On the complexity of propositional knowledge base revision, updates, and counterfactuals
Artificial Intelligence
Finding all minimal unsatisfiable subsets
Proceedings of the 5th ACM SIGPLAN international conference on Principles and practice of declaritive programming
Approximating minimal unsatisfiable subformulae by means of adaptive core search
Discrete Applied Mathematics - The renesse issue on satisfiability
AMUSE: a minimally-unsatisfiable subformula extractor
Proceedings of the 41st annual Design Automation Conference
Local-search Extraction of MUSes
Constraints
Generalized filtering algorithms for infeasibility analysis
Computers and Operations Research
Extracting MUCs from Constraint Networks
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
QUICKXPLAIN: preferred explanations and relaxations for over-constrained problems
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Journal of Artificial Intelligence Research
A comparison of ATMS and CSP techniques
IJCAI'89 Proceedings of the 11th international joint conference on Artificial intelligence - Volume 1
Diagnosing and solving over-determined constraint satisfaction problems
IJCAI'93 Proceedings of the 13th international joint conference on Artifical intelligence - Volume 1
Boosting a complete technique to find MSS and MUS thanks to a local search oracle
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
On finding all minimally unsatisfiable subformulas
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
A branch-and-bound algorithm for extracting smallest minimal unsatisfiable formulas
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
Deriving minimal conflict sets by CS-trees with mark set indiagnosis from first principles
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Integrating systematic and local search paradigms: a new strategy for MaxSAT
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Towards a notion of unsatisfiable cores for LTL
FSEN'09 Proceedings of the Third IPM international conference on Fundamentals of Software Engineering
Towards a notion of unsatisfiable and unrealizable cores for LTL
Science of Computer Programming
Restoring CSP Satisfiability with MaxSAT
Fundamenta Informaticae - RCRA 2009 Experimental Evaluation of Algorithms for Solving Problems with Combinatorial Explosion
On computing minimal equivalent subformulas
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
Preserving partial solutions while relaxing constraint networks
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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In this paper, a new form of explanation and recovery technique for the unsatisfiability of discrete CSPs is introduced. Whereas most approaches amount to providing users with a minimal number of constraints that should be dropped in order to recover satisfiability, a finer-grained alternative technique is introduced. It allows the user to reason both at the constraints and tuples levels by exhibiting both problematic constraints and tuples of values that would allow satisfiability to be recovered if they were not forbidden. To this end, the Minimal Set of Unsatisfiable Tuples (MUST) concept is introduced. Its formal relationships with Minimal Unsatisfiable Cores (MUCs) are investigated. Interestingly, a concept of shared forbidden tuples is derived. Allowing any such tuple makes the corresponding MUC become satisfiable. From a practical point of view, a two-step approach to the explanation and recovery of unsatisfiable CSPs is proposed. First, a recent approach proposed by Hemery et al.'s is used to locate a MUC. Second, a specific SAT encoding of a MUC allows MUSTs to be computed by taking advantage of the best current technique to locate Minimally Unsatisfiable Sub-formulas (MUSes) of Boolean formulas. Interestingly enough, shared tuples coincide with protected clauses, which are one of the keys to the efficiency of this SAT-related technique. Finally, the feasibility of the approach is illustrated through extensive experimental results.