Quasi conjunction, quasi disjunction, t-norms and t-conorms: Probabilistic aspects

摘要: We make a probabilistic analysis related to some inference rules which play an important role in nonmonotonic reasoning. In coherence-based setting, we study the extensions of probability assessment defined on n conditional events their quasi conjunction, and by exploiting duality, disjunction. The lower upper bounds coincide with well known t-norms t-conorms: minimum, product, Lukasiewicz, Hamacher dual t-conorms. On this basis obtain Quasi And Or rules. These are for any finite family p-entails associated conjunction examine cases logical dependencies, relations among coherence, inclusion events, p-entailment. also consider rule, where disjunction premises conclusion. analyze further aspects disjunction, computing from conclusions. Finally, biconditional introduce notion n-conditional event. Then give interpretation generalized Loop rule. appendix provide explicit expressions t-norm t-conorm unitary hypercube.