Quasi Conjunction and Inclusion Relation in Probabilistic Default Reasoning (bibtex)

by Angelo Gilio, Giuseppe Sanfilippo

Abstract:

We study in the setting of probabilistic default reasoning under coherence the quasi conjunction, which is a basic notion for defining consistency of conditional knowledge bases, and the Goodman & Nguyen inclusion relation for conditional events. We deepen two results given in a previous paper: the first result concerns p-entailment from a finite family F of conditional events to the quasi conjunction C(S), for each nonempty subset S of F; the second result analyzes the equivalence between p-entailment from F and p-entailment from C(S), where S is some nonempty subset of F. We also characterize p-entailment by some alternative theorems. Finally, we deepen the connections between p-entailment and inclusion relation, by introducing for a pair (F,E|H) the class of the subsets S of F such that C(S) implies E|H. This class isadditive and has a greatest element which can be determined by applying a suitable algorithm.

Reference:

Angelo Gilio, Giuseppe Sanfilippo, "Quasi Conjunction and Inclusion Relation in Probabilistic Default Reasoning", Chapter in Symbolic and Quantitative Approaches to Reasoning with Uncertainty, Lecture Notes in Computer Science, Springer Berlin / Heidelberg, vol. 6717, pp. 497-508, 2011.

Bibtex Entry:

@INCOLLECTION{2011:1ECSQARU, author = {Gilio, Angelo and Sanfilippo, Giuseppe}, title = {Quasi Conjunction and Inclusion Relation in Probabilistic Default Reasoning}, booktitle = {Symbolic and Quantitative Approaches to Reasoning with Uncertainty}, publisher = {Springer Berlin / Heidelberg}, year = {2011}, editor = {Liu, Weiru}, volume = {6717}, series = {Lecture Notes in Computer Science}, pages = {497-508}, note = {10.1007/978-3-642-22152-1_42}, abstract = {We study in the setting of probabilistic default reasoning under coherence the quasi conjunction, which is a basic notion for defining consistency of conditional knowledge bases, and the Goodman & Nguyen inclusion relation for conditional events. We deepen two results given in a previous paper: the first result concerns p-entailment from a finite family F of conditional events to the quasi conjunction C(S), for each nonempty subset S of F; the second result analyzes the equivalence between p-entailment from F and p-entailment from C(S), where S is some nonempty subset of F. We also characterize p-entailment by some alternative theorems. Finally, we deepen the connections between p-entailment and inclusion relation, by introducing for a pair (F,E|H) the class of the subsets S of F such that C(S) implies E|H. This class isadditive and has a greatest element which can be determined by applying a suitable algorithm.}, doi = {10.1007/978-3-642-22152-1_42}, isbn = {978-3-642-22151-4}, issn = {0302-9743}, keyword = {Computer Science}, mrclass = {62A99 (03B47 60A99 68T27 68T37)}, mrnumber = {2831201 (2012h:62019)}, scopus = {{2-s2.0-79960134640}}, url = {http://dx.doi.org/10.1007/978-3-642-22152-1_42} }

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