Artificial Intelligence
On the complexity of the maximum satisfiability problem for Horn formulas
Information Processing Letters
Integer and combinatorial optimization
Integer and combinatorial optimization
Journal of Complexity
A class of logic problems solvable by linear programming
Journal of the ACM (JACM)
Complexity versus stability for classes of propositional formulas
Information Processing Letters
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Easy Cases of Probabilistic Satisfiability
Annals of Mathematics and Artificial Intelligence
Simplification Rules for the Coherent Probability Assessment Problem
Annals of Mathematics and Artificial Intelligence
A MINSAT Approach for Learning in Logic Domains
INFORMS Journal on Computing
An Investigation of the Laws of Thought
An Investigation of the Laws of Thought
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Both probabilistic satisfiability (PSAT) and the check of coherence of probability assessment (CPA) can be considered as probabilistic counterparts of the classical propositional satisfiability problem (SAT). Actually, CPA turns out to be a particular case of PSAT; in this paper, we compare the computational complexity of these two problems for some classes of instances. First, we point out the relations between these probabilistic problems and two well known optimization counterparts of SAT, namely Max SAT and Min SAT. We then prove that Max SAT with unrestricted weights is NP-hard for the class of graph formulas, where Min SAT can be solved in polynomial time. In light of the aforementioned relations, we conclude that PSAT is NP-complete for ideal formulas, where CPA can be solved in linear time.