Degrees of truthlikeness, independence, equality and order in probabilistic propositional knowledge representation

Abstract

Abstract Probabilistic propositional knowledge representation, as here conceived, deals with knowledge representation in the form of probabilistic (p-)valuations of the atomic propositions of a propositional language, of probability (p-)distributions over propositional state descriptions and with their relation. The aim of the paper is conceptual: introducing and illustrating a number of related, normalized concepts regarding both valuations and distributions: degrees of truthlikeness, (internal) independence, equality and order. The backbone of these concepts is the relevant sum of absolute distances. All degrees are in the unit interval and will be illustrated at the relevant place by data about the co-morbidity of psychiatric syndromes (Van Loo et al., 2016). In a new section we illustrate all concepts by an example of weather conditions, to be precise: (not) windy, (not) hot, (not) rainy days in March 2023, in De Bilt (NL). We also briefly discuss some other approaches: other distance measures, covariance as a measure of mutual dependence and various degrees of equality. In the final section we enlist several further research questions and issues, among which the question whether this paper is relevant for propositional probability logics. The paper is highly inspired by the rich paper of Gustavo Cevolani and Roberto Festa (2021).