Borderlines and probabilities of borderlines: On the interconnection between vagueness and uncertainty

详细信息    查看全文

• 作者：Jonathan Lawry ^{j.lawry@bris.ac.uk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Vagueness ; Uncertainty ; Borderline cases ; Three-valued valuations
• 刊名：Journal of Applied Logic
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：14
• 期：Complete
• 页码：113-138
• 全文大小：564 K

文摘

We describe an integrated approach to vagueness and uncertainty within a propositional logic setting and based on a combination of three valued logic and probability. Three valued valuations are employed in order to model explicitly borderline cases and in this context we give an axiomatic characterisation of two well known three valued models; supervaluations and Kleene valuations. We then demonstrate the close relationship between Kleene valuations and a sub-class of supervaluations. Belief pairs are lower and upper measures on the sentences of the language generated from a probability distribution defined over a finite set of three valued valuations. We describe links between these measures and other uncertainty theories and we show the close relationship between Kleene belief pairs and a sub-class of supervaluation belief pairs. Finally, a probabilistic approach to conditioning is explored within this framework.