  As data become more precise, estimating theoretical uncertainties in global
PDF determinations is likely to become increasingly necessary to obtain
correspondingly precise PDFs. Here we present a next generation of global
proton PDFs (NNPDF4.0) that include theoretical uncertainties due to the use of
heavy nuclear and deuteron data in the fit. We estimate these uncertainties by
comparing the values of the nuclear observables computed with the nuclear PDFs
against those computed with proton PDFs. For heavy nuclear PDFs we use the
nuclear nNNPDF2.0 set, while for deuteron PDFs we develop an iterative
procedure to determine proton and deuteron PDFs simultaneously, each including
the uncertainties in the other. Accounting for nuclear uncertainties resolves
some of the tensions in the global fit of the proton PDFs, especially those
between the nuclear data and the extended LHC data set used in NNPDF4.0.
