A system for paraconsistent reasoning

The purpose of this article is to discuss how the idea of models can be used to relate the knowledge of a reasoning agent across different temporal moments. The environment chosen as the most appropriate to accommodate the agent's knowledge at each moment is that of paraconsistent logics. For this reason, the Tarskian concept of model is reformulated to accommodate paraconsistent reasoning. The point of view championed in this work is that inconsistency is an epistemic phenomenon. In accordance with this line of thought, models are regarded as states of knowledge that contain safe and unsafe information and can be refined to increase the safe segment. The notion of refining models is developed as a tool for extracting additional safe information from the unsafe information within a model. Finally, an axiomatisation for the new system is provided.