Representation Results for Default Logics

Normal forms play an important role in computer science, for example in the areas of logic and databases. This paper provides a study of normal forms for some prominent logics for default reasoning. In particular we show that in Constrained and in Justified Default Logic, semi--normal default theories can represent arbitrary default theories. The main result for Justified Default Logic requires the signature (logical language) to be enhanced in order to obtain the desired outcome. 1 Introduction Normal forms play an important role in computer science. They help restrict the study of some properties to specific classes of items, and thus make the task at hand easier. Examples of areas where normal forms have proved fruitful include logic, where normal forms of formulae are used both for the proof of theoretical results and in theorem proving, and relational databases [2], where normal forms have been the driving force in the development of database theory and principles of good data mo..