A logical basis for object oriented programming
We develop the proof theory and semantics of 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. The proof theory takes into account the precedence structure between rules as implied by the partial order.
OL is nonmonotonic under the natural model-theoretic semantics. However, there is an intuitive preference relation between models such that there is a unique "best" (minimal) model M if and only if all sentences in M can be proven. For "choice" theories that have several minimal models, there is a backtracking procedure that generates all such models as fixpoints. These theories can also be characterized syntactically.
We show that "classical" logic programs with negation by failure are a special case of 2-object ordered theories. Applications of results in ordered logic then yield a proof procedure for theories with well-founded models and a syntactical characterization of theories that have stable models (which are exactly the OL minimal models).
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