Abstract

Our long-range goal is to implement a program for the machine verification of textbook proofs. The problem was first tackled by Simon [Sim88]. However, Simon does not claim to have used or developed an adequate theory for semantics construction. A prerequisite for parsing textbook proofs is to being able to parse terms and formulae that occur in these proofs. We analyze a typical textbook proof and describe some of the linguistic phenomena one has to cope with, focusing on problems that involve the handling of terms and formulae. We propose, contrarily to Simon, an adequate theory for semantics construction, namely DRT, which, however, must be adapted to fit our needs. 2 Linguistic analysis Fig. 1 depicts a typical proof taken from a standard textbook on elementary number theory. We analyze it from the linguistics perspective focusing on potential difficulties: Constants and variables have a domain and scope which extends across text and formulae. Obviously, the occurrences of p in p | ab, p | a and p | b (Fig. 1, line 4) refer to their first occurrence in if p is prime (same line). However, it is not required that the occurrences of p, a and b in line 8 refer to the occurrences of p, a and b in line 4. The term abc...l (line 8) describes the factorization of objects a,b,c,...,l. Albeit the missing c, the phrase a,b,... l (line 9) enumerates also the factors a,b,c,...,l. Equally, q b1 1... qbj j the terms p a1 (line 13) refers to the same mathematical entity as qb1 1 qb2 2...qbj j

Citations

627	From Discourse to Logic - Kamp, Reyle - 1993
34	Representation and Inference for Natural Language. A - Blackburn, Bos - 2005
9	Checking natural language proofs - Simon - 1988