Work

Order in Partial Markov Categories

Year: 2025

Type: article

Abstract: Partial Markov categories are a recent framework for categorical probability theory that provide an abstract account of partial probabilistic computation with updating semantics. In this article, we discuss two order relations on the morphisms of a partial Markov category. In particular, we prove that every partial Markov category is canonically preorder-enriched, recovering several well-known order enrichments. We also demonstrate that the existence of codiagonal maps (comparators) is closely related to order properties of partial Markov categories. Finally, we introduce a synthetic version of the Cauchy--Schwarz inequality and, from it, we prove that updating increases validity. 20 pages, MFPS XVI. In a previous version, an invocation of the restriction preorder in quasi-Markov categories [FGLPS25, Proposition 2.16] was missing the positivity hypothesis; we thank Areeb Shah Mohammed for pointing it out

Source: Electronic Notes in Theoretical Informatics and Computer Science

DOI: 10.46298/entics.16686

Authors: Elena Di Lavore, Mario Román, Paweł Sobociński, Márk Széles

Institutions: University of Oxford, Tallinn University of Technology, Radboud University Nijmegen

Language: English

Topic: Logic, programming, and type systems

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: bronze

Funders: European Commission, Eesti Teadusagentuur, Air Force Office of Scientific Research

Awards: G1523888516, G1785147656, G4516736450, Artificial intelligence in cybersecurity