TY - CHAP

T1 - Quasi conjunction and inclusion relation in probabilistic default reasoning

AU - Sanfilippo, Giuseppe

AU - Gilio, Angelo

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10447/54946

UR - http://link.springer.com/chapter/10.1007%2F978-3-642-22152-1_42

M3 - Chapter

SN - 978-3-642-22151-4

T3 - LECTURE NOTES IN ARTIFICIAL INTELLIGENCE

SP - 497

EP - 508

BT - Symbolic and quantitative approaches to reasoning with uncertainty. 11th European Conference, ECSQARU 2011

ER -