The well-founded semantics for general logic programs
Journal of the ACM (JACM)
Extending and implementing the stable model semantics
Artificial Intelligence
Knowledge Representation, Reasoning, and Declarative Problem Solving
Knowledge Representation, Reasoning, and Declarative Problem Solving
Logic programs with stable model semantics as a constraint programming paradigm
Annals of Mathematics and Artificial Intelligence
Extending Classical Logic with Inductive Definitions
CL '00 Proceedings of the First International Conference on Computational Logic
Theory and Practice of Logic Programming
ASSAT: computing answer sets of a logic program by SAT solvers
Artificial Intelligence - Special issue on nonmonotonic reasoning
A framework for representing and solving NP search problems
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
A logic of nonmonotone inductive definitions
ACM Transactions on Computational Logic (TOCL)
Grounding for model expansion in k-guarded formulas with inductive definitions
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Integrating inductive definitions in SAT
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and 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
Verifying Properties of Infinite Sequences of Description Logic Actions
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
Grounding FO and FO(ID) with bounds
Journal of Artificial Intelligence Research
Satisfiability checking for PC(ID)
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Constraint Propagation for First-Order Logic and Inductive Definitions
ACM Transactions on Computational Logic (TOCL)
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The FO(ID) logic is an extension of classical first-order logic with a uniform representation of various forms of inductive definitions. The definitions are represented as sets of rules and they are interpreted by two-valued well-founded models. For a large class of combinatorial and search problems, knowledge representation in FO(ID) offers a viable alternative to the paradigm of Answer Set Programming. The main reasons are that (i) the logic is an extension of classical logic and (ii) the semantics of the language is based on well-understood principles of mathematical induction. In this paper, we define a reduction from the propositional fragment of FO(ID) to SAT. The reduction is based on a novel characterization of two-valued well-founded models using a set of inequality constraints on level mappings associated with the atoms. We also show how the reduction to SAT can be adapted for logic programs under the stable model semantics. Our experiments show that when using a state of the art SAT solver both reductions are competitive with other answer set programming systems — both direct implementations and SAT based.