Artificial Intelligence
Boole's logic and probability: a critical exposititon from the standpoint of contemporary algebra, logic, and probability theory
More complicated questions about maxima and minima, and some closures of NP
Theoretical Computer Science
Journal of Complexity
A logic for reasoning about probabilities
Information and Computation - Selections from 1988 IEEE symposium on logic in computer science
Constraint propagation with imprecise conditional probabilities
Proceedings of the seventh conference (1991) on Uncertainty in artificial intelligence
A catalog of complexity classes
Handbook of theoretical computer science (vol. A)
On the consistency of defeasible databases
Artificial Intelligence
A taxonomy of complexity classes of functions
Journal of Computer and System Sciences
Anytime deduction for probabilistic logic
Artificial Intelligence
Computing functions with parallel queries to NP
Theoretical Computer Science
Algorithms for precise and imprecise conditional probability assessments
Mathematical models for handling partial knowledge in artificial intelligence
Nonmonotonic reasoning, conditional objects and possibility theory
Artificial Intelligence
CIKM '97 Proceedings of the sixth international conference on Information and knowledge management
Handbook of defeasible reasoning and uncertainty management systems: Volume 4 abductive reasoning and learning
Information Sciences: an International Journal
Default reasoning from conditional knowledge bases: complexity and tractable cases
Artificial Intelligence
Probabilistic logic programming with conditional constraints
ACM Transactions on Computational Logic (TOCL)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On the Linear Structure of Betting Criterion and the Checking of Coherence
Annals of Mathematics and Artificial Intelligence
Probabilistic Reasoning Under Coherence in System P
Annals of Mathematics and Artificial Intelligence
Probabilistic Default Reasoning with Conditional Constraints
Annals of Mathematics and Artificial Intelligence
Probabilistic Consistency of Conditional Probability Bounds
IPMU'94 Selected papers from the 5th International Conference on Processing and Management of Uncertainty in Knowledge-Based Systems, Advances in Intelligent Computing
Computing probability intervals under independency constraints
UAI '90 Proceedings of the Sixth Annual Conference on Uncertainty in Artificial Intelligence
An Investigation of the Laws of Thought
An Investigation of the Laws of Thought
Weak nonmonotonic probabilistic logics
Artificial Intelligence
Probabilistic deduction with conditional constraints over basic events
Journal of Artificial Intelligence Research
Models and algorithms for probabilistic and Bayesian logic
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 2
On the checking of G-coherence of conditional probability bounds
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
International Journal of Approximate Reasoning
Probabilistic abduction without priors
International Journal of Approximate Reasoning
Expressive probabilistic description logics
Artificial Intelligence
A logic with approximate conditional probabilities that can model default reasoning
International Journal of Approximate Reasoning
Artificial Intelligence
Algorithms for possibility assessments: Coherence and extension
Fuzzy Sets and Systems
Generalized Bayesian inference in a fuzzy context: From theory to a virtual reality application
Computational Statistics & Data Analysis
Generalizing inference rules in a coherence-based probabilistic default reasoning
International Journal of Approximate Reasoning
International Journal of Approximate Reasoning
Quasi conjunction, quasi disjunction, t-norms and t-conorms: Probabilistic aspects
Information Sciences: an International Journal
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
Conditional random quantities and iterated conditioning in the setting of coherence
ECSQARU'13 Proceedings of the 12th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
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In previous work [V. Biazzo, A. Gilio, T. Lukasiewicz and G. Sanfilippo, Probabilistic logic under coherence, model-theoretic probabilistic logic, and default reasoning in System P, Journal of Applied Non-Classical Logics 12(2) (2002) 189---213.], we have explored the relationship between probabilistic reasoning under coherence and model-theoretic probabilistic reasoning. In particular, we have shown that the notions of g-coherence and of g-coherent entailment in probabilistic reasoning under coherence can be expressed by combining notions in model-theoretic probabilistic reasoning with concepts from default reasoning. In this paper, we continue this line of research. Based on the above semantic results, we draw a precise picture of the computational complexity of probabilistic reasoning under coherence. Moreover, we introduce transformations for probabilistic reasoning under coherence, which reduce an instance of deciding g-coherence or of computing tight intervals under g-coherent entailment to a smaller problem instance, and which can be done very efficiently. Furthermore, we present new algorithms for deciding g-coherence and for computing tight intervals under g-coherent entailment, which reformulate previous algorithms using terminology from default reasoning. They are based on reductions to standard problems in model-theoretic probabilistic reasoning, which in turn can be reduced to linear optimization problems. Hence, efficient techniques for model-theoretic probabilistic reasoning can immediately be applied for probabilistic reasoning under coherence (for example, column generation techniques). We describe several such techniques, which transform problem instances in model-theoretic probabilistic reasoning into smaller problem instances. We also describe a technique for obtaining a reduced set of variables for the associated linear optimization problems in the conjunctive case, and give new characterizations of this reduced set as a set of non-decomposable variables, and using the concept of random gain.