Preferential Structures for Comparative Probabilistic Reasoning
University of California, Berkeley（加州大学伯克利分校）；Stanford University（斯坦福大学）
Matthew Harrison-Trainor, Wesley H. Holliday, Thomas F. Icard
备注：
Postprint of AAAI 2017 paper, corrected to include a distinguished set of states in Definitions 2-3 and 5 (resp. before Theorem 3) to match the appropriate special case of the semantics of Holliday and Icard 2013 (resp. van der Hoek 1996)
Qualitative and quantitative approaches to reasoning about uncertainty can lead to different logical systems for formalizing such reasoning, even when the language for expressing uncertainty is the same. In the case of reasoning about relative likelihood, with statements of the form $φ\succsimψ$ expressing that $φ$ is at least as likely as $ψ$, a standard qualitative approach using preordered preferential structures yields a dramatically different logical system than a quantitative approach using probability measures. In fact, the standard preferential approach validates principles of reasoning that are incorrect from a probabilistic point of view. However, in this paper we show that a natural modification of the preferential approach yields exactly the same logical system as a probabilistic approach--not using single probability measures, but rather sets of probability measures. Thus, the same preferential structures used in the study of non-monotonic logics and belief revision may be used in the study of comparative probabilistic reasoning based on imprecise probabilities.
A conditional, a fuzzy and a probabilistic interpretation of self-organising maps
DISIT - Università del Piemonte Orientale（DISIT - 皮埃蒙特东方大学）；Center for Logic, Language and Cognition, Dipartimento di Informatica, Università di Torino（逻辑、语言与认知中心，都灵大学计算机系）
