The well-founded semantics for general logic programs
Journal of the ACM (JACM)
Stratified least fixpoint logic
Theoretical Computer Science
Logic programming revisited: logic programs as inductive definitions
ACM Transactions on Computational Logic (TOCL) - Special issue devoted to Robert A. Kowalski
The Well-Founded Semantics Is the Principle of Inductive Definition
JELIA '98 Proceedings of the European Workshop on Logics in Artificial Intelligence
DATE '03 Proceedings of the conference on Design, Automation and Test in Europe - Volume 1
A logic of nonmonotone inductive definitions
ACM Transactions on Computational Logic (TOCL)
FO(ID) as an Extension of DL with Rules
ESWC 2009 Heraklion Proceedings of the 6th European Semantic Web Conference on The Semantic Web: Research and Applications
Well-founded semantics and the algebraic theory of non-monotone inductive definitions
LPNMR'07 Proceedings of the 9th international conference on Logic programming and nonmonotonic reasoning
LPNMR'07 Proceedings of the 9th international conference on Logic programming and nonmonotonic reasoning
SAT(ID): satisfiability of propositional logic extended with inductive definitions
SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
Tableau calculi for answer set programming
ICLP'06 Proceedings of the 22nd international conference on Logic Programming
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The logic FO(ID) uses ideas from the field of logic programming to extend first order logic with non-monotone inductive definitions. The goal of this paper is to extend Gentzen's sequent calculus to obtain a deductive inference method for FO(ID). The main difficulty in building such a proof system is the representation and inference of unfounded sets. It turns out that we can represent unfounded sets by least fixpoint expressions borrowed from stratified least fixpoint logic (SLFP), which is a logic with a least fixpoint operator and characterizes the expressibility of stratified logic programs. Therefore, in this paper, we integrate least fixpoint expressions into FO(ID) and define the logic FO(ID,SLFP). We investigate a sequent calculus for FO(ID,SLFP), which extends the sequent calculus for SLFP with inference rules for the inductive definitions of FO(ID). We show that this proof system is sound with respect to a slightly restricted fragment of FO(ID) and complete for a more restricted fragment of FO(ID).