A Sheaf Model of Contradictions and Disagreements. Preliminary Report and Discussion

Abstract

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. 1

Computing Conceptual Distances between Breast Cancer Screening Guidelines: An Implementation of a Near-Peer Epistemic Model of Medical Disagreement

“…As shown in Fig.1, reproduced from our earlier workHematialam & Zadrozny (2016) andZadrozny & Garbayo (2018), there are several clear disagreements in the recommendations.Conceptual Analysis:Figure 2 shows a manually generated graph showing the differences between the guidelines, also presented in Garbayo et al (2019a). There are two sides to the circle.…”

“…Since medical guidelines are developed by different medical associations which count on experts with different specialties and sub-specialties, there is a high possibility that there may be disagreement in the guidelines. And indeed, as noted by CDC (2017) and discussed in Zadrozny & Garbayo (2018); Zadrozny et al (2017), breast cancer screening guidelines contradict each other.…”

“…Zadrozny & Garbayo (2018) Zadrozny et al (2017) Garbayo (2019) we have not made a distinction between contradictions and disagreements. Thus, some of our ongoing work is about incorporating logical structures of documents and finding metrics reflecting them.Description of individual contributions to this research: HH performed the majority of experiments discussed in this article, and substantially contributed to writing.…”

Non-locality, contextuality and valuation algebras: a general theory of disagreement

“…Example 3.1. Our first example is inspired by a recent paper by Zadrozny & Garbayo [27], where breast cancer screening guidelines from three different accredited sources are analysed.…”

A Sheaf Theoretical Approach to Uncertainty Quantification of Heterogeneous Geolocation Information

“…Many sheaf encodings of standard models (such as dynamical systems, differential equations, and Bayesian networks) have been catalogued [42]. Furthermore, these techniques can be easily applied in a number of different settings, for instance in air traffic control [43,44] and in formal semantic techniques [45]. Sheaf-based techniques for fundamental tasks in signal processing have also been developed [1].…”