Capturing complexity classes by fragments of second-order logic
Theoretical Computer Science - Special issue on logic and applications to computer science
The alternating fixpoint of logic programs with negation
PODS '89 Selected papers of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
The OPL optimization programming language
The OPL optimization programming language
Logic programming revisited: logic programs as inductive definitions
ACM Transactions on Computational Logic (TOCL) - Special issue devoted to Robert A. Kowalski
Logic programs with stable model semantics as a constraint programming paradigm
Annals of Mathematics and Artificial Intelligence
Combining Relational Algebra, SQL, and Constraint Programming
FroCoS '02 Proceedings of the 4th International Workshop on Frontiers of Combining Systems
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
Elements Of Finite Model Theory (Texts in Theoretical Computer Science. An Eatcs Series)
Predicate-calculus-based logics for modeling and solving search problems
ACM Transactions on Computational Logic (TOCL)
Well-founded and stable semantics of logic programs with aggregates
Theory and Practice of Logic Programming
Artificial Intelligence
A logic of nonmonotone inductive definitions
ACM Transactions on Computational Logic (TOCL)
Expressive power and abstraction in Essence
Constraints
Building a Knowledge Base System for an Integration of Logic Programming and Classical Logic
ICLP '08 Proceedings of the 24th International Conference on Logic Programming
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
ICLP '09 Proceedings of the 25th International Conference on Logic Programming
Using Lightweight Inference to Solve Lightweight Problems
LPNMR '09 Proceedings of the 10th International Conference on Logic Programming and Nonmonotonic Reasoning
The Second Answer Set Programming Competition
LPNMR '09 Proceedings of the 10th International Conference on Logic Programming and Nonmonotonic Reasoning
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Grounding for model expansion in k-guarded formulas with inductive definitions
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Declarative programming of search problems with built-in arithmetic
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
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
Logic programming for knowledge representation
ICLP'07 Proceedings of the 23rd international conference on Logic programming
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
FO(ID) as an extension of DL with rules
Annals of Mathematics and Artificial Intelligence
An approximative inference method for solving ∃¬so satisfiability problems
JELIA'10 Proceedings of the 12th European conference on Logics in artificial intelligence
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
PBINT, a logic for modelling search problems involving arithmetic
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
Grounding formulas with complex terms
Canadian AI'11 Proceedings of the 24th Canadian conference on Advances in artificial intelligence
A semantic account for modularity in multi-language modelling of search problems
FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining systems
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
Enfragmo: a system for modelling and solving search problems with logic
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
An approximative inference method for solving ∃∀SO satisfiability problems
Journal of Artificial Intelligence Research
Constraint Propagation for First-Order Logic and Inductive Definitions
ACM Transactions on Computational Logic (TOCL)
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NP search and decision problems occur widely in AI, and a number of general-purpose methods for solving them have been developed. The dominant approaches include propositional satisfiability (SAT), constraint satisfaction problems (CSP), and answer set programming (ASP). Here, we propose a declarative constraint programming framework which we believe combines many strengths of these approaches, while addressing weaknesses in each of them. We formalize our approach as a model extension problem, which is based on the classical notion of extension of a structure by new relations. A parameterized version of this problem captures NP. We discuss properties of the formal framework intended to support effective modelling, and prospects for effective solver design.