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CATEGORIES:NLIP Seminar Series
SUMMARY:Natural mathematical language for the computer - A
rnold Neumaier\, University of Vienna
DTSTART;TZID=Europe/London:20100625T120000
DTEND;TZID=Europe/London:20100625T130000
UID:TALK25139AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/25139
DESCRIPTION:This is joint work with Peter Schodl and Kevin Kof
ler\, also from Vienna.\nWe are currently working
towards the creation of an automatic\nmathematical
research system that can support mathematicians i
n their\ndaily work\, providing services for abstr
act mathematics as easily as\nLatex provides types
etting services\, the arXiv provides access to\npr
eprints\, Google provides web services\, Matlab pr
ovides numerical\nservices\, or Mathematica provid
es symbolic services.\n\nThe ultimate goal is to b
e able to read\, understand\, and process\nautomat
ically ordinary mathematical text of the kind foun
d in\nscholarly articles and books\, as far as the
y do not involve historical\,\nanecdotal\, or othe
r content that requires cultural knowledge from\no
utside core mathematics.\nThis restriction reduces
the difficult problems of automatic natural\nlang
uage processing to a manageable level.\n\nA limite
d part of our vision -- expected to take 50 man ye
ars to bring\na system far enough that it will gro
w by itself in a wikipedia-like\nfashion -- is bei
ng realized through the project\n``A modeling syst
em for mathematics'' (MoSMath)\, currently\nsuppor
ted by a grant of the Austrian Science Foundation
FWF.\nWithin this project\, we attempt to create a
modeling and documentation\nlanguage for conceptu
al and numerical mathematics called FMathL\n(forma
l mathematical language)\, suited to the habits of
mathematicians.\n\nFMathL allows to specify probl
ems in their natural mathematical form\,\nwith fun
ctions\, sets\, operators\, measures\, quantifiers
\, tables\, cases\,\netc.\nFormal models are speci
fied close to how they would be communicated\ninfo
rmally when describing them in a lecture or paper\
, except that\nno relevant details are suppressed.
\n\nA faithful representation of the semantics in
terms of a so-called\nsemantic matrix is the heart
of our approach.\nFMathL enables users to express
arbitrary mathematics in a form that\nis faithful
ly translated into the semantic matrix.\nApplicati
on modules can therefore be fed by algorithms that
extract\nfrom the semantic matrix the relevant in
formation.\n\nAt present we have a fragment of FMa
thL designed to encode parts of\nmathematics (main
ly related to optimization problems) in the semant
ic\nmatrix\, checking it for semantic adequacy (cu
rrently on the level of\ntypes only\, ignoring man
y more subtle issues)\, and preparing it for\nauto
matic re-rendering in natural language.\n\nAn inte
rface to the controlled natural language of Naproc
he (developped\nin Germany for representing human-
readable formal proofs) enables us\nto read and re
present texts written in this language\, and to re
create\nNaproche-texts from texts represented in t
he semantic matrix.\n\nWe are currently working on
an interface to the Grammatical Framework\,\nwhic
h has multiple language support with correct infle
ction.\n
LOCATION:SW01\, Computer Laboratory
CONTACT:Laura Rimell
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