Elimination of Negation in a Logical Framework
- Cite this paper as:
- Momigliano A. (2000) Elimination of Negation in a Logical Framework. In: Clote P.G., Schwichtenberg H. (eds) Computer Science Logic. CSL 2000. Lecture Notes in Computer Science, vol 1862. Springer, Berlin, Heidelberg
Logical frameworks with a logic programming interpretation such as hereditary Harrop formulae (HHF)  cannot express directly negative information, although negation is a useful specification tool. Since negation-as-failure does not fit well in a logical framework, especially one endowed with hypothetical and parametric judgments, we adapt the idea of elimination of negation introduced in  for Horn logic to a fragment of higher-order HHF. This entails finding a middle ground between the Closed World Assumption usually associated with negation and the Open World Assumption typical of logical frameworks; the main technical idea is to isolate a set of programs where static and dynamic clauses do not overlap.
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