Efficient algorithms for combinatorial problems on graphs with bounded, decomposability—a survey
BIT - Ellis Horwood series in artificial intelligence
Tree automata and logic programs
Proceedings on STACS 85 2nd annual symposium on theoretical aspects of computer science
Information Processing Letters
On the relationship between circumscription and negation as failure
Artificial Intelligence
Easy problems for tree-decomposable graphs
Journal of Algorithms
Graph rewriting: an algebraic and logic approach
Handbook of theoretical computer science (vol. B)
Propositional circumscription and extended closed-world reasoning are &Pgr;p2-complete
Theoretical Computer Science
Monadic second-order evaluations on tree-decomposable graphs
Theoretical Computer Science - Special issue on selected papers of the International Workshop on Computing by Graph Transformation, Bordeaux, France, March 21–23, 1991
The complexity of propositional closed world reasoning and circumscription
Journal of Computer and System Sciences
The complexity of logic-based abduction
Journal of the ACM (JACM)
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Languages, automata, and logic
Handbook of formal languages, vol. 3
All structured programs have small tree width and good register allocation
Information and Computation
Discrete Applied Mathematics - Special issue on international workshop of graph-theoretic concepts in computer science WG'98 conference selected papers
Query evaluation via tree-decompositions
Journal of the ACM (JACM)
The Treewidth of Java Programs
ALENEX '02 Revised Papers from the 4th International Workshop on Algorithm Engineering and Experiments
DAG-width: connectivity measure for directed graphs
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Safe Reduction Rules for Weighted Treewidth
Algorithmica
Monadic datalog over finite structures with bounded treewidth
Proceedings of the twenty-sixth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Counting truth assignments of formulas of bounded tree-width or clique-width
Discrete Applied Mathematics
Digraph measures: Kelly decompositions, games, and orderings
Theoretical Computer Science
Bounded treewidth as a key to tractability of knowledge representation and reasoning
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Abduction with bounded treewidth: from theoretical tractability to practically efficient computation
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 3
Answer-set programming with bounded treewidth
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Tree acceptors and some of their applications
Journal of Computer and System Sciences
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Combinatorial Optimization on Graphs of Bounded Treewidth
The Computer Journal
Exploiting bounded treewidth with datalog (a survey)
Datalog'10 Proceedings of the First international conference on Datalog Reloaded
On the parameterized complexity of default logic and autoepistemic logic
LATA'12 Proceedings of the 6th international conference on Language and Automata Theory and Applications
On the tractability of query compilation and bounded treewidth
Proceedings of the 15th International Conference on Database Theory
Abstract argumentation via monadic second order logic
SUM'12 Proceedings of the 6th international conference on Scalable Uncertainty Management
Efficient symbolic implementation of graph automata with applications to invariant checking
ICGT'12 Proceedings of the 6th international conference on Graph Transformations
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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Several forms of reasoning in AI - like abduction, closed world reasoning, circumscription, and disjunctive logic programming - are well known to be intractable. In fact, many of the relevant problems are on the second or third level of the polynomial hierarchy. In this paper, we show how the notion of treewidth can be fruitfully applied to this area. In particular, we show that all these problems become tractable (actually, even solvable in linear time), if the treewidth of the involved formulae or programs is bounded by some constant. Clearly, these theoretical tractability results as such do not immediately yield feasible algorithms. However, we have recently established a new method based on monadic datalog which allowed us to design an efficient algorithm for a related problem in the database area. In this work, we exploit the monadic datalog approach to construct new algorithms for logic-based abduction.