### Abstract

We study the quasi conjunction and the Goodman & Nguyen inclusion relation for conditional events, in the setting of probabilistic default reasoning under coherence. We deepen two recent results given in (Gilio and Sanfilippo, 2010): the first result concerns p-entailment from a family F of conditional events to the quasi conjunction C(S) associated with each nonempty subset S of F; the second result, among other aspects, 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 the Goodman & Nguyen inclusion relation; in particular, for a pair (F,E|H), we study the class K of the subsets S of F such that C(S) is included in E|H. We show that K is additive and has a greatest element which can be determined by applying a suitable algorithm.

Lingua originale | English |
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Titolo della pubblicazione ospite | Symbolic and quantitative approaches to reasoning with uncertainty. 11th European Conference, ECSQARU 2011 |

Pagine | 497-508 |

Numero di pagine | 12 |

Stato di pubblicazione | Published - 2011 |

### Serie di pubblicazioni

Nome | LECTURE NOTES IN ARTIFICIAL INTELLIGENCE |
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### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cita questo

Sanfilippo, G., & Gilio, A. (2011). Quasi conjunction and inclusion relation in probabilistic default reasoning. In

*Symbolic and quantitative approaches to reasoning with uncertainty. 11th European Conference, ECSQARU 2011*(pagg. 497-508). (LECTURE NOTES IN ARTIFICIAL INTELLIGENCE).