Full Idea
Strong foundationalists require truth-preserving inferential links between the foundations and what the foundations support, while weaker versions allow weaker connections, such as inductive support, or best explanation, or probabilistic support.
Gist of Idea
Strong foundationalism needs strict inferences; weak version has induction, explanation, probability
Source
Jonathan Kvanvig (Epistemic Justification [2011], II)
Book Reference
'Routledge Companion to Epistemology', ed/tr. Bernecker,S/Pritchard,D [Routledge 2014], p.27
A Reaction
[He cites Alston 1989] Personally I'm a coherentist about justification, but I'm a fan of best explanation, so I'd vote for that. It's just that best explanation is not a very foundationalist sort of concept. Actually, the strong version is absurd.