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In many commonsense contexts only incoherent and conflicting information is available. In such contexts reasonable conclusions must be derived from inconsistent sets of premises. This is especially the case in legal reasoning: legal norms can be issued by different authorities, in different times, to reach incompatible socio-political objectives, and the meaning of those norms can be semantically indeterminate.Logic deduction alone is insufficient to derive justified conclusions out of inconsistent legal premises, since in the most popular logical systems (such as classical or intuitionistic logic) everything can be deduced from any contradiction. Nevertheless, much research now underway shows that formal methods can be developed for reasoning with conflicting information. The possibility of obtaining justified conclusions from an inconsistent set of premises increases when an ordering is defined over that set, since the ordering of the premises can be translated into an ordering of the competing arguments. This fact is particularly relevant for legal reasoning, since lawyers effectively solve normative conflicts by using ordering relations.In the following page, a model for reasoning with ordered defaults, interpreted as unidirectional inference rules, is proposed: a language for representing (possibly) contradictory rules is introduced, a notion of argument is defined, and types of arguments are distinguished. A simple interpreter in Prolog able to develop those arguments is also illustrated. Finally, the significance of the proposed model (and, more generally, of the acceptance of inconsistency) for the formal analysis of legal systems is discussed.

A simple computational model for nonmonotonic and adversarial legal reasoning