4 citations · 6 across the 3 of their papers we have counts for
6 papers
A Complete Finite Axiomatisation of the Equational Theory of Common Meadows
Jan A Bergstra, John V Tucker
We analyse abstract data types that model numerical structures with a concept of error. Specifically, we focus on arithmetic data types that contain an error value whose mai…
The dynamics of belief: continuously monitoring and visualising complex systems
Edwin J. Beggs, John V. Tucker
The rise of AI in human contexts places new demands on automated systems to be transparent and explainable. We examine some anthropomorphic ideas and principles relevant to such ac…
A model of systems with modes and mode transitions
Edwin Beggs, John V. Tucker
We propose a method of classifying the operation of a system into finitely many modes. Each mode has its own objectives for the system's behaviour and its own mathematical models a…
Monitoring and Intervention: Concepts and Formal Models
Kenneth Johnson, John V. Tucker, Victoria Wang
Our machines, products, utilities, and environments have long been monitored by embedded software systems. Our professional, commercial, social and personal lives are also subject…
Meadows and the equational specification of division
J. A. Bergstra, Y. Hirshfeld, J. V. Tucker
The rational, real and complex numbers with their standard operations, including division, are partial algebras specified by the axiomatic concept of a field. Since the class of fi…
Skew Meadows
J. A. Bergstra, Y. Hirshfeld, J. V. Tucker
A skew meadow is a non-commutative ring with an inverse operator satisfying two special equations and in which the inverse of zero is zero. All skew fields and products of skew fie…