### A universal fixpoint semantics for ordered logic

*E. Laenens, D. Vermeir*

#### Abstract

Ordered logic is the theoretical foundation of the LOCO programing language [9] which combines the declarative elegance and power of logic programming with asvantages of object-oriented systems. Ordered logic is based on a partially ordered structure of logical theories or objects. Objects are entities that may contain positive as well as negative information represented by rules. The partial order allows for the definition of a preference structure on these objects and consequently also on the information they contain. The result is a simple yet powerful logic that models classical as well as non-monotonic inference mechanisms. The central issue of this paper is the definition of a universal fixpoint semantics for ordered logic programs which constitutes an important extension and generalization of the fixpoint semantics prresented in [11, in the sense that it computes all partial models (well-founded and stable partial models included) instead of only ´total´ models (a possibly empty subset of the stable partial models), thus overcoming the limitations of the previous approach.