Argumentation between agents through dialogue is an important cognitive activity. There have been a number of proposals for formalizing dialogical argumentation. However, each proposal involves a number of quite complex definitions, and there is significant diversity in the way different proposals define similar features. This complexity and diversity has hindered analysis and comparison of the space of proposals. To address this, we present a general approach to defining a wide variety of systems for dialogical argumentation. Our solution is to use an executable logic to specify individual systems for dialogical argumentation. This means we have a common language for specifying a wide range of systems, we can compare systems in terms of a range of standard properties, we can identify interesting classes of system, and we can execute the specification of each system to analyse it empirically.