We introduce a new formal model -- based on the mathematical construct of sheaves -- for representing contradictory information in textual sources. This model has the advantage of letting us (a) identify the causes of the inconsistency; (b) measure how strong it is; (c) and do something about it, e.g. suggest ways to reconcile inconsistent advice. This model naturally represents the distinction between contradictions and disagreements. It is based on the idea of representing natural language sentences as formulas with parameters sitting on lattices, creating partial orders based on predicates shared by theories, and building sheaves on these partial orders with products of lattices as stalks. Degrees of disagreement are measured by the existence of global and local sections. Limitations of the sheaf approach and connections to recent work in natural language processing, as well as the topics of contextuality in physics, data fusion, topological data analysis and epistemology are also discussed.
Our original motivation in @cite_7 came from modeling medical guidelines, but, as noted above, contradictory sets of documents are pervasive. In the last ten years the field of computational linguistics recognized this phenomenon, and initiated ongoing computational research on reasoning with textual and contradictory information ( @cite_32 , @cite_22 ). The motivation for a new formalization of compatibility comes partially from an opportunity to improve on the methods proposed in @cite_9 .
@cite_9 @cite_22 @cite_32 @cite_7
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We present a computational theory of the paragraph. Within it we formally define coherence, give semantics to the adversative conjunction "but" and to the Gricean maxim of quantity, and present some new methods for anaphora resolution.The theory precisely characterizes the relationship between the content of the paragraph and background knowledge needed for its understanding. This is achieved by introducing a new type of logical theory consisting of an object level, corresponding to the content of the paragraph, a referential level, which is a new logical level encoding background knowledge, and a met alevel containing constraints on models of discourse (e.g. a formal version of Gricean maxims). We propose also specific mechanisms of interaction between these levels, resembling both classical provability and abduction. Paragraphs are then represented by a class of structures called p-models. This paper introduces the Multi-Genre Natural Language Inference (MultiNLI) corpus, a dataset designed for use in the development and evaluation of machine learning models for sentence understanding. In addition to being one of the largest corpora available for the task of NLI, at 433k examples, this corpus improves upon available resources in its coverage: it offers data from ten distinct genres of written and spoken English--making it possible to evaluate systems on nearly the full complexity of the language--and it offers an explicit setting for the evaluation of cross-genre domain adaptation. We introduce a formal distinction between contradictions and disagreements in natural language texts, motivated by the need to formally reason about contradictory medical guidelines. This is a novel and potentially very useful distinction, and has not been discussed so far in NLP and logic. We also describe a NLP system capable of automated finding contradictory medical guidelines; the system uses a combination of text analysis and information retrieval modules. We also report positive evaluation results on a small corpus of contradictory medical recommendations.