A Sheaf Model of Contradictions and Disagreements. Preliminary Report and Discussion
This work addresses the problem of handling inconsistencies in textual data for researchers in natural language processing and related fields, but it is presented as a preliminary report, indicating incremental development.
The authors introduced a formal sheaf-based model to represent contradictory information in textual sources, enabling identification of inconsistency causes, measurement of its strength, and suggestions for reconciliation, while distinguishing between contradictions and disagreements.
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.