Innnitary Default Logic for Speciication of Nonmonotonic Reasoning

In this paper we study constructions leading to the formation of belief sets by agents. We focus on the situation when possible belief sets are built incrementally in stages. We call an innnite sequence of theories that represents such a process a reasoning trace. A set of reasoning traces describing all possible reasoning scenarios for the agent is called a reasoning frame. Default logic by Reiter is not powerful enough to represent reasoning frames. In the paper we introduce a generalization of default logic of Reiter by allowing innnite sets of justiications. We call this formalism innnitary default logic. In the main result of the paper we show that every reasoning frame can be represented by an innnitary default theory. A similar representability result for antichains of theories (belief frames) is also presented.