An Argumentative Framework for Reasoning with Inconsistent and Incomplete Information

We present here a knowledge representation language, where defeasible and non-defeasible rules can be expressed. The language has two different negations: classical negation, which is represented by the symbol “∼” used for representing contradictory knowledge; and negation as failure, represented by the symbol “not” used for representing incomplete information. Defeasible reasoning is done using a argumentation formalism. Thus, systems for acting in a dynamic domain, that properly handle contradictory and/or incomplete information can be developed with this language. An argument is used as a defeasible reason for supporting conclusions. A conclusion q will be considered justified only when the argument that supports it becomes a justification. Building a justification involves the construction of a nondefeated argument A for q. In order to establish that A is a non-defeated argument, the system looks for counterarguments that could be defeaters for A. Since defeaters are arguments, there may exist defeaters for the defeaters, and so on, thus requiring a complete dialectical analysis. The system also detects, avoids, circular argumentation. The language was implemented using an abstract machine defined and developed as an extension of the Warren Abstract Machine (wam).