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

Giuseppe Sanfilippo, Angelo Gilio

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)

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 CS 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.
Original languageEnglish
Pages (from-to)513-525
Number of pages13
JournalInternational Journal of Approximate Reasoning
Volume54
Publication statusPublished - 2013

All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science
  • Artificial Intelligence
  • Applied Mathematics

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