Approximation Logics for Subclasses of Probabilistic Conditional Independence and Hierarchical Dependence on Incomplete Data

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dc.contributor.author Link, Sebastian en
dc.contributor.editor Abramsky, S en
dc.contributor.editor Kontinen, J en
dc.contributor.editor Vaananen, J en
dc.contributor.editor Vollmer, H en
dc.date.accessioned 2016-08-18T05:01:01Z en
dc.date.issued 2016-06-01 en
dc.identifier.citation Dependence Logic, 2016, pp. 183 - 217 en
dc.identifier.isbn 978-3-319-31803-5 en
dc.identifier.uri http://hdl.handle.net/2292/30063 en
dc.description.abstract Probabilistic conditional independence constitutes a principled approach to handle knowledge and uncertainty in artificial intelligence, and is fundamental in probability theory and multivariate statistics. Similarly, first-order hierarchical dependence provides an expressive framework to capture the semantics of an application domain within a database system, and is essential for the design of databases. For complete data it is well known that the implication problem associated with probabilistic conditional independence is not axiomatizable by a finite set of Horn rules, and the implication problem for first-order hierarchical dependence is undecidable. Moreover, both implication problems do not coincide and neither of them is equivalent to the implication problem of some fragment of Boolean propositional logic. In this article, generalized saturated conditional independence and full first-order hierarchical dependence over incomplete data are investigated as expressive subclasses of probabilistic conditional independence and first-order hierarchical dependence, respectively. The associated implication problems are axiomatized by a finite set of Horn rules, and both shown to coincide with that of a propositional fragment under interpretations in the well-known approximation logic S-3. Here, the propositional variables in the set S are interpreted classically, and correspond to random variables as well as attributes on which incomplete data is not permitted to occur. en
dc.publisher Birkhäuser en
dc.relation.ispartof Dependence Logic en
dc.rights Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. Details obtained from http://www.springer.com/gp/open-access/authors-rights/self-archiving-policy/2124 en
dc.rights.uri https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm en
dc.title Approximation Logics for Subclasses of Probabilistic Conditional Independence and Hierarchical Dependence on Incomplete Data en
dc.type Book Item en
dc.identifier.doi 10.1007/978-3-319-31803-5_9 en
pubs.begin-page 183 en
dc.description.version AM - Accepted Manuscript en
dc.rights.holder Copyright: Birkhäuser en
pubs.end-page 217 en
pubs.place-of-publication Basel en
dc.rights.accessrights http://purl.org/eprint/accessRights/OpenAccess en
pubs.elements-id 536185 en
pubs.org-id Science en
pubs.org-id School of Computer Science en
pubs.record-created-at-source-date 2016-07-21 en


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