Non-Additive Riemann Integration - Better than Choquet?
Non-Additive Riemann Integration
Mark Kortink
In this paper I develop an integral that generalises the real-valued Riemann-Stieltjes integral using a non-additive measure defined on a ring of sets. The integral is simple and has many of the basic properties of the Riemann and other integrals. It is different to the more familiar non-additive Choquet integral, and is possibly more applicable and intuitive to use.
DOI: 10.13140/RG.2.2.29713.13929
The Algebra of Computer Programs
The Algebra of Computer Programs - Based on my Masters Thesis submitted to Victoria University of Wellington NZ, 1983
Mark Kortink
It is a common phenomenon in Mathematics that once a logic has been created one can extract from it a species of algebras that mimic the behaviour of the logic. For example, Boolean algebra comes from propositional logic, cylindric algebra comes from first order logic, and dynamic algebra comes from dynamic logic.
In Rob Goldblatt's book "Axiomatising the Logic of Computer Programming" a series of new logics is created.
This thesis extracts two new species of algebras from two of the logics in this book, namely command modules and L-command modules. The thesis is then concerned with proving representation theorems for these algebras and relating these theorems back to the completeness theorems for the original parent logics.
DOI: 10.13140/RG.2.2.27333.92647/1
Command Algebra - Original Masters Thesis submitted to Victoria University of Wellington NZ, 1983
Mark Kortink
It is a common phenomenon in Mathematics that once a logic has been created one can extract from it a species of algebras that mimic the behaviour of the logic. For example, Boolean algebra comes from propositional logic, cylindric algebra comes from first order logic, and dynamic algebra comes from dynamic logic. In Rob Goldblatt's book "Axiomatising the Logic of Computer Programming" a series of new logics is created. This thesis extracts two new species of algebras from two of the logics in this book, namely command modules and L-command modules. The thesis is then concerned with proving representation theorems for these algebras and relating these theorems back to the completeness theorems for the original parent logics.
DOI: 10.13140/RG.2.2.33068.58247