Custom hypergraph categories via generalized relations

Conference item

Process theories combine a graphical language for compositional reasoning with an underlying categorical semantics. They have been successfully applied to fields such as quantum computation, natural language processing, linear dynamical systems and network theory. When investigating a new application, the question arises of how to identify a suitable process theoretic model. We present a conceptually motivated parameterized framework for the construction of models for process theories. Our framework generalizes the notion of binary relation along four axes of variation, the truth values, a choice of algebraic structure, the ambient mathematical universe and the choice of proof relevance or provability. The resulting categories are preorder-enriched and provide analogues of relational converse and taking graphs of maps. Our constructions are functorial in the parameter choices, establishing mathematical connections between different application domains. We illustrate our techniques by constructing many exis

Authors: Marsden, D; Genovese, F

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Schloss Dagstuhl
• Host title: 7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017)
• Journal: 7th Conference on Algebra and Coalgebra in Computer Science
• Volume: 72
• Pages: 17:1--17:16
• Series: Leibniz International Proceedings in Informatics
• Publication date: 2017-11-02
• Acceptance date: 2017-05-15
• DOI: 10.4230/LIPIcs.CALCO.2017.17
• ISSN: 1868-8969
• ISBN: 9783959770330
• Keywords: hypergraph category; process theory; categorical compositional semantics; compact closed category; generalized relations