Matrix representation of Husserl's part-whole-foundation theory.

Representation of Part-Whole Relationships in SNOMED CT

In this paper we investigate representation of the part-whole relationship in SNOMED CT. We discuss the current approach, based on “SEP” triples, and several translations of it, which involve DLs at different levels of expressivity. We intend that our analysis will concretely inform the SNOMED community about the important tradeoffs of expressivity for their ontology, and help with future decis...

A Foundation for Metareasoning Part I: The Proof Theory

We propose a framework, called OM pairs, for the formalization of metareasoning. OM pairs allow us to generate deductively pairs composed of an object theory and a metatheory related via a so called reflection principle. This is done by imposing, via appropriate reflection rules, the relation we want to hold between the object theory and the metatheory. In this paper we concentrate on the proof...

A Foundation for Metareasoning Part II: The Model Theory

Part I Reduced Density Matrix Functional Theory

Matrix Representation of Renormalization in Perturbative Quantum Field Theory

We formulate the Hopf algebraic approach of Connes and Kreimer to renormalization in perturbative quantum field theory using triangular matrix representation. We give a Rota– Baxter anti-homomorphism from general regularized functionals on the Feynman graph Hopf algebra to triangular matrices with entries in a Rota–Baxter algebra. For characters mapping to the group of unipotent triangular matr...