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}
}