A three-valued approach to default logic
Anna Maria Radzikowska · Journal of Applied Non-Classical Logics · 1996
In this paper we present a new, three-valued approach to default logic, DL3. We employ the Lukasiewicz three-valued logic as a basis. This proposal is in the spirit of a slightly modified Reiter's default formalism. The key feature of our system is its ability to express the possibility character of default conclusions. Technically, this is achieved by using the possibility operator definable in the Lukasiewicz logic. Our approach increases expressibility in comparison to the standard formalism and allows for greater flexibility from the standpoint of the knowledge representation. We investigate basic formal properties of DL3 and provide a model theoretic characterization of extensions. A proof theory is also studied. We present a method, based on the classical linear resolution, to find a default proof.