Nonmonotonic reasoning, preferential models and cumulative logics
Artificial Intelligence
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
Probabilistic Reasoning Under Coherence in System P
Annals of Mathematics and Artificial Intelligence
Probabilistic Consistency of Knowledge Bases in Inference Systems
ECSQARU '93 Proceedings of the European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty
On the checking of G-coherence of conditional probability bounds
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Probabilistic logic under coherence: complexity and algorithms
Annals of Mathematics and Artificial Intelligence
Fuzzy inclusion and similarity through coherent conditional probability
Fuzzy Sets and Systems
Managing uncertainty and vagueness in description logics for the Semantic Web
Web Semantics: Science, Services and Agents on the World Wide Web
Correction of incoherent conditional probability assessments
International Journal of Approximate Reasoning
Information Sciences: an International Journal
Aggregation functions: Construction methods, conjunctive, disjunctive and mixed classes
Information Sciences: an International Journal
Relational probabilistic conditional reasoning at maximum entropy
ECSQARU'11 Proceedings of the 11th European conference on Symbolic and quantitative approaches to reasoning with uncertainty
Quasi conjunction and inclusion relation in probabilistic default reasoning
ECSQARU'11 Proceedings of the 11th European conference on Symbolic and quantitative approaches to reasoning with uncertainty
Constraint propagation with imprecise conditional probabilities
UAI'91 Proceedings of the Seventh conference on Uncertainty in Artificial Intelligence
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
Towards a General Class of Operators for Fuzzy Systems
IEEE Transactions on Fuzzy Systems
Incoherence correction strategies in statistical matching
International Journal of Approximate Reasoning
International Journal of Approximate Reasoning
Inferential processes leading to possibility and necessity
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
Statistical analysis of parametric t-norms
Information Sciences: an International Journal
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We make a probabilistic analysis related to some inference rules which play an important role in nonmonotonic reasoning. In a coherence-based setting, we study the extensions of a probability assessment defined on n conditional events to their quasi conjunction, and by exploiting duality, to their quasi disjunction. The lower and upper bounds coincide with some well known t-norms and t-conorms: minimum, product, Lukasiewicz, and Hamacher t-norms and their dual t-conorms. On this basis we obtain Quasi And and Quasi Or rules. These are rules for which any finite family of conditional events p-entails the associated quasi conjunction and quasi disjunction. We examine some cases of logical dependencies, and we study the relations among coherence, inclusion for conditional events, and p-entailment. We also consider the Or rule, where quasi conjunction and quasi disjunction of premises coincide with the conclusion. We analyze further aspects of quasi conjunction and quasi disjunction, by computing probabilistic bounds on premises from bounds on conclusions. Finally, we consider biconditional events, and we introduce the notion of an n-conditional event. Then we give a probabilistic interpretation for a generalized Loop rule. In an appendix we provide explicit expressions for the Hamacher t-norm and t-conorm in the unitary hypercube.