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.Comment: This paper was presented at ISAIM 2018, International Symposium on
Artificial Intelligence and Mathematics. Fort Lauderdale, FL. January 3 5,
2018. Minor typographical errors have been correcte
