Transitivity in coherence-based probability logic

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• 作者：Angelo Gilio^a ; ^{angelo.gilio@sbai.uniroma1.it" class="auth_mail" title="E-mail the corresponding author} ; Niki Pfeifer^b ; ¹ ; ³ ; ^{niki.pfeifer@lmu.de" class="auth_mail" title="E-mail the corresponding author} ; Giuseppe Sanfilippo^c ; ² ; ³ ; ^{giuseppe.sanfilippo@unipa.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Coherence ; Defaults ; Generalized coherence ; Imprecise probability ; p-Consistency ; p-Entailment ; Probability logic ; Square of opposition ; Syllogisms ; Transitivity
• 刊名：Journal of Applied Logic
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：14
• 期：Complete
• 页码：46-64
• 全文大小：623 K

文摘

We study probabilistically informative (weak) versions of transitivity by using suitable definitions of defaults and negated defaults in the setting of coherence and imprecise probabilities. We represent p-consistent sequences of defaults and/or negated defaults by g-coherent imprecise probability assessments on the respective sequences of conditional events. Moreover, we prove the coherent probability propagation rules for Weak Transitivity and the validity of selected inference patterns by proving p-entailment of the associated knowledge bases. Finally, we apply our results to study selected probabilistic versions of classical categorical syllogisms and construct a new version of the square of opposition in terms of defaults and negated defaults.