Nonmonotonic logics formalise commonsense reasoning with incomplete, uncertain or inconsistent information. My favourite type of nonmonotonic logic is argument-based. In such logics arguments can be constructed and conflicting arguments can be compared, to see which of them come out as 'undefeated' or 'in force'. I especially like argument-based systems since they are 'modular' (with e.g. separate definitions of constructing arguments and comparing conflicting arguments), and since they are based on very natural concepts (such as argument, counterargument, rebuttal, defeat, dialogue and dispute).
Nowadays systems for argumentation-based inference are studied within the field of computational argumentation. I have therefore moved my further remarks on this topic to my page on Computational Argumentation.