theory graphs which mixes specifications and
implementations sharing the module system and typing information. We present
automated knowledge management work flows that interface to existing
specification/programming tools and enable an OpenMath Machine, that
operationalizes biform theories, evaluating expressions by exhaustively
applying the implementations of the respective operators. We evaluate the new
biform framework by adding implementations to the OpenMath standard content
dictionaries.Comment: Conferences on Intelligent Computer Mathematics, CICM 2013 The final
publication is available at http://link.springer.com
Ontology: A Linked Data Hub for Mathematics
In this paper, we present an ontology of mathematical knowledge concepts that
covers a wide range of the fields of mathematics and introduces a balanced
representation between comprehensive and sensible models. We demonstrate the
applications of this representation in information extraction, semantic search,
and education. We argue that the ontology can be a core of future integration
of math-aware data sets in the Web of Data and, therefore, provide mappings
onto relevant datasets, such as DBpedia and ScienceWISE.Comment: 15 pages, 6 images, 1 table, Knowledge Engineering and the Semantic
Web - 5th International Conferenc
A Vernacular for Coherent Logic
We propose a simple, yet expressive proof representation from which proofs
for different proof assistants can easily be generated. The representation uses
only a few inference rules and is based on a frag- ment of first-order logic
called coherent logic. Coherent logic has been recognized by a number of
researchers as a suitable logic for many ev- eryday mathematical developments.
The proposed proof representation is accompanied by a corresponding XML format
and by a suite of XSL transformations for generating formal proofs for
Isabelle/Isar and Coq, as well as proofs expressed in a natural language form
(formatted in LATEX or in HTML). Also, our automated theorem prover for
coherent logic exports proofs in the proposed XML format. All tools are
publicly available, along with a set of sample theorems.Comment: CICM 2014 - Conferences on Intelligent Computer Mathematics (2014
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