A fixpoint semantics for ordered logicA fixpoint semantics for ordered logic
Faculty of Sciences. Mathematics and Computer Science
Department of Mathematics - Computer Sciences
Individual research mathematics/informatics
Journal of logic and computation. - Oxford
1(1990):2, p. 159-185
University of Antwerp
We develop semantics for a logic, called ordered logic (OL), which models the most important aspects of object-oriented programming languages, such as object identity, multiple inheritance and defaults. The logic is based on a partially ordered structure of logical theories, which play the role of objects. OL is non-monotonic under the natural modeltheoretic semantics. A non-deterministic procedure is defined that has all models as fixpoints. It is shown that, for a well-behaved subclass of theories, this procedure can be used to generate exactly the set of preferred models, where preference is based on the lack of assumptions. Classical logic programs with negation by failure are special cases of OL theories. From the above we can then derive a syntactic characterization of logic programs with stable models.