Composition Operators for Logic Theories
Some basic meta-level operators for putting logic theories together are introduced, which relate to set-theoretic union, intersection and difference. Both a transformational and an interpretive characterization of the operators are provided and proved equivalent. The former definition says how to syntactically construct a new theory out of two given theories, the latter provides a meta-level interpretation of the same operators. A declarative — both model-theoretic and fixpoint — semantics of the operators is also provided, allowing one to assign the minimal model of the resulting theory as a function of the models of the argument theories. Some examples from default reasoning, knowledge assimilation, inheritance networks and hypothetical reasoning are presented to demonstrate the expressive power of the operators.
KeywordsLogic Program Composition Operator Logic Programming Logic Theory Ground Instance
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