Meta level reasoning and default reasoning

In this paper, we propose a logic framework for meta level reasoning as well as default reasoning in a general sense, based on an arbitrary underlying logic. In this framework, meta level reasoning is the task of how to deduce new meta level rules by giving a set of rules, whilst default reasoning is the problem of what are the possible candidate beliefs by giving them. We define the semantics for both meta level reasoning and default reasoning and investigate their relationships. We show that this framework captures various nonmonotonic paradigms, including answer set programming, default logic, contextual default reasoning, by applying the underlying logic to different classes. Finally, we show that this framework can be reduced into answer set programming.