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From Proof Texts to Logic. Discourse Representation Structures for Proof Texts in Mathematics
(2009)
We present an extension to Discourse Representation Theory that can be used to analyze mathematical texts written in the commonly used semi-formal language of mathematics (or at least a subset of it). Moreover, we describe an algorithm that can be used to check the resulting Proof Representation Structures for their logical validity and adequacy as a proof.
Repairs for Reasoning
(2013)
We describe and experimentally investigate phenomena of modal enrichment, that is, phenomena in which a recipient non-literally interprets an utterance by creating and applying a modal operator. We give competing explanations for these phenomena - namely an explanation according to which modal enrichment is a repair procedure for making the utterance match a script of information processing vs. an explanation according to which modal enrichment is triggered by rhetorical structure.
This paper discusses the semi-formal language of mathematics and presents the Naproche CNL, a controlled natural language for mathematical authoring. Proof Representation Structures, an adaptation of Discourse Representation Structures, are used to represent the semantics of texts written in the Naproche CNL. We discuss how the Naproche CNL can be used in formal mathematics, and present our prototypical Naproche system, a computer program for parsing texts in the Naproche CNL and checking the proofs in them for logical correctness.