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Journal of Logic and Computation 1990 1(2):159-185; doi:10.1093/logcom/1.2.159
© 1990 by Oxford University Press
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Original Articles

A Fixpoint Semantics for Ordered Logic

E. LAENENS* and D. VERMEIR{dagger}

*Philips Applications and Software Services, Advanced Information Technology, Building HCM5 PO Box 218, 5600 MD Eindhoven, The Netherlands
{dagger}Department of Mathematics and Computer Science, University of Antwerp, UIA, Universiteitsplein 1 B2610 Wilrijk, Belgium

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.


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