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.
This opens the question whether sheaves can be used these contextual effects. The work of @cite_31 suggests they can. The contradictory judgments could be perhaps explained by different defaults or external information brought to bear on the situation, and they could be represented as local sections with different starting points.
@cite_31
2554492152 2166650854 1936155969 2085731449
Recent work by Abramsky and Brandenburger used sheaf theory to give a mathematical formulation of non-locality and contextuality. By adopting this viewpoint, it has been possible to define cohomological obstructions to the existence of global sections. In the present work, we illustrate new insights into different aspects of this theory. We shed light on the power of detection of the cohomological obstruction by showing that it is not a complete invariant for strong contextuality even under symmetry and connectedness restrictions on the measurement cover, disproving a previous conjecture. We generalise obstructions to higher cohomology groups and show that they give rise to a refinement of the notion of cohomological contextuality: different "levels" of contextuality are organised in a hierarchy of logical implications. Finally, we present an alternative description of the first cohomology group in terms of torsors, resulting in a new interpretation of the cohomological obstructions. Deciding whether a claim is true or false often requires understanding the evidence supporting and contradicting the claim. However, when learning about a controversial claim, human biases and viewpoints may affect which evidence documents are considered "trustworthy" or credible. It is important to overcome this bias and know both viewpoints to get a balanced perspective. In this paper, we study various factors that affect learning about the truthfulness of controversial claims. We designed a user study to understand the impact of these factors. Specifically, we studied the impact of presenting evidence with contrasting viewpoints and source expertise rating on how users accessed the evidence documents. This would help us optimize how to teach users about controversial topics in the most effective way, and to design better claim verification systems. We find that users do not seek contrasting viewpoints by themselves, but explicitly presenting contrasting evidence helps them get a well-rounded understanding of the topic. Furthermore, explicit knowledge of the source credibility and the context not only affects what users read, but also how credible they perceive the document to be. In many decision-making scenarios, people can benefit from knowing what other people's opinions are. As more and more evaluative documents are posted on the Web, summarizing these useful resources becomes a critical task for many organizations and individuals. This paper presents a framework for summarizing a corpus of evaluative documents about a single entity by a natural language summary. We propose two summarizers: an extractive summarizer and an abstractive one. As an additional contribution, we show how our abstractive summarizer can be modified to generate summaries tailored to a model of the user preferences that is solidly grounded in decision theory and can be effectively elicited from users. We have tested our framework in three user studies. In the first one, we compared the two summarizers. They performed equally well relative to each other quantitatively, while significantly outperforming a baseline standard approach to multidocument summarization. Trends in the results as well as qualitative comments from participants suggest that the summarizers have different strengths and weaknesses. After this initial user study, we realized that the diversity of opinions expressed in the corpus (i.e., its controversiality) might play a critical role in comparing abstraction versus extraction. To clearly pinpoint the role of controversiality, we ran a second user study in which we controlled for the degree of controversiality of the corpora that were summarized for the participants. The outcome of this study indicates that for evaluative text abstraction tends to be more effective than extraction, particularly when the corpus is controversial. In the third user study we assessed the effectiveness of our user tailoring strategy. The results of this experiment confirm that user tailored summaries are more informative than untailored ones. Deciding whether a claim is true or false often requires a deeper understanding of the evidence supporting and contradicting the claim. However, when presented with many evidence documents, users do not necessarily read and trust them uniformly. Psychologists and other researchers have shown that users tend to follow and agree with articles and sources that hold viewpoints similar to their own, a phenomenon known as confirmation bias. This suggests that when learning about a controversial topic, human biases and viewpoints about the topic may affect what is considered "trustworthy" or credible. It is an interesting challenge to build systems that can help users overcome this bias and help them decide the truthfulness of claims. In this article, we study various factors that enable humans to acquire additional information about controversial claims in an unbiased fashion. Specifically, we designed a user study to understand how presenting evidence with contrasting viewpoints and source expertise ratings affect how users learn from the evidence documents. We find that users do not seek contrasting viewpoints by themselves, but explicitly presenting contrasting evidence helps them get a well-rounded understanding of the topic. Furthermore, explicit knowledge of the credibility of the sources and the context in which the source provides the evidence document not only affects what users read but also whether they perceive the document to be credible. Language: en