Axioms and algorithms for inferences involving probabilistic independence
Information and Computation
Directed hypergraphs and applications
Discrete Applied Mathematics - Special issue: combinatorial structures and algorithms
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A note on reliable full-duplex transmission over half-duplex links
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A complete axiomatization for functional and multivalued dependencies in database relations
SIGMOD '77 Proceedings of the 1977 ACM SIGMOD international conference on Management of data
Dependence Logic: A New Approach to Independence Friendly Logic (London Mathematical Society Student Texts)
ACM Transactions on Information and System Security (TISSEC)
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On interdependence of secrets in collaboration networks
Proceedings of the 12th Conference on Theoretical Aspects of Rationality and Knowledge
An Independence Relation for Sets of Secrets
WoLLIC '09 Proceedings of the 16th International Workshop on Logic, Language, Information and Computation
The functional dependence relation on hypergraphs of secrets
CLIMA'11 Proceedings of the 12th international conference on Computational logic in multi-agent systems
IEEE Transactions on Information Theory
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Studia Logica
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The article considers interdependencies between secrets in a multiparty system. Each secret is assumed to be known only to a certain fixed set of parties. These sets can be viewed as edges of a hypergraph whose vertices are the parties of the system. The properties of interdependencies are expressed through a multi-argument relation called independence, which is a generalization of a binary relation also known as nondeducibility. The main result is a complete and decidable logical system that describes interdependencies that may exist on a fixed hypergraph. Additionally, the axioms and inference rules in this system are shown to be independent in the standard logical sense.