A bipolar model of assertability and belief

作者：Lawry Jonathan^*; Gonzalez Rodriguez Ines

来源：International Journal of Approximate Reasoning, 2011, 52(1): 76-91.

DOI：10.1016/j.ijar.2010.05.005

• Bipolar belief
• Vagueness
• Label semantics
• Interval-sets
• Intuitionistic/interval fuzzy logic
• Max-min fuzzy logic

Valuation pairs are introduced as a bipolar model of the assertability of propositions. These correspond to a pair of dual valuation functions, respectively, representing the strong property of definite assertability and the dual weaker property of acceptable assertability. In the case where there is uncertainty about the correct valuation pair for a language then a probability distribution is defined on possible valuation pairs. This results in two measures, giving the probability that a sentence is definitely assertable, and mu(-) giving the probability that a sentence is acceptable to assert. It is shown that mu(+) and mu(-) can be determined directly from a two dimensional mass function m defined on pairs of sets of propositional variables. Certain natural properties of mu(+) and mu(-) are easily expressed in terms of m, and in particular we introduce certain consonance or nestedness assumptions. These capture qualitative information in the form of assertability orderings for both the propositional variables and the negated propositional variables. On the basis of these consonance assumptions we show that label semantics, intuitionistic fuzzy logic and max-min fuzzy logic can all be viewed as special cases of this bipolar model. We also show that bipolar belief measures can be interpreted within an interval-set model.

• 出版日期2011-1