A universal fixpoint semantics for ordered logic

Ordered logic is the theoretical foundation of the LOGO programming languag e [9] which combines the declarative elegance and power of logic programmin g with advantages of object-oriented systems. Ordered logic is based on a p artially ordered structure of logical theories or objects. Objects are enti ties that may contain positive as well as negative information represented by rules. The partial order allows for the definition of a preference struc ture on these objects and consequently also on the information they contain .-The result is a simple yet powerful logic that models classical as well a s non-monotonic inference mechanisms. The central issue of this paper is th e definition of a universal fixpoint semantics for ordered logic programs w hich constitutes an important extension and generalization of the fixpoint semantics presented in [11], in the sense that it computes all partial mode ls (well-founded and stable partial models included) instead of only 'total ' models (a possibly empty subset of the stable partial models), thus overc oming the limitations of the previous approach.