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SUMMARY:Natural mathematical language for the computer - Arnold Neumaier\,
  University of Vienna
DTSTART:20100625T110000Z
DTEND:20100625T120000Z
UID:TALK25139@talks.cam.ac.uk
CONTACT:Laura Rimell
DESCRIPTION:This is joint work with Peter Schodl and Kevin Kofler\, also f
 rom Vienna.\nWe are currently working towards the creation of an automatic
 \nmathematical research system that can support mathematicians in their\nd
 aily work\, providing services for abstract mathematics as easily as\nLate
 x provides typesetting services\, the arXiv provides access to\npreprints\
 , Google provides web services\, Matlab provides numerical\nservices\, or 
 Mathematica provides symbolic services.\n\nThe ultimate goal is to be able
  to read\, understand\, and process\nautomatically ordinary mathematical t
 ext of the kind found in\nscholarly articles and books\, as far as they do
  not involve historical\,\nanecdotal\, or other content that requires cult
 ural knowledge from\noutside core mathematics.\nThis restriction reduces t
 he difficult problems of automatic natural\nlanguage processing to a manag
 eable level.\n\nA limited part of our vision -- expected to take 50 man ye
 ars to bring\na system far enough that it will grow by itself in a wikiped
 ia-like\nfashion -- is being realized through the project\n``A modeling sy
 stem for mathematics'' (MoSMath)\, currently\nsupported by a grant of the 
 Austrian Science Foundation FWF.\nWithin this project\, we attempt to crea
 te a modeling and documentation\nlanguage for conceptual and numerical mat
 hematics called FMathL\n(formal mathematical language)\, suited to the hab
 its of mathematicians.\n\nFMathL allows to specify problems in their natur
 al mathematical form\,\nwith functions\, sets\, operators\, measures\, qua
 ntifiers\, tables\, cases\,\netc.\nFormal models are specified close to ho
 w they would be communicated\ninformally 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 m
 athematics in a form that\nis faithfully translated into the semantic matr
 ix.\nApplication modules can therefore be fed by algorithms that extract\n
 from the semantic matrix the relevant information.\n\nAt present we have a
  fragment of FMathL designed to encode parts of\nmathematics (mainly relat
 ed to optimization problems) in the semantic\nmatrix\, checking it for sem
 antic adequacy (currently on the level of\ntypes only\, ignoring many more
  subtle issues)\, and preparing it for\nautomatic re-rendering in natural 
 language.\n\nAn interface to the controlled natural language of Naproche (
 developped\nin Germany for representing human-readable formal proofs) enab
 les us\nto read and represent texts written in this language\, and to recr
 eate\nNaproche-texts from texts represented in the semantic matrix.\n\nWe 
 are currently working on an interface to the Grammatical Framework\,\nwhic
 h has multiple language support with correct inflection.\n
LOCATION:SW01\, Computer Laboratory
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