Explicit representation of terms defined by counter examples
Journal of Automated Reasoning
A transformational approach to negation in logic programming
Journal of Logic Programming
A framework for defining logics
Journal of the ACM (JACM)
Hypothetical reasoning with intuitionistic logic
Nonstandard queries and nonstandard answers
The relative complement problem for higher-order patterns
Proceedings of the 1999 international conference on Logic programming
Automated Theorem Proving in a Simple Meta-Logic for LF
CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
A Logic for Reasoning with Higher-Order Abstract Syntax
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Automating the meta theory of deductive systems
Automating the meta theory of deductive systems
Proof-theoretic and higher-order extensions of logic programming
A 25-year perspective on logic programming
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Logical frameworks with a logic programming interpretation such as hereditary Harrop formulae (HHF) [12] 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 [17] 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.