Sheaving—a universal construction for semantic compositionality. (16th December 2019)

• Record Type: Journal Article
• Authors: Phillips, Steven
• Is Part Of: Philosophical transactions. Volume 375:Number 1791(2020)
• Publication Date: 2019-12-16
• Subjects: compositionality -- category theory -- sheaf -- sheaving -- topology; Biology -- Periodicals; Science -- Periodicals; 570
• DOI: 10.1098/rstb.2019.0303
• Languages: English
• ISSNs: 0962-8436

Abstract

Abstract : Semantic compositionality—the way that meanings of complex entities obtain from meanings of constituent entities and their structural relations—is supposed to explain certain concomitant cognitive capacities, such as systematicity. Yet, cognitive scientists are divided on mechanisms for compositionality: e.g. a language of thought on one side versus a geometry of thought on the other. Category theory is a field of (meta)mathematics invented to bridge formal divides. We focus on sheaving—a construction at the nexus of algebra and geometry/topology, alluding to an integrative view, to sketch out a category theory perspective on the semantics of compositionality. Sheaving is a universal construction for making inferences from local knowledge, where meaning is grounded by the underlying topological space. Three examples illustrate how topology conveys meaning, in terms of the inclusion relations between the open sets that constitute the space, though the topology is not regarded as the only source of semantic information. In this sense, category (sheaf) theory provides a general framework for semantic compositionality. This article is part of the theme issue 'Towards mechanistic models of meaning composition'.