The well-founded semantics for general logic programs
Journal of the ACM (JACM)
Conjunctive-query containment and constraint satisfaction
PODS '98 Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Robbers, marshals, and guards: game theoretic and logical characterizations of hypertree width
PODS '01 Proceedings of the twentieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Datalog LITE: a deductive query language with linear time model checking
ACM Transactions on Computational Logic (TOCL)
Query evaluation via tree-decompositions
Journal of the ACM (JACM)
The DLV system for knowledge representation and reasoning
ACM Transactions on Computational Logic (TOCL)
Compact propositional encoding of first-order theories
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
A framework for representing and solving NP search problems
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 1
A tractability result for reasoning with incomplete first-order knowledge bases
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Reducing inductive definitions to propositional satisfiability
ICLP'05 Proceedings of the 21st international conference on Logic Programming
Satisfiability checking for PC(ID)
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Declarative programming of search problems with built-in arithmetic
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Constraint processing in relational database systems: from theory to implementation
Proceedings of the 2010 ACM Symposium on Applied Computing
Grounding FO and FO(ID) with bounds
Journal of Artificial Intelligence Research
On the complexity of model expansion
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
Speed-up techniques for negation in grounding
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
Towards computing revised models for FO theories
INAP'09 Proceedings of the 18th international conference on Applications of declarative programming and knowledge management
Grounding formulas with complex terms
Canadian AI'11 Proceedings of the 24th Canadian conference on Advances in artificial intelligence
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Mitchell and Ternovska [2005] proposed a constraint programming framework based on classical logic extended with inductive definitions. They formulate a search problem as the problem of model expansion (MX), which is the problem of expanding a given structure with new relations so that it satisfies a given formula. Their long-term goal is to produce practical tools to solve combinatorial search problems, especially those in NP. In this framework, a problem is encoded in a logic, an instance of the problem is represented by a finite structure, and a solver generates solutions to the problem. This approach relies on propositionalisation of high-level specifications, and on the efficiency of modern SAT solvers. Here, we propose an efficient algorithm which combines grounding with partial evaluation. Since the MX framework is based on classical logic, we are able to take advantage of known results for the so-called guarded fragments. In the case of k-guarded formulas with inductive definitions under a natural restriction, the algorithm performs much better than naive grounding by relying on connections between k-guarded formulas and tree decompositions.