Frames are a concept in knowledge representation that explains how the receiver, using background information, completes the information conveyed by the sender. This concept is used in different disciplines, most notably in cognitive linguistics and artificial intelligence. This paper argues that frames can serve as the basis for describing mathematical proofs. The usefulness of the concept is illustrated by giving a partial formalisation of proof frames, specifically focusing on induction proofs, and relevant parts of the mathematical theory within which the (...) proofs are conducted; for the latter, we look at natural numbers and trees specifically. (shrink)

Frames are a concept in knowledge representation that explains how the receiver, using background information, completes the information conveyed by the sender. This concept is used in different disciplines, most notably in cognitive linguistics and artificial intelligence. This paper argues that frames can serve as the basis for describing mathematical proofs. The usefulness of the concept is illustrated by giving a partial formalisation of proof frames, specifically focusing on induction proofs, and relevant parts of the mathematical theory within which the (...) proofs are conducted; for the latter, we look at natural numbers and trees specifically. (shrink)

We investigate an approach to improving statistical text classification by combining machine learners with an ontology-based identification of domain-specific topic categories. We apply this approach to ad hoc disclosures by public companies. This form of obligatory publicity concerns all information that might affect the stock price; relevant topic categories are governed by stringent regulations. Our goal is to classify disclosures according to their effect on stock prices (negative, neutral, positive). In the study reported here, we combine natural language parsing with (...) a formal background ontology to recognize disclosures concerning particular topics from a prescribed list. The semantic analysis identifies some of these topics with reasonable accuracy. We then demonstrate that machine learners benefit from the additional ontology-based information when predicting the cumulative abnormal return attributed to the disclosure at hand. (shrink)