Agent based Modelling is now a standard form of modelling in the field of social simulations. One of the outstanding issues in this field is known as the Replication Problem. Simply stated this is the inability of researchers to independently replicate the results of Agent Based Models published by other researchers. This thesis outlines a two-part proposed solution to this problem that uses formal methods to precisely specify Agent Based Models and employs multiple updating strategies to demonstrate that any simulation results are independent of updating strategy. A novel synchronous updating algorithm is presented that allows synchronous updating to be extended from Cellular Automata based simulations to Agent Based Simulations. Asymptotic analysis of the novel synchronous algorithm shows that it is O(n log n) in time and O(n) in space. It is demonstrated that the new algorithm does not suffer from the deficiencies of existing asynchronous algorithms and that it also allows collision detection to be incorporated into agent behaviours. The applicability of this approach is demonstrated by specifying and then reproducing the results of Sugarscape, a well known and complex Agent Based Social Simulation. The first formal specification of Sugarscape is presented and used to identify the ambiguities that have made replication of the original results so difficult. A framework is developed that implements the new algorithm alongside existing asynchronous algorithms and is used to implement Sugarscape and compare the different updating approaches. This is the first synchronous implementation of Sugarscape and the only synchronous implementation of any Agent Based Model of comparable complexity. It is also the first comparison of synchronous and asynchronous updating applied to the same Agent Based Model.