Later approaches of the same idea coning out of the academic Databases community reinvented this particular wheel with far better PR and branded it the Semantic Web with 'Ontologies' and RDF, OWL and its ilk.
While reasonable (pun intended) for small vertical domains, the approach has never made inroads in more broad general intelligence as IMHO it does not deal well with ambiguities, contradictions, multi level or perspective modeling and circular referential meaning in 'real world' reasoning and also tends to ignore agentive, transformative and temporal situatedness.
Its ideal seems to be a single thruth never changing model of the universe that is simply accepted by all.
I'm also not sure that fuzzy or probabilistic properties automatically translate into reasonable transitive properties or reasoning even if the individual weights are reasonable.
(Fuzzy logic is of course exactly about formal logic and reasoning in non-absolute terms, but the idea has been around for a long time and AFAIK largely superseded by probability.)
Not that I have any deeper idea about recent work in that area. I did a couple of years' stint in semantic web stuff back in the day, and weighted relationships were one of the obvious ideas for dealing with the rigidity of explicit relationships. They also came with obvious problems and at least back then my impression was that the idea wasn't actually as useful as it initially sounded.
But as I said, I haven't really been following the field in years, so there might have been some useful developments.