Probabilistic entailment in the setting of coherence:The role of quasi conjunction and inclusion relation. Gilio, A. & Sanfilippo, G. International Journal of Approximate Reasoning, 54(4):513–525, 2013. doi 10.1016/j.ijar.2012.11.001
Paper doi abstract bibtex In this paper, by adopting a coherence-based probabilistic approach to default reasoning, we focus the study on the logical operation of quasi conjunction and the Goodman-Nguyen inclusion relation for conditional events. We recall that quasi conjunction is a basic notion for defining consistency of conditional knowledge bases. By deepening some results given in a previous paper we show that, given any finite family of conditional events F and any nonempty subset S of F, the family F p-entails the quasi conjunction C(S); then, given any conditional event E|H, we analyze the equivalence between p-entailment of E|H from F and p-entailment of E|H from C(S), where S is some nonempty subset of F. We also illustrate some alternative theorems related with p-consistency and p-entailment. Finally, we deepen the study of the connections between the notions of p-entailment and inclusion relation by introducing for a pair (F,E|H) the (possibly empty) class K of the subsets S of F such that C(S) implies E|H. We show that the class K satisfies many properties; in particular K is additive and has a greatest element which can be determined by applying a suitable algorithm.
@ARTICLE{2013:4IJAR,
author = {Angelo Gilio and Giuseppe Sanfilippo},
title = {Probabilistic entailment in the setting of coherence:The role of
quasi conjunction and inclusion relation},
journal = {International Journal of Approximate Reasoning},
year = {2013},
volume = {54},
pages = {513--525},
number = {4},
note = {doi 10.1016/j.ijar.2012.11.001},
abstract = {In this paper, by adopting a coherence-based probabilistic approach
to default reasoning, we focus the study on the logical operation
of quasi conjunction and the Goodman-Nguyen inclusion relation for
conditional events. We recall that quasi conjunction is a basic notion
for defining consistency of conditional knowledge bases. By deepening
some results given in a previous paper we show that, given any finite
family of conditional events F and any nonempty subset S of F, the
family F p-entails the quasi conjunction C(S); then, given any conditional
event E|H, we analyze the equivalence between p-entailment of E|H
from F and p-entailment of E|H from C(S), where S is some nonempty
subset of F. We also illustrate some alternative theorems related
with p-consistency and p-entailment. Finally, we deepen the study
of the connections between the notions of p-entailment and inclusion
relation by introducing for a pair (F,E|H) the (possibly empty) class
K of the subsets S of F such that C(S) implies E|H. We show that
the class K satisfies many properties; in particular K is additive
and has a greatest element which can be determined by applying a
suitable algorithm.},
comment = {
<a href="https://www.researchgate.net/publication/234059990_Probabilistic_entailment_in_the_setting_of_coherence_The_role_of_quasiconjunction_and_inclusion_relation" target="_blank"
>[ResearchGate]</a>
<a href="http://arxiv.org/abs/1301.0958" target="_blank">[Arxiv]</a>},
doi = {10.1016/j.ijar.2012.11.001},
issn = {0888-613X},
mrclass = {68T37 (03B48)},
mrnumber = {3041115},
scopus = {{2-s2.0-84875225966}},
url = {http://dx.doi.org/10.1016/j.ijar.2012.11.001},
wos = {{WOS:000317379500007}}
}
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We recall that quasi conjunction is a basic notion for defining consistency of conditional knowledge bases. By deepening some results given in a previous paper we show that, given any finite family of conditional events F and any nonempty subset S of F, the family F p-entails the quasi conjunction C(S); then, given any conditional event E|H, we analyze the equivalence between p-entailment of E|H from F and p-entailment of E|H from C(S), where S is some nonempty subset of F. We also illustrate some alternative theorems related with p-consistency and p-entailment. Finally, we deepen the study of the connections between the notions of p-entailment and inclusion relation by introducing for a pair (F,E|H) the (possibly empty) class K of the subsets S of F such that C(S) implies E|H. We show that the class K satisfies many properties; in particular K is additive and has a greatest element which can be determined by applying a suitable algorithm.","comment":"<a href=\"https://www.researchgate.net/publication/234059990_Probabilistic_entailment_in_the_setting_of_coherence_The_role_of_quasiconjunction_and_inclusion_relation\" target=\"_blank\" >[ResearchGate]</a> <a href=\"http://arxiv.org/abs/1301.0958\" target=\"_blank\">[Arxiv]</a>","doi":"10.1016/j.ijar.2012.11.001","issn":"0888-613X","mrclass":"68T37 (03B48)","mrnumber":"3041115","scopus":"2-s2.0-84875225966","url":"http://dx.doi.org/10.1016/j.ijar.2012.11.001","wos":"WOS:000317379500007","bibtex":"@ARTICLE{2013:4IJAR,\n author = {Angelo Gilio and Giuseppe Sanfilippo},\n title = {Probabilistic entailment in the setting of coherence:The role of\n\tquasi conjunction and inclusion relation},\n journal = {International Journal of Approximate Reasoning},\n year = {2013},\n volume = {54},\n pages = {513--525},\n number = {4},\n note = {doi 10.1016/j.ijar.2012.11.001},\n abstract = {In this paper, by adopting a coherence-based probabilistic approach\n\tto default reasoning, we focus the study on the logical operation\n\tof quasi conjunction and the Goodman-Nguyen inclusion relation for\n\tconditional events. We recall that quasi conjunction is a basic notion\n\tfor defining consistency of conditional knowledge bases. By deepening\n\tsome results given in a previous paper we show that, given any finite\n\tfamily of conditional events F and any nonempty subset S of F, the\n\tfamily F p-entails the quasi conjunction C(S); then, given any conditional\n\tevent E|H, we analyze the equivalence between p-entailment of E|H\n\tfrom F and p-entailment of E|H from C(S), where S is some nonempty\n\tsubset of F. We also illustrate some alternative theorems related\n\twith p-consistency and p-entailment. Finally, we deepen the study\n\tof the connections between the notions of p-entailment and inclusion\n\trelation by introducing for a pair (F,E|H) the (possibly empty) class\n\tK of the subsets S of F such that C(S) implies E|H. 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