Probabilistic entailment in the setting of coherence:The role of quasi conjunction and inclusion relation (bibtex)

by Angelo Gilio, Giuseppe Sanfilippo

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.

Reference:

Angelo Gilio, Giuseppe Sanfilippo, "Probabilistic entailment in the setting of coherence:The role of quasi conjunction and inclusion relation", In International Journal of Approximate Reasoning, vol. 54, no. 4, pp. 513-525, 2013. (
[ResearchGate]
[Arxiv])

Bibtex Entry:

@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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