Negation in Cognitive Reasoning (2012.12641v3)

Abstract: Negation is both an operation in formal logic and in natural language by which a proposition is replaced by one stating the opposite, as by the addition of "not" or another negation cue. Treating negation in an adequate way is required for cognitive reasoning, which aims at modeling the human ability to draw meaningful conclusions despite incomplete and inconsistent knowledge. One task of cognitive reasoning is answering questions given by sentences in natural language. There are tools based on discourse representation theory to convert sentences automatically into a formal logic representation, and additional knowledge can be added using the predicate names in the formula and knowledge databases. However, the knowledge in logic databases in practice always is incomplete. Hence, forward reasoning of automated reasoning systems alone does not suffice to derive answers to questions because, instead of complete proofs, often only partial positive knowledge can be derived, while negative knowledge is used only during the reasoning process. In consequence, we aim at eliminating syntactic negation, strictly speaking, the negated event or property. In this paper, we describe an effective procedure to determine the negated event or property in order to replace it by its inverse. This lays the basis of cognitive reasoning, employing both logic and machine learning for general question answering. We evaluate our procedure by several benchmarks and demonstrate its practical usefulness in our cognitive reasoning system.