Possibilistic and probabilistic logic under coherence: default reasoning and system P.

*(English)*Zbl 1363.60001This paper shows some results on coherence-based probability logic and on coherence-based possibility logic. These results are extended to conditional decomposable measure and applied to study some inference rules in nonmonotonic reasoning. In particular, by referring to conditional necessities and to some suitable conditional decomposable measures (e.g., conditional probability), the authors show the validity of the well-known inference rules in system P (reflexivity, left logical equivalence, right weakening, cut, cautious monotonicity, and, or). The following inference rules are also verified: negation rationality, disjunctive Rrationality, and rational monotonicity. Moreover, other properties (monotonicity, transitivity, and contraposition) are also studied. Finally, based on conditional independence, the irrelevance problem has been studied in both probabilistic and possibilistic contexts.

Reviewer: Giuseppe Sanfilippo (Palermo)

##### MSC:

60A05 | Axioms; other general questions in probability |

03B42 | Logics of knowledge and belief (including belief change) |