Command algebra

Abstract

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 "Axiomatizing the Logic of Computer Programming" a series of new logics has been 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.