Nonmonotonic reasoning, preferential models and cumulative logics
Artificial Intelligence
CIKM '97 Proceedings of the sixth international conference on Information and knowledge management
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
On the Linear Structure of Betting Criterion and the Checking of Coherence
Annals of Mathematics and Artificial Intelligence
Locally Strong Coherence in Inference Processes
Annals of Mathematics and Artificial Intelligence
Probabilistic Reasoning Under Coherence in System P
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
Algorithms for Conditioning on Events of Zero Lower Probability
Proceedings of the Fifteenth International Florida Artificial Intelligence Research Society Conference
Probabilistic logic under coherence: complexity and algorithms
Annals of Mathematics and 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
Some theoretical properties of conditional probability assessments
ECSQARU'05 Proceedings of the 8th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
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
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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We illustrate an approach to uncertain knowledge based on lower conditional probability bounds. We exploit the coherence principle of de Finetti and a related notion of generalized coherence (g-coherence), which is equivalent to the "avoiding uniform loss" property introduced by Walley for lower and upper probabilities. Based on the additive structure of random gains, we define suitable notions of non relevant gains and of basic sets of variables. Exploiting them, the linear systems in our algorithms can work with reduced sets of variables and/or constraints. In this paper, we illustrate the notions of non relevant gain and of basic set by examining several cases of imprecise assessments defined on families with three conditional events. We adopt a geometrical approach, obtaining some necessary and sufficient conditions for g-coherence. We also propose two algorithms which provide new strategies for reducing the number of constraints and for deciding g-coherence. In this way, we try to overcome the computational difficulties which arise when linear systems become intractable. Finally, we illustrate our methods by giving some examples.