The Naproche Project Controlled Natural Language Proof Checking of Mathematical Texts

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Abstract. The Naproche system is a system for linguistically analysing and proof-checking mathematical texts written in a controlled natural language. The aim is to have an input language that is as close as possible to the language that mathematicians actually use when writing textbooks or papers. Mathematical texts consist of a combination of natural language and symbolic mathematics, with symbolic mathematics obeying its own syntactic rules. We discuss the difficulties that a program for parsing and disambiguating symbolic mathematics must face and present how these difficulties have been tackled in the Naproche system. One of these difficulties is the fact that information provided in the preceding contextincluding information provided in natural language -can influence the way a symbolic expression has to be disambiguated.

Section: The Naproche Systemmentioning

confidence: 99%

Section: Possible Approaches To Disambiguationmentioning

confidence: 99%

Parsing and Disambiguation of Symbolic Mathematics in the Naproche System

Cramer

Koepke

Schröder

2011

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“…The Naproche CNL [2] is a controlled natural language for mathematical texts, i.e. a controlled subset of the semi-formal language of mathematics (SFLM) as used in mathematical journals and textbooks.…”

Section: Introductionmentioning

confidence: 99%

“…a controlled subset of the semi-formal language of mathematics (SFLM) as used in mathematical journals and textbooks. The Naproche system translates Naproche CNL texts first into Proof Representation Structures (PRSs, [2]), an adapted version of Discourse Representation Structures, which are further translated into lists of first-order formulae which are used for checking the logical correctness of a Naproche text using automated theorem provers.…”

Section: Introductionmentioning

confidence: 99%

Interpreting Plurals in the Naproche CNL

Cramer

Schröder

2012

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Abstract. The Naproche CNL is a controlled natural language for mathematical texts. A recent addition to the Naproche CNL are plural statements. We discuss the collective-distributive ambiguity in the context of mathematical language, as well as pairwise interpretations of collective plurals. Additionally, we present a special scope ambiguity conjunctions give rise to. Finally, we describe an innovative plural interpretation algorithm implemented in Naproche for disambiguating plurals in DRT and giving them the interpretation that would normally be preferred in a mathematical context.

“…It has motivated systems like STUDENT [2], Mathematical Vernacular [3], Mizar [4], OMEGA [5], Isar [6], Vip [7], Theorema [8], MathLang [9], Naproche [10], and FMathL [11]. These systems permit user interaction in a notation that resembles English more than logical symbolisms do.…”

Section: Introductionmentioning

confidence: 99%

Translating between Language and Logic: What Is Easy and What Is Difficult

Ranta

2011

Abstract. Natural language interfaces make formal systems accessible in informal language. They have a potential to make systems like theorem provers more widely used by students, mathematicians, and engineers who are not experts in logic. This paper shows that simple but still useful interfaces are easy to build with available technology. They are moreover easy to adapt to different formalisms and natural languages. The language can be made reasonably nice and stylistically varied. However, a fully general translation between logic and natural language also poses difficult, even unsolvable problems. This paper investigates what can be realistically expected and what problems are hard.