Expressing preferences in logic programming using an infinite-valued logic

We propose the new logic programming language PrefLog, which is based on an infinite-valued logic in order to support operators for expressing preferences. We demonstrate that if the operators used are continuous over the infinite-valued underlying domain, then the resulting logic programming language retains the well-known properties of classical logic programming (and most notably the existence of a least Herbrand model). We argue that one can define simple and natural new continuous operators by using a small set of operators that are easily shown to be continuous. Finally, we demonstrate that despite the fact that the underlying truth domain and the set of possible interpretations of a PrefLog program are infinite, we can define a terminating bottom-up proof procedure for implementing a significant and useful fragment of the language.