Artificial Intelligence
On the complexity of the maximum satisfiability problem for Horn formulas
Information Processing Letters
Journal of Complexity
The basic algorithm for pseudo-Boolean programming revisited
Selected papers on First international colloquium on pseudo-boolean optimization and related topics
Directed hypergraphs and applications
Discrete Applied Mathematics - Special issue: combinatorial structures and algorithms
Decision Support Systems - Special issue on logic modeling
Characterizing consistency in probabilistic logic for a class of Horn clauses
Mathematical Programming: Series A and B
A class of logic problems solvable by linear programming
Journal of the ACM (JACM)
Boole's conditions of possible experience and reasoning under uncertainty
Discrete Applied Mathematics - Special volume: Aridam VI and VII, Rutcor, New Brunswick, NJ, USA (1991 and 1992)
On-line algorithms for satisfiability problems with uncertainty
Selected papers from the international workshop on Uncertainty in databases and deductive systems
Max Horn SAT and the minimum cut problem in directed hypergraphs
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computing probability intervals under independency constraints
UAI '90 Proceedings of the Sixth Annual Conference on Uncertainty in Artificial Intelligence
Probability Logic and Optimization SAT: The PSAT and CPA Models
Annals of Mathematics and Artificial Intelligence
Measuring inconsistency in probabilistic knowledge bases
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
A logic based algorithm for solving probabilistic satisfiability
IBERAMIA'10 Proceedings of the 12th Ibero-American conference on Advances in artificial intelligence
Probabilistic satisfiability: logic-based algorithms and phase transition
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
Probabilistic satisfiability and coherence checking through integer programming
ECSQARU'13 Proceedings of the 12th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
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The Probabilistic Satisfiability problem (PSAT) can be considered as a probabilistic counterpart of the classical SAT problem. In a PSAT instance, each clause in a CNF formula is assigned a probability of being true; the problem consists in checking the consistency of the assigned probabilities. Actually, PSAT turns out to be computationally much harder than SAT, e.g., it remains difficult for some classes of formulas where SAT can be solved in polynomial time. A icolumn generation approach has been proposed in the literature, where the pricing sub-problem reduces to a Weighted Max-SAT problem on the original formula. Here we consider some easy cases of PSAT, where it is possible to give a compact representation of the set of consistent probability assignments. We follow two different approaches, based on two different representations of CNF formulas. First we consider a representation based on idirected hypergraphs. By extending a well-known integer programming formulation of SAT and Max-SAT, we solve the case in which the hypergraph does not contain cycles; a linear time algorithm is provided for this case. Then we consider the co-occurrence graph associated with a formula. We provide a solution method for the case in which the co-occurrence graph is a partial 2-tree, and we show how to extend this result to partial ik-trees with ik2.